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Personalized driver assistance systems based on driver/vehicle models

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Personalized driver assistance systems based on driver/vehicle models

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Content i

PERSONALIZED DRIVER ASSISTANCE SYSTEMS
BASED ON DRIVER/VEHICLE MODELS

by

Vadim Butakov

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

December 2014

Copyright 2014 Vadim Butakov

ii

TABLE OF CONTENTS

List of Tables ..................................................................................................................... iv
List of Figures ..................................................................................................................... v
Abstract ............................................................................................................................. vii
1. Introduction ..................................................................................................................... 1
2. Driver/Vehicle Response Diagnostic System for the Vehicle Following Case ............. 6
2.1. Introduction ............................................................................................................. 6
2.2. Driver/Vehicle Modeling and Diagnostics ............................................................. 8
2.3. GMM and Short-Term Diagnostics ...................................................................... 11
2.4. Probability Distributions of Dynamic Characteristics and Long-run Diagnostics 24
2.5. Integrated approach and decision making ............................................................. 29
2.6. Experiments .......................................................................................................... 30
2.7. Conclusion ............................................................................................................ 43
3. Personalized Driver/Vehicle Lane Change Models ..................................................... 44
3.1. Introduction ........................................................................................................... 44
3.2. Longitudinal Adjustment and Acceptable Gaps ................................................... 48
3.3. Modeling of Lane Change Kinematics ................................................................. 57
3.4. Experiments .......................................................................................................... 64
3.5. Conclusion ............................................................................................................ 72
4. Vehicle Lateral Position Prediction .............................................................................. 74
4.1. Introduction ........................................................................................................... 74
4.2. Artificial Neural Networks ................................................................................... 75
4.3. Lateral Trajectory Modeling and Prediction ......................................................... 78
4.4. Experiments .......................................................................................................... 83
4.5. Conclusions ........................................................................................................... 90
5. Personalized Driver Assistance for Signalized Intersections Using V2I I
Communication ................................................................................................................. 92
5.1. Introduction ........................................................................................................... 92
iii

5.2. Vehicle and Traffic Light Models......................................................................... 95
5.3. Optimization Problem and Personalization .......................................................... 99
5.4. Simulation Results .............................................................................................. 111
5.5. Conclusion .......................................................................................................... 119
6. Autopilot personalization ........................................................................................... 120
6.1. Introduction ......................................................................................................... 120
6.2. Personalization based on Models ........................................................................ 123
6.3. Experiments ........................................................................................................ 131
6.4. Conclusion .......................................................................................................... 133
7. Concluding Remarks and Proposed Research Directions .......................................... 134
References ....................................................................................................................... 137

iv

LIST OF TABLES

Table 2.1: Fit accuracy versus number of GMM components.......................................... 34
Table 2.2: Mean prediction error on 1-hour training and raw sets for different drivers ... 35
Table 2.3: Mean prediction error over speed intervals ..................................................... 36
Table 2.4: Driving style coefficient for two different benchmark sets ............................. 36
Table 2.5: Driving characteristics pdf parameters for two drivers ................................... 40
Table 3.1: Contingency table of the data – number of samples ........................................ 69
Table 3.2: Longitudinal adjustment of the drivers ............................................................ 69
Table 3.3: Mean values of lane change parameters for all available data ........................ 69
Table 3.4: Linear regression coefficients and their significance ...................................... 70
Table 3.5: Linear regression model characteristics........................................................... 70
Table 3.6: Fit accuracy versus number of GMM components.......................................... 72
Table 3.7: Kinematic characteristics of lane changes ....................................................... 72
Table 4.1: Accuracy dependence on prediction horizon ................................................... 87
Table 5.1: Traffic light characteristics ............................................................................ 112
Table 5.2: Drivers profile ................................................................................................ 114
Table 5.3: Crossing windows configuration ................................................................... 115

v

LIST OF FIGURES

Figure 2.1: Tactical level of driving task ............................................................................ 9
Figure 2.2: Vehicle following case ..................................................................................... 9
Figure 2.3: Bimodal shape of the probability density as a function of vehicle ee
acceleration ....................................................................................................................... 16
Figure 2.4: Distribution types ........................................................................................... 26
Figure 2.5: Integrated diagnostics approach flow chart .................................................... 29
Figure 2.6: Maximum acceleration of the car versus speed .............................................. 34
Figure 2.7: Threshold initialization................................................................................... 37
Figure 2.8: Comparison of predicted and real value of vehicle acceleration when GMM s
is adjusted for Driver 1 ..................................................................................................... 38
Figure 3.1: Models associated with the lane change maneuver ........................................ 45
Figure 3.2: Example of distribution curves of the peak relative speed during s
longitudinal adjustments ................................................................................................... 52
Figure 3.3: Pre-lane change trafic configuration .............................................................. 53
Figure 3.4: Two-layer model structure ............................................................................. 58
Figure 3.5: Lane change kinematic model layout ............................................................. 61
Figure 3.6: Layout of the vehicle’s sensors ...................................................................... 64
Figure 3.7: Vehicle’s lateral position with respect to lanes and lane change detection .... 66
Figure 3.8: Object detection from the radar data .............................................................. 67
Figure 4.1: Traffic environment forecasting ..................................................................... 74
Figure 4.2: A typical Time Lagged Feedforward Neural Network (TLFNN) .................. 77
Figure 4.3: Homogenous stretches with respect to lane keeping, overtaking from the
right, and the left ............................................................................................................... 81
Figure 4.4: Sensor data formalized as a Cartesian coordinate system .............................. 83
Figure 4.5: Model signals: predictors and prediction ....................................................... 85
Figure 4.6: The architecture of MLP-sw used in the current study .................................. 85
Figure 4.7: Prediction accuracies for different window sizes ........................................... 86
vi

Figure 4.8: Prediction accuracies for different number of hidden units ........................... 86
Figure 4.9: Vehicle lateral position prediction ................................................................. 88
Figure 4.10: Histogram of the deviations in prediction at the prediction horizons of 1 2
and 2 seconds .................................................................................................................... 89
Figure 5.1: A chain of traffic lights .................................................................................. 92
Figure 5.2: Sample graph of available paths to cross intersections on the green ........... 100
Figure 5.3: Decision tree of possible paths to cross intersections on the green.............. 100
Figure 5.4: Example of acceleration profile and its corresponding speed curve ............ 103
Figure 5.5: Possible speed profiles to cover a fixed interval in a fixed time .................. 107
Figure 5.6: Route configuration ...................................................................................... 111
Figure 5.7: Acceleration data and its approximation for the drivers .............................. 113
Figure 5.8: Deceleration data and its approximation for the driver ................................ 113
Figure 5.9: Green windows configuration and possible crossings ................................. 115
Figure 5.10: Cost function for available crossing windows ........................................... 116
Figure 5.11: Optimized and natural driving paces .......................................................... 118
Figure 6.1: Google self-driving car on a test track ......................................................... 120
Figure 6.2: Head-up display concept .............................................................................. 124
Figure 6.3: Tactical level of driving task ........................................................................ 125
Figure 6.4: Manual and automated driving modes ......................................................... 126
Figure 6.5: Application of current performance and manual tuning .............................. 129
Figure 6.6: Acceleration limiter ...................................................................................... 130
Figure 6.7: Spacing model curves ................................................................................... 132

vii

ABSTRACT

Driving, while a necessary and sometimes enjoyable experience, can become
stressful and often challenging in city environments due to congestion, difficult
environmental conditions, and the mistakes of other drivers. The latest trend of improving
the urban driving experience is equipping cars with Advanced Driver Assistance Systems
(ADAS). These systems aim to make driving safer and more comfortable. They can
advise the driver when performing certain maneuvers is safe and even assist the driver in
performing these maneuvers. An ADAS can also monitor driver and vehicle response in
order to detect and avoid potentially dangerous situations by comparing current values of
parameters with expected ones. In addition, an ADAS can assume control of the vehicle.
The assistance system can be effective only if it captures personal driving style as
well as the dynamics of the driver/vehicle system. However, the conventional way of
manually adjusting car systems to tailor them to a driver’s personal desires is hardly
appropriate for an ADAS. This type of performance requires a large number of
parameters that would need to be manually adjusted by the driver over many iterations of
trial and error before driving begins. Most ADAS are designed having the average
driver’s characteristics in mind. This may lead to a system that aggressive drivers find
annoying and passive drivers find too aggressive. Consequently, by adding stress and
disappointment, this could dissuade drivers from using the very system that is supposed
to make driving easier and more joyful.
In this work we present modeling techniques that allow extracting knowledge of
driver/vehicle behavior for the most stressful and accident-provoking driving tasks:
viii

vehicle following, lane change and intersection crossing. The models capture the personal
characteristics associated to a particular driver and vehicle. The models, along with the
corresponding parameter learning techniques, recommendation personalization
algorithms and diagnostics methodology can be used as a kernel for a system that can
provide personalized driving assistance and behavior monitoring. In addition, the
presence of skewed model parameters can be used to evaluate a driver’s level of
aggression.
We demonstrate the effectiveness of the proposed techniques by applying the
methods to experimental data collected on a customized vehicle. The results demonstrate
that the models are able to capture personal habits (such as following distance and lane
change duration) and distinguish between different drivers. In addition, we show that the
developed intersection assistance algorithm that takes into account driver’s habits and
preferences helps to reduce fuel consumption.
1

1. INTRODUCTION

Driving through the urban jungle of a modern city can be stressful and often
challenging. Due to an increase in the population of personal car owners, traffic
congestion in megacities and suburban areas has increased as well. Driving in rush hour
conditions on arterial streets and urban highways requires diligent concentration and fast
thinking from the driver to avoid potentially dangerous situations. As a result, the
experience of driving becomes at best less joyful and at worst very stressful and accident-
prone.
In fact, the contribution of human error to the rate of car accidents (as either a main
or secondary cause) is almost 95% [1]. The National Traffic Safety Administration
(NHTSA) reports that human factors were found to be a main cause in 70.7% of
automobile crashes [2]. These factors include inattention, obstructed vision, driving under
the influence (DUI), drowsiness, etc. Regardless of the nature, the words “human factors”
represent an inadequate reaction of the driver to the road situation, resulting in an
accident. Even though the problem of improving driving experience and reducing the
impact of human factors in car accidents appeared with the first produced vehicle, only
recently have car manufacturers started to equip their cars with assistance systems aimed
to improve safety and comfort in driving.
The latest trend of improving this urban driving experience is equipping cars with
Advanced Driver Assistance Systems (ADAS) such as blind spot detection systems,
fatigue monitoring systems, lane departure warning systems, and collision avoidance
system [3].
2

The functionality of such systems can include advising the driver when performing
certain maneuvers is safe and even assisting the driver in performing these maneuvers.
For example, when a driver wants to change lanes, the system can assess if the gap in the
destination lane is safe to initiate a lane change, and would be deemed acceptable by that
specific driver. It can also suggest the appropriate amount of acceleration or deceleration
needed to find an opening in the destination lane. ADAS can also monitor driver and
vehicle response in order to detect and avoid potentially dangerous situations. The system
does this by comparing the current values of parameters with the expected ones. For
instance, the system could notice that the driver is following a vehicle at an unusually
close distance and could make recommendations to the driver to adjust this amount to
either a safer or more typical following distance. An ADAS could even assume control of
the vehicle to perform routine driving tasks such as vehicle following in stop-and-go
traffic, parking etc. In addition, an ADAS can help in reducing fuel consumption, e.g. by
regulating driving pace in order to avoid stopping at the red traffic light.
An assistance system is only effective if it captures personal driving style as well as
the dynamics of the driver/vehicle system. The conventional method to personalize or
adjust a vehicle requires reading an often lengthy manual and making physical changes to
the car’s system. However, with all the new gadgets and expanded features of modern
cars, this type of manual adjustment is hardly appropriate for an ADAS. Doing this would
require the driver to understand and implement instructions from a manual to alter a large
number of parameters. This process could take many iterations of trial and error before
driving begins; a process many drivers would rather figure out heuristically or avoid
altogether.
3

Most ADAS are designed having the average driver’s characteristics in mind. This
may lead to a system that aggressive drivers find annoying and passive drivers find too
aggressive. Consequently, by adding stress and disappointment, this could dissuade
drivers from using the very system that is supposed to make driving easier and more
joyful. Using systems configured for the average driver, rather than each driver
personally, may lead to most drivers not using ADAS and taking advantage of its
benefits. With personalization algorithms such as those discussed here, ADAS could
become more popular and effective by eliminating the difficult process of manual
adjustment in favor of more automatic methods.
Currently, research institutions and car manufacturers are only making a handful of
attempts to develop automatic adaptation algorithms for ADAS. The focus of studies is
mainly on customization of the infotainment system content [4-7] and navigation [8, 9].
If the system were to be more strongly focused on driver assistance and monitoring,
it could be based on different types of measurements such as [10]:
• Driver physical measurements: eye closure duration, nodding frequency, etc.
• Driving performance measurements: vehicle following distance, steering angle, etc.
• Subjective report measurements: the driver is asked to report his/her feeling of
drowsiness, fatigue, etc. to the system.
• Driver biological measurements: pulse, blood pressure, etc.
• Hybrid measurements: a combination of any of the above measurements.
Some of the above measurements are not as suitable for ADAS systems. For
example, biological measurements are intrusive as they involve installation of sensors on
the driver which is unlikely to be acceptable. However, they can serve as ground-truth
4

indicators during the system development phase. Subjective report measurements cannot
be effectively used due to the difficulty of measuring mental processes quantitatively and
objectively. The most promising approach that would give the smallest false alarm rate is
to combine physical and performance measurements to create a hybrid system which also
takes into account how behavior is shaped by interaction with the environment, i.e. a
“stimulus-response” relationship [ 11].
In this work, we rely on driving performance measurements in order to develop a
driver/vehicle models that can be used as a kernel for a personalized ADAS. As a driver
performs daily trips, the model parameters are tailored to a particular driver using
parameter estimation algorithms on data sets collected by the driver. We show how
skewed models can be used to provide personalized recommendations, driver/vehicle
diagnostics and personalized autopiloted driving. In addition, model parameters can be
used to evaluate a driver’s aggressiveness. We cover the most challenging and accident-
provoking driving cases: vehicle following, lane changing and intersection crossing. The
methodology can be easily extended to other driving tasks.
The experimental data used to train the models was collected on a customized
vehicle equipped with sensors that detect various kinematic parameters of the subject and
surrounding vehicles. The experiments indicate that the models are able to grasp personal
characteristics of the driver on training data sets, reasonably well predict driver’s
response on a raw data set, and distinguish between drivers. This indicates that the
models can be used to provide personalized assistance to drivers. In addition, we show
that proposed personalized algorithm for intersection assistance improves comfort and
reduces fuel economy.
5

We expect the proposed methodology to be a useful tool in improving ADAS in
order to increase safety and reduce a driver’s stress. In addition , that methodology can be
applied not only to vehicles, but to any practical system that is controlled by humans and
whose behavior is shaped by human. In addition, the models based on performance
measurements can be coupled with ones based on visual analysis of the driver and
environment. This will allow reducing false alarm rates and providing more accurate
assistance.
The terminology and the mathematical notations used are standard and presumably
clear from the context. Each chapter includes an introduction for specific background
material such as basic concepts and related work, and a brief summary appears in the
conclusion section of each chapter highlighting the important topics covered.
In Chapter 2 the vehicle following modeling and diagnostics is described. Chapter 3
introduces the lane change modeling methodology. In Chapter 4 we present how machine
learning techniques can be used to forecast the position of the vehicle. Chapter 5
introduces the personalized intersection assistance using V2I communication. Chapter 6
demonstrates how personalization can improve safety and comfort of self-driving
vehicles. Chapter 7 contains concluding remarks and suggestions for future work.

6

2. DRIVER/VEHICLE RESPONSE DIAGNOSTIC
SYSTEM FOR THE VEHICLE FOLLOWING CASE

2.1. INTRODUCTION

According to the National Highway Traffic Safety Administration (NHTSA), rear-
end collision is the most frequently occurring type of accident - around 29% of all
crashes [12]. Rear-end collisions happen when a driver fails to perform the vehicle
following tasks of controlling relative distance and speed between the subject and the
preceding vehicles. Factors that might lead to the task failing are vehicle malfunction
(brake failures or other mechanical defects), driver misjudgment of the situation
(following too closely and not having enough time to stop), and driver distraction
(texting, talking to passenger etc.).
In order to reduce the chance of the rear-end collision an ADAS system can be
introduced that monitors the driver and the relative position between the subject and the
preceding vehicle. Several auto companies introduced various systems that are aimed to
assist the driver when needed. Because detailed information about these approaches is
classified, only brief descriptions are available:
• Toyota was the first company to introduce a driver inattention monitoring system
in 2006. The system has been installed mainly on Lexus models. It utilizes an infrared
camera installed on the steering column to detect if the driver pays attention to the road
[13]. If the driver is not facing towards the road and the probability of a frontal collision
7

is high, Toyota’s pre -crash safety system is activated [14]. Later, the system was
augmented by drowsiness detection which detects the driver’s eyelid status.
• Saab’s Driver Attention Warning System [15] counters inattention and
drowsiness. It utilizes two infrared cameras focused on the driver’s eyes. Conclusion on
driver inattention or drowsiness is made based on image processing algorithms that
depend upon eye-lid movement.
• Mercedes Benz introduced the Attention Assist System that observes the driver’s
behavior and creates an individual driver profile during the first few minutes of every
journey [16]. The system relies on dynamic driving data (speed, acceleration), turn
indicators, pedals and other control inputs and uses steering behavior as the key indicator
of drowsiness. The system is active at speeds between 80 and 180km/h.
• Volvo’s Driver Alert Control system uses a forward -looking camera to monitor
the car’s position on the road in relation to the road markings [17]. In addition, various
dynamic sensors are used to monitor the car. The system is activated at speeds of 64km/h,
and instead of focusing on human behavior, it monitors the car’s progress on the road.
• Ford’s Drive r Alert system uses a forward-looking camera installed on the
backside of the rear-view mirror. The system identifies lane markings and judges the
vehicle’s position relative to them. In case abnormal behavior is detected the system
provides initial soft audible and visual warnings that intensify if the driver doesn't react
[18].
• Volkswagen introduced the Fatigue Detection System that relies on a camera
focused on the driver’s face that allows detecting both head pose and eyelid status. The
measurement data are used to judge the driver’s status. Audio and visual warnings are
8

provided to the driver in case fatigue symptoms are detected [19]. In addition to that
Volkswagen introduced their Driver Alert System, which judges driver status by looking
at steering wheel movement and lane deviations [20].
In this chapter we introduce the Driver/Vehicle Response Diagnostics (DVRD)
system for a vehicle following case based on driving performance measurements. The
system learns the characteristics of the driving behavior of a particular driver/vehicle in
the longitudinal direction. It then uses that data to perform driver/vehicle diagnostics to
determine whether the driver is performing as expected. In addition to driving
performance measurements such as acceleration, following distance etc., we take into
account environmental condition parameters: rain and luminance. This allows the model
to be valid when a driver’s behavior changes due to a change in the environment. In order
to validate the model we use experimental data collected on a customized vehicle driven
by three drivers in diverse traffic and environment conditions.
The developed system can be used as a kernel of a driver monitoring system or such
devices as: safety warning devices, navigation devices where the aggressiveness of the
driver is taken into account in estimating travel times, etc. In Section 2.2 we describe
driver/vehicle response modeling techniques and response diagnostics framework. The
results of experiments are given in Section 2.3. Conclusions are formulated in Section
2.4.

2.2. DRIVER/VEHICLE MODELING AND DIAGNOSTICS

In order to perform driver/vehicle diagnostics, first we need to learn the way a
particular driver/vehicle responds to the traffic environment. The most challenging part of
9

the problem is to incorporate into the model human behavior patterns, which dictate the
response of the driver/vehicle system. Overall, the driving task can be represented as a
hierarchical structure with three levels [14]: strategic (long-term goals) – route choice and
trip schedule; tactical (short-term goals) – following, passing, lane changing, etc. (Figure
2.1); operational (low-level tasks) – pedal use, steering wheel, etc.
In this work we focus on tactical level driving tasks in order to implement a
diagnostics system for vehicle following. In particular, we concentrate our efforts on
analyzing the driver/vehicle response during vehicle following on a single straight lane
without passing (Figure 2.2).
Our approach to modeling is to view the driver and vehicle as an integrated system.
The inputs of the system are vehicle dynamic parameters like vehicle speed, relative
distance to the preceding vehicle, etc. The output is acceleration of the vehicle. Several
different modeling techniques could be used to model such a system. These include the
PieceWise AutoRegressive eXogenous (PWARX) model [15, 16], Gaussian Mixture
Figure 2.1: Tactical level of driving task

Figure 2.2: Vehicle following case
X
r
, V
r

Subject vehicle Preceding vehicle
Flow
V
f
, a
f

10

Model (GMM) [15], Neural Network (NN) [17, 18], and Hidden Markov Model (HMM)
[19].
Driver reaction time is a significant modeling parameter which varies from driver to
driver [20, 21]. However, the reaction time modeling is out of the scope of this work - we
exclude this parameter from our model. This may alter the accuracy of the model. Yet,
our proposed modeling framework and diagnostics are effective, allowing the validity of
the model without introducing reaction time. Nonetheless, augmentation of a model to
include driver reaction as a parameter can improve overall model accuracy.
In this work we combined two different approaches to model the driver/vehicle
response: GMM and probability density functions (pdf) of dynamic characteristics. The
GMM approach is adopted because of its effectiveness in general and its superior
performance of personalized GMM over PWARX in particular [15]. In our approach the
parameters of the model are being adjusted to each particular driver/vehicle based on
collected data. Then the adjusted model is used to evaluate the driver/vehicle response
during driving. Knowing the dynamic characteristics in the form of pdf allows us to
extract information about the particular aspects of a driver’s behavior. The GMM allows
for diagnostics of driver/vehicle status at every moment in time to detect dangerous
situations, while the insight to driver characteristics captured by the pdf models allows
checking of the driver/vehicle status in longer intervals of time. By combining these two
approaches we: reduce the false alarm rate of abnormal driver/vehicle response detection
generated by either one of the two methods separately; monitor different aspects of
abnormal driver behavior: short-term behavior deviation (due to distractions), and long-
term effects (drowsiness, DUI etc.).
11

2.3. GMM AND SHORT-TERM DIAGNOSTICS

The GMM model is used to represent the relationship between driver/vehicle system
inputs (speed, following distance etc.) and the output (vehicle acceleration). The main
assumption made, during development of the modeling framework, is that at each
moment in time the driver of the subject vehicle adjusts its acceleration by assessing
stimuli in the form of the dynamic parameters of his own and the preceding vehicle. The
GMM model represents the following driver/vehicle behavior in the form of a joint
distribution function of stimuli parameters and the driver/vehicle response.
A. Model definition
Let us define the 7 x 1 stimuli parameters vector at time t in the following manner:

T
v
f
t
r
t
r
t
r
t
f
t t
R E da dV V X V s ] , , , , , , [  , (2.1)

where V
t
f
– speed of the following vehicle, X
t
r
– relative distance between the leading and
following vehicle, V
t
r
– relative speed, E
v
– illuminance (total luminous flux incident on a
surface, per unit area), R – rain intensity, dV
t
r
and da
t
f
represent the change of relative
speed and the following vehicle acceleration over a time window T
d
(we set this value to
1 second) correspondingly:

d
r
T t
r
t r
t
T
V V
dV
d


 (2.2)
12

d
f
T t
f
t f
t
T
a a
da
d


 , (2.3)

where a
t
f
– acceleration of the following vehicle at time t. The augmented vector, which
also contains the following vehicle acceleration, is of 8 x 1 size and has the form:

T f
t
T
t t
a s r ] , [  (2.4)

The joint probability density function between the stimuli vector (2.1) and the
vehicle acceleration a
t
f
is modeled as the weighted sum of multivariate Gaussian
distribution functions:

, ) μ ( ) ( ) μ (
2
1
exp
) π 2 (
1
ω
) , μ ; ( ω ) , μ , ω ; (
1
2 / 1
2 /
1
1






   


  





i t i
T
i t
i
D
M
i
i
i i t
M
i
i i i i i t
r r
r N r p
(2.5)

where

(

) – multivariate Gaussian distribution of dimension D (in our case D =
8), with mean vector

of size D x 1 and covariance matrix

of size D x D, M – number
of Gaussian components,

– the mixture weights that satisfy the condition:




M
i
i
1
1 ω (2.6)

13

We refer to model (2.5), (2.6) as the GMM [29]. Let us denote the GMM parameters
as follows:

M i
i i i
,..., 1 }, , μ , ω { θ    (2.7)

Then the GMM in (2.5) is denoted as p(r
t
;θ). The covariance matrices

could be in
general or diagonal form. Even though [29] showed that for speaker recognition, GMM
with diagonal covariance matrices can reach the performance of those in the general form
by increasing the number of components M, our results demonstrated that driver/vehicle
performance is best described by GMM with full covariance matrices.
B. Model parameter estimation
Given a set of dynamic data for a particular driver/vehicle, the GMM parameters θ
can be estimated using the Maximum Likelihood (ML) parameter estimation method.
Given the model configuration and training data set

, that consists of
vectors defined in (2.4) with time intervals t denoted by natural numbers, the goal of the
ML estimator is to find the set of model parameters θ that maximizes the likelihood of the
GMM function:




N
t
t
r p L
1
) θ ; ( ) θ ( (2.8)

We assume that the data vectors are independent random variables. The
corresponding data log likelihood function has the form:
14

 



N
t
t
r p l
1
) θ ; ( log ) θ ( (2.9)

Due to the function’s nonlinearity with respect to the set of parameters θ, direct
maximization of the log likelihood function is difficult if at all possible. Therefore we use
the iterative version of the Expectation Maximization (EM) algorithm [30], which
guarantees a monotonic increase in the model’s likelihood value at each step of iteration
with the objective of finding the set of parameters θ that maximizes ( 2.9) as described
below.
Let the EM estimate of θ = {

at instant k be
̂

. The update of
̂
is generated
as follows. At every iteration we start by calculating the a posteriori probability for each
component i by using the GMM parameter set from the previous iteration
̂

:







M
j
k
j
k
j t j
k
j
k
i
k
i t i
k
i
t
l
i
r N
r N
r
1
1
) , μ ; ( ω
) , μ ; ( ω ˆ
) ( Pr

 


(2.10)

The distribution parameters are calculated at each step as follows:



 

N
t
t
k
i
k
i
r
N
1
1 1
) ( Pr
1
ω

(2.11)








N
t
t
k
i
N
t
t t
k
i
k
i
r
r r
1
1
1
1
1
) ( Pr
) ( Pr
μ

(2.12)
15






  

 
 
N
t
t
k
i
N
t
T k
i t
k
i t t
k
i
k
i
r
r r r
1
1
1
1 1 1
1
) ( Pr
) μ )( μ )( ( Pr
 

(2.13)

At the end of each iteration we update the value of the log likelihood function
l(
̂

):

 


 

N
t
k
t
k
r p l
1
1 1
) θ ; ( log ) θ (
 
(2.14)

The iteration (2.10) – (2.14) is repeated until the increase of the log likelihood
function becomes smaller than a specified value:

α ) θ ( ) θ (
1
 
 k k
l l
 
(2.15)

In this work we set the value of the threshold α to be 10
-10
.
C. Acceleration prediction
Using the set of estimated model parameters θ and knowing the stimuli vector

at
time t, the vehicle acceleration value can be predicted by finding the argument that
maximizes the value of the GMM probability density function:

), θ ; , ( max arg

t
f
t
a
f
tp
s a p a
f
t
 (2.16)

16

where θ

is the final value of GMM parameters of the EM algorithm that satisfies (2.15).
We use a maximization algorithm on an acceleration value interval from -6m/s
2
to 6m/s
2

based on golden section search and parabolic interpolation. The detailed description of
this method can be found in [31].
The probability density

;
̂
, as a function of vehicle acceleration, has a
bimodal shape (Figure 2.3) with two extrema lying to the right and to the left of the zero.
In order to guarantee that we obtain the absolute maximum of the function, we split the
search intervals into two: (-6,0) and (0,6). We perform search of the maximum value on
both intervals and pick the largest of them as the absolute maximum on the whole (-6,6)
interval.
Alternatively to the above search of the pdf’s extremum, one can search for the
expected value of the acceleration at each time period which may provide more
information. Such an approach has a high computational cost and is not suitable for real
time application.

Figure 2.3: Bimodal shape of the probability density as a function of vehicle acceleration
-6 -4 -2 0 2 4 6
17

D. Data set filtering and Improvement of model parameters
After the parameters θ were estimated using the data set

, we perform
training data set filtering and implement another iteration of parameter estimation.
Let us set up a threshold value thr
f
on the difference between the value of
acceleration a
tp
f
, predicted by trained GMM, and its actual value a
t
f
from the training data
set R. We create a new data set R
1
that consists of sample points that satisfy the condition:

f
m
f
tp
f
t
thr
a
a a


, (2.17)

where a
m
– maximum possible acceleration of the car at current speed if a
t
f
> 0 or
maximum possible deceleration if a
t
f
< 0. That is to say, we exclude sample points that
are far from what is indicated by the GMM to be appropriate driver/vehicle response.
This allows us to filter out events that formally correspond to the vehicle following task
and can’t be excluded by simpl e logic; for instance, a situation where a driver slows
down before making a turn while the preceding vehicle keeps on going straight, or the
cases right before or after lane changing when longitudinal control differs from the pure
following case. Consequently, we exclude sample points that correspond to unrealistic
driver/vehicle following response in order to perform more effective model training. As a
result, we create a dataset

, where N
1
< N. Then we perform another run
of the EM algorithm on the data set R
1
to estimate the GMM parameters θ.

18

E. Driver/vehicle response diagnostics
The predicted acceleration value a
f
tp

from (2.16) is compared with current vehicle
acceleration in order to make a conclusion as to whether the driver/vehicle system
behaves in the expected way. We propose two methods of determining the diagnostics
threshold.
1) Flexible threshold: The threshold value should be flexible in order to
accommodate different traffic situations. For instance, a low speed mode implies greater
inconsistency in the response due to the driver applying high acceleration values. And the
opposite is true as well – during high speeds the driver tends to apply lower values of
acceleration, and therefore the standard mean deviation of acceleration is smaller. A
confidence interval of acceleration can be determined after the acceleration prediction
value a
f
tp
is found from the trained GMM with given stimuli vector input s
t
. The GMM
probability density function (2.5) doesn’t allow ap plying simple techniques used for
Gaussian distribution to find a confidence interval. In order to determine the interval we
need to establish a conditional density function of acceleration a
f
given the stimuli vector
s
t
:

) (
) , (
) | (
t
t
f
t
t
f
t
r p
r a p
r a p  (2.18)

The probability that the acceleration lies in the interval (a
min
, a
max
) is the area under
the curve of p(a
t
f
| r
t
) on this interval:

19

 
 
max
min
max
min
) | ( ) , (
) (
1
a
a
f
t t
f
t
a
a
f
t t
f
t
t
da r a p da r a p
r p
p (2.19)

In order to keep the diagnostics level consistent, the probability value p is set up to
be a constant by varying values of the interval endpoints a
min
and a
max
, which are to be
determined. The search is performed by splitting the interval into two, with a
f
tp
as a
middle point, and implementing numerical integration of the curve value until the p/2
area value is reached for both parts separately:









 








 


2 / ) , (
) (
1
arg
2 / ) , (
) (
1
arg
f
tp
min
min
max
f
tp
max
a
min
a
max
p da r a p
r p
a
p da r a p
r p
a
a
f t f
t
a
a
f t f
t
a
(2.20)

Therefore, for each instant of time a driver/vehicle status check is performed by
assessing if the actual vehicle acceleration belongs to the following interval:

max min
a a a
f
t
  (2.21)

In order to formulate this algorithm to be suitable for online data processing, its
implementation on a low application level language like C++ is required to reach
satisfactory application productivity. Matlab does not allow it, therefore we leave the
online implementation of this proposed approach at the concept stage and will explore the
results of this method during offline data processing.
20

2) Constant threshold: Due to the high computational cost of the flexible threshold
method, we propose a simpler logic rule that still addresses the difference between
drivers. The threshold is set up on normalized value of difference between actual and
predicted by model acceleration values similar to (2.17). We say that the behavior
deviation is at a tolerable level and considered to be normal, when:

d
m
f
tp
f
t
thr
a
a a


, (2.22)

We adjust the GMM diagnostics threshold to a particular driver by using the
knowledge of mean prediction error value over a training set. The mean prediction error
value is determined as the mean difference between actual acceleration and predicted by
model values over the set. The mean prediction error value over trained set indicates how
consistent the driver/vehicle response is. That is, a high prediction error over a trained set
indicates that the driver behaves very differently for the same traffic situations contained
in the set. The mean prediction error value differs from driver to driver due to age,
experience, driving style and other factors. In order to keep the false alarm rate on the
same level for drivers with different consistency levels, we set up the GMM diagnostics
threshold to be proportional to the mean prediction error over the trained set:

e f thr
thr d
ˆ   , (2.23)

21

where f
thr
is a threshold factor coefficient, and ̂ is the mean error of acceleration
prediction over the training set normalized with respect to maximum possible car
acceleration/deceleration. Given the above threshold, in addition to determining whether
the driver/vehicle response is within the boundaries of normal driving characteristics for
the particular driver, we can also provide information to a driver monitoring system on
whether there is a safety concern. In particular, if (2.22) is violated and within the
absolute value function, the determined value of actual and predicted acceleration
difference is positive, and therefore the vehicle acceleration rate is significantly less than
the road situation dictates. We call this a “yellow warning” because there is no significant
danger apparent. In contrast, if the vehicle acceleration rate is significantly greater than
the road situation dictates, we call it a “red warning” because of the potential of unsafe
situation.
F. Universal background model (UBM) and driver style classification
By collecting data for a number of drivers we can establish a UBM for the average
driver by training the GMM with merged data sets [29]. Trained GMM-UBM provides
the following:
 It can be used as an initial guess for GMM adaptation. This allows us to avoid
obtaining an ill-conditioned or poorly trained model during stages when the
number of data for the driver/vehicle response is small.
 Driver classification by comparing a particular driver’s GMM to the GMM -
UBM.
Knowledge about driving style might be useful for a routing system, when the travel
time is adjusted depending on the driver’s aggressiveness. In the literature drivers are
22

usually classified into three main categories [32 - 33]: calm, normal, and aggressive. This
classification can be further extended by performing sub-categorization. Different sources
provide dissimilar explanation of terms aggressive, normal and calm and focus on
different measurements to classify drivers: speed [34], acceleration [35, 36], jerk [33],
pedals manipulation [37] or their combination [38]. However, they classify drivers based
on their actual response, which might be affected by road and traffic conditions during
particular data set collection. We propose assigning the driver a particular style according
to the comparison between his/her GMM and the GMM-UBM. The benefit of using a
well-established driver’s model instead of the actual driver/vehicle response is an
opportunity to use a predefined benchmark data set to perform style assessment. That is,
it allows for the exclusion of error related to different traffic conditions, weather, or time
of day.
In order to make a conclusion on driver’s style we focus on determining whether the
driver tends to use larger or smaller values of acceleration for a benchmark datasets by
comparing areas under the acceleration curve. An aggressive driver’s GMM response
compared to a calm driver’s GMM output would indicate the aggressive driver’s
tendency to apply a higher acceleration values for the same traffic situations. The GMM-
UBM as a trained model of an average driver is set to represent the normal type of the
driver.
Areas under positive S
+
and negative S
-
curves of acceleration values are used to
classify drivers. Their difference ΔS S
+
- S
-
indicates the general tendency of a model’s
response on the benchmark data set, for instance a positive ΔS value indicates that the
modeled driver would prefer to apply acceleration more often on the benchmark data set.
23

We compare ΔS values corresponding to the GMM-UBM and the driver of interest. The
style coefficient is determined as follows:

 

  

UBM UBM
UBM
S S
S S
p (2.24)

The numerator represents the difference between responses of a particular driver and
the GMM-UBM on the benchmark dataset. The denominator is a normalizing factor and
it’s introduced in order to keep the coefficient values independent on dataset length.
Additional threshold logic is established to perform assessment of (2.24) in order to
classify driver’s style:







 

aggressive thr p
normal thr p thr
calm thr p
agg
agg calm
calm
,
,
,
(2.25)

The threshold values in (2.25) could be adjusted for the needs of the particular
application that this classification is used for. For instance, if it is used to adjust travel
time calculation in a navigation system, then a series of simulations should be performed
in order to set up appropriate values. In order to get more elaborate driver’s style
classification, additional sub-categories can be introduced.

24

2.4. PROBABILITY DISTRIBUTIONS OF DYNAMIC
CHARACTERISTICS AND LONG-RUN DIAGNOSTICS

Different drivers have different styles of vehicle following in terms of relative
distance control. The vehicle following driving task can be characterized by a variety of
dynamic characteristics such as following headway time, inverse time to collision, peak
acceleration and deceleration values, reaction time, jerk and different measurements
related to pedals operation [39, 40]. Knowledge of driving style characteristics allows us
to design a diagnostics system that focuses on long-run driver/vehicle status check. It can
also provide a comparison between the drivers in terms of consistency.
A. Dynamic characteristics
The GMM was designed to model vehicle acceleration as driver/vehicle instant
response to traffic situations. Keeping that in mind, for a list of dynamic characteristics
used for the long-run diagnostics, we chose those parameters that would provide
additional information to what is already presented by the GMM.
 Following time headway (h) – the distance between the rear bumper of the
preceding vehicle to the front bumper of the following vehicle divided by the
speed of the following vehicle.
 Relative stopping distance (X
stop
) – the distance between the rear bumper of the
preceding vehicle to the front bumper of the following vehicle after both
vehicles come to a complete stop.
25

 Inverse Time to Collision (TTCi) which is equal to the inverse of time to
collision (TTC) defined as the ratio of relative inter vehicle spacing and relative
speed:

r
r
V
X
TTC  (2.26)
TCC
TTCi
1
 (2.27)

If TTC is positive, it is equal to the time to reach collision for a constant relative
speed. The inverse time to collision i.e. TTCi is considered to be more appropriate than
TTC due to its continuous dependence on collision risk [41], i.e. high TTCi implies high
collision risk and vice versa. We record TTCi at the time instants of throttle activation,
throttle release, brake activation and brake release. We select only the data points that fall
into the conditions: throttle is activated when the relative speed is positive (the relative
distance is increasing); throttle is released when the relative speed is negative; brake is
activated when the relative speed is negative; brake is released when the relative speed is
positive. These conditions are imposed in order to record only those TTCi points which
correspond to the driver need to take countermeasures to mitigate TTCi change rate and
therefore the risk for collision. The dynamic parameters h, X
stop
, TTCi defined above
encompass different aspects of vehicle following tasks and provide information about the
driver’s style. We treat these parameters as random variables with certain distribution
types. Our approach of estimating them involves collecting and processing data in real
time in order to generate their corresponding probability density functions (pdf’s )
26

associated with a particular driver/vehicle response. We store the pdf parameters along
with GMM in the corresponding driver’s profile. In the following subsection we describe
the development of the appropriate probability distributions of the dynamic parameters
that fit real data.
B. Dynamic characteristics distribution
It was observed during experiments that the dynamic parameters approximately have
the following distribution types (Figure 2.4):
 Normal distribution (relative stopping distance).
 Log-Normal distribution (following time headway and TTCi).
These conclusions were made based on the interquartile range test for normality and
a normal probability plots evaluation [42]. The conclusions on distribution types are
consistent with the results in other studies [43, 44]. Let us note that if x is a random
variable with normal distribution, then the random variable y=e
x
has a log-normal
distribution. Therefore, in the rest of the section only the case for normally distributed
driving characteristics will be covered. Expressions corresponding to the log-normal
distribution case can be obtained by applying the appropriate transformation between the

(a) Following headway constant, s

(b) Relative stopping distance, m

0 1 2 3 0 2 4 6 8
Figure 2.4: Distribution types
27

variables.
C. Driver/vehicle response diagnostics
The knowledge of the key aspects of a driver’s style can be used to assess the
driver/vehicle status by comparing the distribution parameters stored in the driver’s
profile with the pdf’s of the characteristics established during a particular trip. We use
hypothesis testing to check if the driver/vehicle shows the same performance as is
expected.
Let us denote the distribution mean and variance of relative stopping distance X
stop

stored in driver’s profile to be
0
and σ
0
2
. We consider the driver/vehicle to be
performing in normal way when the dynamic characteristic pdf is close to its respective
distribution stored in the profile from both mean and variance perspective. We denote the
tolerance interval width as δ, and the interval endpoints as:
1
=
0
- δ and
2
=
0
+ δ.
The two one-sided hypothesis tests are applied to assess if the sample mean is close to its
profile counterpart.
The hypothesis test for being outside normal driving but on the slower side is given
by:






1
1 0
:
:
 
 
a
H
H
(2.28)

and that of being outside normal driving but on the aggressive side is given by:

28






2
2 0
:
:
 
 
a
H
H
(2.29)

If one of the null hypotheses in (2.28) and (2.29) is violated, then we say that an
abnormal driver/vehicle response was detected. The conclusion is made based on a
sample data set. The hypothesis tests are performed with an a priori chosen level of
significance α. The t -test is applied for number of samples n < 30 and z-test for n ≥ 30.
Other dynamic diagnostics are performed in a manner similar to that described above for
the X
stop
value.
In addition to testing for the mean, we use a chi-square test to detect cases where the
driver demonstrates similar performance in terms of mean, but has a significantly larger
variance of dynamic characteristics:

,
:
:
0 1
2
1
2
2
1
2
0
 
 
 
w
H
H
a








(2.30)
where w – tolerance coefficient.
We define a “yellow” type of warning when the hypothesis test shows an abnormal
driver/vehicle response that is slower than the driver’s profile indicates and a “red” type
of warning when the hypothesis test shows an abnormal driver/vehicle response that is
more aggressive than it is predicted by the profile or for the case of abnormally large
variance. For instance, for the relative stopping distance parameter, we say that we have a
“red” type of warning if our test indicates that the driver stopped the vehicle much closer
to the point of collision than he/she usually does.
29

2.5. INTEGRATED APPROACH AND DECISION MAKING

We combine the diagnostics based on the GMM with the dynamic characteristics
probability distributions, allowing for a more accurate warning case classification as
shown in Figure 2.5. For the case when the pdf’s indicate a normal or slow driver/vehicle
response, there is no potential danger implied. Therefore additional logic for this case is
not required. On the other hand, when the pdf’s diagnostics show an aggressive response
or an abnormally large variance, we can logically imply that the driver is stressed, drowsy
etc., and is expected to make mistakes that might lead to dangerous situations.
Consequently, there is a need to adjust the system alertness by reducing the threshold of
the GMM diagnostics in (2.23). If the GMM indicates an abnormal response in this case
as well, then there is a strong concern for the driver/vehicle status, which is denoted as
“strong warning”. These warnings can be further used as inputs for a driver monitoring

Figure 2.5: Integrated diagnostics approach flow chart
30

system.
In addition to safety warnings the results of this methodology that allows us to
characterize the driver/vehicle response characteristics can be used to improve the travel
time estimation in vehicle navigation devices. An aggressive driver for example may
reach destination in shorter time on the average than a passive driver under the same
traffic conditions and by following the same route.

2.6. EXPERIMENTS

In this section we describe experiments carried out using real data obtained from
actual drivers driving in a designated Los Angeles area. The experimental data was
collected on a customized vehicle. The built-in PC was connected to the Controller Area
Network (CAN) of the vehicle which allowed data to be available in real time and stored
for off-line processing. The vehicle was equipped to measure dynamic parameters used in
the GMM and pdf’s of the driving characteristics: speed of the following vehicle, r elative
distance between the leading and the following vehicle, relative speed, illuminance, rain
intensity and vehicle acceleration.
The model learning and diagnostics algorithms were implemented in Matlab. The
system worked with a frequency of approximately 7Hz. Diagnostics were performed in
real time for every application cycle. For GMM they were performed based on data given
at the current moment in time, while for probability distributions they were performed by
using a shifting window of data.
31

In order to perform effective GMM training, the algorithm requires a significant
amount of stored data. This is because a driver’s style might evolve over time, especially
during the period of adaptation to the new car. However, implementing the EM algorithm
with large amounts of data becomes virtually impossible in real-time. Taking these two
factors into account, we set up a minimum number of following sample data points to
perform GMM training to be 3,000 and the initial data to be overwritten after the 50,000
sampling points mark is reached for each of the conditions (dry day, dry night etc, etc.)
separately. Therefore, overall 200,000 sample points could be stored in a driver’s profile,
corresponding to approximately 8 hours of vehicle following data. Considering the fact
that the amount of pure following data during urban driving was, on average,
approximately half of all the obtained data, the urban driver needed an average of 16
hours to completely fill up the profile. The profile was updated during the system’s run
every 15 minutes of driving and every time the application was closed. We consider
having enough data to generate the probability distribution model, when the number of
samples exceeds 30. In most of the cases, the first 15 minutes was enough to allow for
diagnostics based on the GMM and the following headway constant. Other parameters,
like relative stopping distance, took at least 30 minutes of urban driving to fulfill our
criteria and start diagnostics.
Diagnostics were performed in real time for every application cycle. For GMM they
were performed based on data given at the current moment in time, while for probability
distributions they were performed by using a shifting window of data. We consider the
amount of data to be significant when the number of sample points during the test period
exceeds 7. The number of sample points of TTCi corresponding to pedal operation and
32

X
stop
data is significantly less than the following time headway data, therefore in order to
fulfill the condition of minimum sample points during shifting window, different lengths
of windows were set up: 3 minutes for headway following data, 6 and 30 minutes for
TTCi and X
stop
respectively.
The experimental setup was designed to demonstrate the robustness of the approach
– its ability to distinguish between the drivers and to show that the model is valid under
different driving conditions. We can demonstrate the validity of the model in
distinguishing between diverse drivers by showing that it can discern minute differences
between drivers with similar backgrounds. The drivers were of similar age (26, 27, and
30 years old), same gender (male), similar driving experience (3, 4, and 5 years), and
identical education level (PhD students). They had the opportunity to take the car for
several days’ use to perform casual or daily home -to-work trips. Therefore, the
participants were able to adapt to the car and feel comfortable demonstrating their natural
driving habits.
The drivers were not restricted to a particular route or environmental conditions –
they faced daytime and nighttime conditions. In addition Driver 1 faced rain during
daytime and nighttime conditions on one of his trips. Overall, the amount of collected
data for the drivers was 18 hours – 6 hours for Driver 1 (27% nighttime, 7% rain), 4
hours for Driver 2 (23% nighttime), and 3 hours for Driver 3 (32% nighttime).
A. Effectiveness of GMM approach
It is important to validate if the GMM is able to adequately describe driver/vehicle
response. We use the mean prediction error value (the mean difference over the set
between the actual acceleration and the value predicted by the model) over the training
33

set in order to characterize how well the model fits the data. In order to standardize this
value for the characteristics of the particular car used in the experiments, we normalize
the mean prediction error value with respect to the maximum possible acceleration of the
car at current speed. Thereby, the prediction error is presented in percent. The curve of
the maximum possible acceleration of the car versus initial speed based on the
experimental date is given in Figure 2.6. The maximum deceleration value is
approximately independent of the initial speed and has a value of -8.5m/s
2
.
As the number of GMM components M increases, so does the training data fitting
accuracy (Table 2.1). However, at the same time, the computational time increases
significantly as well. Taking these two factors into account, we set the number of GMM
components M to be 15.
Further observations of the data showed that increasing the size of the training set
also increases the mean error of the set. This may be due to factors such as stress level,
level of drowsiness, desired time to destination, etc. It may have fluctuated over the
course of several days and therefore the driver’s performance could be slightly
inconsistent.
Table 2.2 presents the mean prediction error for the drivers for both the training and
raw data sets. The sets were obtained by combining different trips of the drivers. The
only restriction for the training sets was that they must contain all possible environmental
conditions the driver encountered. That is, the training sets contained samples with night
driving. Additionally, the Driver 1 set contained rain conditions. Based on the fact that
the difference between the mean prediction error over training and raw sets is small, the
34

trained model can be effectively applied to the raw data sets in real time regardless of
environmental conditions.
In order to evaluate the proposed training data set filtering technique in (2.17) we
perform the filtering and additional model training iteration. We set the filtering threshold
thr
f
in (2.17) to be 3 normalized mean errors over the training set.

Figure 2.6: Maximum acceleration of the car versus speed

0
2
4
6
max acceleration, m/s
2

8
speed, km/h 80 40
Number of GMM
components
Mean acceleration prediction error over
the training set, %

30-minute set 1-hour set 2-hour set
5 7.7 7.8 7.8
6 7.7 7.7 7.8
7 7.6 7.2 7.8
8 7.2 7.1 7.8
9 7.1 7.1 7.3
10 8.0 7.1 7.3
12 6.9 7.0 7.2
15 6.8 6.8 7.1
20 6.6 6.7 7.0
25 6.5 6.6 6.9

Table 2.1: Fit accuracy versus number of GMM components

35

We denote a used dataset of 1-hour length and around 25,000 sample points, to be R.
The mean prediction error for the trained 15-component GMM over this set is 6.9%. The
filtering technique led to better results. The data reduction amount was insignificant -
only 3.2% (799 sample points) of the data were filtered out. The resulting new set is
denoted by R
1
. Using the set R
1
, another iteration of GMM training is performed. The
mean prediction error for the trained GMM over set R
1
is 5.7%. When the acceleration
prediction algorithm is applied to a raw data set, the mean error prediction for GMM that
was trained over R is 8.5%, while the GMM trained over R
1
is 7.8%. The results
demonstrate that the proposed filtering of the data set and parameter re-estimation by the
EM algorithm improved the GMM acceleration prediction over raw data.
The mean prediction error could be explained by driver’s inconsistency. Similar
stimuli vectors in (2.1) might lead to different driver/vehicle responses. The mean
prediction error value over the training set indicates how much the driver’s behavior
varied for the same road situations, describing how consistent the driver is. This
acceleration deviation is larger for small values of speed since the driver would need to
apply larger acceleration/deceleration values for start/stop maneuvers. Table 2.3 gives
insight into the mean prediction error dependence on the speed interval.
Driver
Mean prediction error, %
Training set

Raw set
1 6.9 8.5
2 8.0 8.8
3 6.3 7.4
average 7.1 8.2

Table 2.2: Mean prediction error for M=15, on 1-hour training and
raw sets for different drivers
36

In order to evaluate the proposed driver’s style classification method we performed
the GMM-UBM training as follows. We merge the same sized training sets and perform
model training. In order to prove the robustness of the proposed driving style evaluation
approach in (2.24), the GMM-UBM and drivers’ GMM are applied to two different
benchmark datasets. Each consisted of 40 vehicle following minutes in length, coming
from different drivers. The results are given in Table 2.4. The UBM-GMM is assigned to
represent an average type of the driver. We can make a conclusion that Driver 1 prefers a
much more aggressive driving style than the other two. The presented style coefficients
have similar values for two different data sets. This supports our approach.
The experimental data processing results for the flexible threshold method are
demonstrated in Figure 2.7(a). Sigma, two-sigma, three-sigma confidence intervals that
correspond to 0.68, 0.95 and 0.997 confidence level were chosen as standard measures to
assess threshold values. As a result of this approach, the diagnostics threshold varies for
different traffic situations. Its values are higher when large acceleration or deceleration
values are applied than when the traffic situation is stable.
Speed interval
Mean acceleration prediction
error over the training set, %
1-10km/h 10.9
10-20km/h 11.5
20-30km/h 11.0
30-40km/h 8.4
40-50km/h 5.5
over 50km/h 4.5

Table 2.3: Mean prediction error over speed intervals

Dataset 1 Dataset 2
Driver 1 0.4 0.4
Driver 2 -0.3 -0.3
Driver 3 -0.4 -0.3
Table 2.4: Driving style coefficient for two different benchmark sets
37

Figure 2.7(b) compares the flexible threshold with 0.997 (3-sigma) confidence level
and the fixed threshold with coefficient in (2.23) is set to be 3. This plot indicates that the
fixed threshold could reasonably well approximate the confidence intervals.
Data collection was performed on actual streets, rather than in test tracks with
professional drivers, therefore we were unable to emulate accident and dangerous
situations. In order to determine whether the system could perform decent abnormal
behavior diagnostics in real life conditions, we leveraged the difference between driver’s
styles.
Driver 1 is set to represent the “normal” model of behavior, while Driver 2, with

(a) Acceleration prediction and confidence intervals

(b) Acceleration prediction (bold gray), 3σ confidence interval
(thin black) and fixed threshold interval (bold black)
Figure 2.7: Threshold initialization

0 10 20 30 40 time, sec
4

2

0

-2

-4

acceleration, m/s
2

acceleration, m/s
2

4

2

0

-2

-4

0 10 20 30 40 time, sec
3σ
2σ
σ
38

different characteristics, the “abnormal” behavior. The trained GMM for the Driver
1/vehicle is used while the driver was switched to Driver 2. We perform diagnostics of
the new Driver 2/vehicle system by comparing the Driver 2/vehicle acceleration value
with the one predicted from Driver 1/vehicle model. We should note that Driver 1 and 2
are of same age with very similar driving experience, yet the approach is able to
distinguish differences in their driving response.
Figure 2.8 shows plots of the real vehicle acceleration and its predicted value for the
two drivers over the typical 50 second intervals when the GMM is adjusted to Driver 1.
Clearly, the prediction error over these intervals is greater for Driver 2.

(a) Driver 1

(b) Driver 2
Figure 2.8: Comparison of predicted (bright line) and real value (black line) of
vehicle acceleration when GMM is adjusted for Driver 1
39

This conclusion is supported by analyzing prediction error values over both 1-hour
raw data sets for the drivers. The normalized mean prediction error for Driver 1’s raw
data set is 8.6%, with a peak error value of 22%. However, the mean prediction error of
the same model fitted to the specific driving style of Driver 1 and Driver 2’s raw data was
11.3%, with a peak error value of 35%. These values are significantly greater because the
model is skewed to the specifications of Driver 1. With a selected threshold coefficient of
3, the system will provide abnormal situation detections.
Based on the results presented in this section, we make a conclusion that the GMM
modeling methodology along with proposed threshold is an effective way to diagnose
driver/vehicle response.
B. Effectiveness of dynamic characteristics probability distributions
The goal of this section is to assess whether the pdf’s of the dynamic characteristics
can reasonably well describe driver/vehicle behavior and detect abnormal response.
In contrast to the GMM, the probability distributions of dynamic characteristics give
insight into long-run driver/vehicle response. By monitoring driver/vehicle status in the
long run, we detect any deviations that are associated with major behavioral changes in
the driver’s mind, like drowsiness, stress or DUI. Collected data for the following time
headway parameter has a lognormal distribution and has a tendency to decrease with
increasing speed of the vehicle for all drivers. TTCi also has an approximately log-normal
distribution, while relative stopping distance has normal distribution.
40

Similar to the GMM, the probability distributions of dynamic characteristics show
significant differences between the drivers. For instance, there is large difference in the
relative stopping distance and following time headway distributions (Table 2.5) – Driver
1 stops much closer to the preceding vehicle and has smaller following headway constant
for low speeds than Driver 2. That is, Driver 1 indicates a habit of staying much closer to
the preceding vehicle with smaller distance deviations.
We can conclude that even though the GMM and probability distributions
diagnostics are measured on different time scales, their results are still in agreement with
each other: the GMM indicates that on the average Driver 1 has a tendency to be more
aggressive than Driver 2, which is confirmed by analysis of the dynamic characteristic
distributions.
Characteristic type Driver 1 Driver 2 p-value
Following headway constant
for 1-10km/h, seconds
Mean 2.49 2.97
Variance

1.05 1.24
Following headway constant
for 10-20km/h, seconds
Mean 2.08 2.56
Variance

1.51 2.09
Following headway constant
for 20-30km/h, seconds
Mean 1.95 2.48
Variance

1.42 2.01
Following headway constant
for 30-40km/h, seconds
Mean 1.67 2.52
Variance

1.22 1.79
Following headway constant
for 40-50km/h, seconds
Mean 1.51 2.45 0.032
Variance

0.51 1.76 0.041
Following headway constant
for >50km/h, seconds
Mean 1.39 2.38 0.012
Variance

0.49 1.67 0.007
Relative stopping distance,
meters
Mean 2.55 4.43 0.002
Variance

1.05 1.59
TTCi corresponding to
throttle activation, 1/second
Mean -0.068 -0.073
Variance

0.004 0.012 0.003
TTCi corresponding to
throttle release, 1/second
Mean 0.097 0.093
Variance

0.016 0.012
TTCi corresponding to
brake activation, 1/second
Mean 0.172 0.153
Variance

0.025 0.018
TTCi corresponding to
brake release, 1/second
Mean -0.109 -0.115
Variance

0.006 0.014 0.071

Table 2.5: Driving characteristics pdf parameters for two drivers

41

With respect to environmental conditions, the difference between day/night and
dry/rain profiles is consistent for all the drivers. They have a tendency to drive more
conservatively during rain or night (the following headway constant was higher, while
TTCi was lower). The difference is less significant between day and night driving and
more significant between dry and rainy driving conditions.
In order to assess if the proposed approach is able to detect abnormal response we
perform the following experiment. As in GMM evaluation section, we assume that the
system evaluates Driver 2 by using the profile of Driver 1. We use z-test with 0.05%
significance level to evaluate if the system can identify whether Driver 2 does not fit the
expected normal behavior response during one trip.
The p-values of the driving characteristics are presented in the Table 2.5. The p-
values marked in bold are smaller than the chosen level of test significance, therefore the
corresponding null hypotheses were rejected. This suggesting that the drivers have
different response for the following parameters: mean and variance of the following
headway constant for 40-50km/h; mean and variance of the following headway constant
when speed is over 50km/h; mean of relative stopping distance; variance of TTCi
corresponding to throttle activation.
Comparison of Driver 1 with Driver 3 also indicated that the driving style difference
is more evident at higher speeds. We have to note that all three drivers were of same age,
gender and education level. Despite that, our approach was able to distinguish between
them. For drivers of different age, gender, experience etc. we expect more pronounced
differences in their driving response. Therefore, we make a conclusion that the proposed
approach showed satisfactory results.
42

C. The effectiveness of the integrated approach
The integrated diagnostics is expected to show more accurate driver/vehicle status
classification. Previously we showed that separate diagnostics based on GMM and the
knowledge of dynamic characteristic pdf’s are able to distinguish drivers’ style. We
combined two diagnostics system based on the logic depicted on Figure 2.5.
Because it is not feasible to replicate accident/dangerous situations on real roads or
test a drowsy/stressed driver response in reality, we again use the experimental technique
utilized in the previous sections. We put one driver behind the wheel, while the models
are skewed to another driver.
When the models were adjusted to Driver 1 and Driver 2 was behind the wheel, the
system indicated that there is no strong concern for the driver/vehicle status. In this case
the system was able to identify the difference in driving but issues no alerts as Driver 2
was less aggressive than the assumed Driver 1 model. When the models were adjusted to
Driver 2 and Driver 1 was behind the wheel, the system’s verdict based on pdf’s of
dynamic characteristics was that the driver reacts significantly more aggressive than it’s
expected from the models. This led to increasing the system’s alertness and concern for
the driver/vehicle when performing diagnostics based on the GMM. This feedback by the
pdf approach to the GMM improved the accuracy of the GMM output. Therefore the
experiment demonstrated by taking into account both approaches in the integrated system
mentioned above improves the driver/vehicle status check.

43

2.7. CONCLUSION

In this chapter we developed a driver/vehicle diagnostics system for the vehicle
following case based on two different types of models: GMM and probability distribution
functions of dynamic characteristics. The system utilized logic and appropriate thresholds
to make a conclusion on driver/vehicle status. In addition to that we proposed additional
GMM filtering techniques during training and defined an effective way of choosing a
diagnostic threshold. We developed a driving style classification algorithm that might be
used in ADAS of the car.
The experimental data indicated that the modeling technique is a good
approximation method for the driver/vehicle. The performed experiments supported our
methods and indicated that the system is capable of detecting an abnormal driver/vehicle
response for both short and long-run diagnostics. The system was implemented in Matlab
as a real time application that was installed on an onboard PC in the car. In addition to
that, modeling techniques demonstrated the ability to distinguish driving style of the
different drivers who participated in the experiments.

44

3. PERSONALIZED DRIVER/VEHICLE LANE
CHANGE MODELS

3.1. INTRODUCTION

Lane changes are stressful maneuvers for drivers, especially during high speed
traffic flows. This is the maneuver that is stressful for drivers as it involves changes in the
longitudinal speed and involves lateral speed and movement in the presence of other
vehicles which are also moving. The National Highway Traffic Safety Administration
(NHTSA) estimates that lane changing and merging collisions made up about 5% of all
police-reported collisions in 2007, and accounted for about 0.5% of all fatal cases [45].
These particular numbers do not indicate the significance of the problem. However,
studies suggest that risky lane changes result in unstable traffic flow [46] and lane
changing/merging accidents contribute to approximately 10% of all crash-caused traffic
delays [47].
The major contributing factor to lane change accidents is failure to detect the other
vehicle. It was found to be the main contributing factor in approximately 75% of lane
change crashes [48]. This suggests that the majority of such accidents can be avoided by
using ADAS that informs the driver about the positions of other vehicles when necessary.
NHTSA reports that 78% of lane change accidents occur at speeds smaller than 25km/h
[49] and on average it takes 1.5 seconds to cross into the adjacent lane from the time of
lane change initiation [50] – the point where a sideswipe collision can occur. Other
studies show that the auditory and visual reaction time of an average person lies in the
45

range of 180-200ms [51]. These facts indicate that there is enough time for ADAS to
notify the driver about potentially dangerous situations.
The assistance system can be effective only if it captures personal driving styles as
well as the dynamics of the driver/vehicle system. Most ADAS are designed with the
average driver characteristics in mind. This may lead to a system that is found to be too
conservative and annoying to the more aggressive drivers and too aggressive to the more
passive drivers. This in turn may inhibit most drivers from using ADAS and taking
advantage of its benefits.
In this chapter, we propose a modeling framework that takes into account the
driver/vehicle response before and during the maneuver that can be utilized by an ADAS
to provide personalized assistance to drivers. We consider the way the driver prefers to
adjust his/her longitudinal position with respect to the surrounding vehicles in order to
find a gap to perform the lane change, the kinematic characteristics of the maneuver, and
the driver’s acceptable gaps to initiate the maneuver (Figure 3.1). The acceptable gaps
describe the distances between the subject vehicle and the surrounding vehicles for which
the driver finds performing a lane change maneuver acceptable [52-54]. When the driver
finds the gaps acceptable, he/she initiates the maneuver.

Figure 3.1: Models associated with the lane change maneuver
Preparation Phase

Lane Change

Longitudinal
Adjustment
Model
Maneuver
Kinematics
Model
Gap
Acceptance
Model
46

There are two common approaches to the trajectory modeling problem: stochastic
and kinematic. Stochastic models are able to establish a relationship between hazards
imposed to the subject vehicle and the lane change trajectory shape. Possible modeling
techniques are: Stochastic Switched AutoRegressive eXogenous model (SS-ARX) [55,
56], Hidden Markov Model (HMM) [54-63], neural network [56, 64-66], fuzzy system
[66-69], Bayesian network [70-74], Support Vector Machine (SVM) [75, 76] and
Gaussian Mixture Model (GMM) [65, 77]. If properly trained, such models are accurate,
flexible, and adjustable for different personalizing aspects of driving. However, when
stochastic models are directly used to model a highly nonlinear function (such as driver’s
behavior or vehicle trajectory), these methods might lack physical meaning for their
model parameters.
On the contrary, kinematic models describe the lane change maneuver in a form of
equations with physical meaning. For example, lateral acceleration versus time. The two
most widely used kinematic models are polynomial [78-80] and sinusoidal [81, 82].
Along with original kinematic models, modified versions of these can also be found [83-
85]. These models provide meaningful kinematic information (trajectory shape,
acceleration curves etc.) about the maneuver, as opposed to other approaches that rely on
input output data to train models whose parameters have no physical meaning. However,
their rigid structure does not take into account all aspects of driving behavior, such as
dependence of trajectory shape on speed and surrounding traffic configuration. In
addition, a system that depends on a human response is non-deterministic by nature.
Therefore, an attempt to describe it solely with a deterministic kinematic model could not
be effective.
47

In this chapter we propose a new maneuver trajectory model that combines
advantages of both modeling methods. The proposed model consists of two layers:
stochastic (GMM) and kinematic (sinusoidal lane change model). We use driving
performance measurements along with information about the surrounding vehicles as
model signals. We focus our effort solely on developing models that can be used as a
kernel of the ADAS to provide personalized recommendations to the driver based on
his/her lane changing characteristics.
We evaluated the proposed methodology using an actual vehicle and real time
experiments involving a considerable number of real time data from different lane change
maneuvers. The experiments are extended to three different drivers in order to
demonstrate the difference in lane change characteristics between different people. We
demonstrated that the method is effective in modeling individual driver/vehicle responses
during lane change by showing a consistency of matching between the model outputs and
raw data.
In our work we assume that the system clearly identifies the driver behind the wheel.
This can be implemented by asking the driver to identify himself before he starts the trip.
This feature is already available in most new cars and allows different drivers to specify
themselves so that the car seat and side mirrors are adjusted automatically. Usually there
are choices of up to 3 drivers. Other more sophisticated methods include face recognition
[44], or performing an analysis of the driver’s style [45 -47] along the course of the trip.
This chapter is organized as follows. Section 3.2 presents our approach on describing
driver’s characteristics on pre -maneuver longitudinal adjustment and gaps acceptance to
initiate the maneuver. In Section 3.3 we describe the modeling technique for lane change
48

trajectory. The results of the experiments are given in Section 3.4 and conclusions are
formulated in Section 3.5.

3.2. LONGITUDINAL ADJUSTMENT AND ACCEPTABLE GAPS

Before we describe our approach, we establish the formal definitions associated with
a lane change maneuver.
A. Definitions
The lane change maneuver belongs to a category of tactical level driving tasks along
with vehicle following, turning, overtaking and other short-term tasks [86]. Alternatively,
the other two task levels are strategic (destination and route selection) and operational
(pedals and steering wheel use). NHTSA defines lane change as “a driving maneuver that
moves a vehicle from one lane to another where both lanes have the same direction of
travel.”
The maneuver can be classified as mandatory lane change (MLC) when the driver
must leave the current lane, or discretionary lane change (DLC) when the driver performs
lane change to improve driving conditions [53]. The type of the lane change affects the
driver’s behavior. For instance, the driver may tolerate smaller gaps between vehicles in
the destination lane for an MLC than for a DLC maneuver, due to the imperative nature
of mandatory lane changes.
Merging maneuvers occur when entering into the main lane from a ramp or when the
two lanes merge into one. It’s a representative c ase of mandatory lane change [54]. The
merging scenario can be detected from the GPS data, e.g. when the vehicle is
49

approaching a ramp. Similarly, other lane change situations, like a mandatory lane
change before the intersection to perform a turn, can be anticipated and classified. In this
work we focus on describing a general class of lane change maneuvers. Particular
scenarios can be derived by placing conditions on the model variables and introducing
other modeling parameters.
We also need to establish definitions for the start and end points of lane changing.
Correct detection of the lane change initiation point is crucial, because it defines when a
driver makes the final decision to start the maneuver based on his judgment of the road
situation. NHTSA proposes several indicators of the lane change initiation [87]. We
adopt the definition which states that lane change initiation is the point where the vehicle
begins lateral movement to the lane. This criterion was selected in contrast to these other
widely used indicators: change in steering input or lateral acceleration, which do not
allow for effective lane change recognition on curvy roads. The lane change initiation
point, end point, and trajectory shape can be effectively determined from yaw rate, lateral
acceleration, and steering angle only on a straight flat road. This is a substantial limitation
on the effectiveness of the lane change assist system. In contrast, data of lane markings
can provide effective maneuver detection in all cases.
One however can argue that lane markings cannot be a reliable source of information
due to the absence or degradation of lane markings on roads. We refute this point with
the following arguments:
 Missing lane marking cases are extremely rare on the urban roads and
highways in the US.
50

 Modern video processing algorithms allow effective lane marking
recognition even in the case of partially missing or degraded markings [88-
90].
In addition, if lane marking are absent on a multiple lane road, then the car’s
alignment in the lanes, and therefore the lane change maneuver, is ad hoc, and no
effective lane change assist can be provided in this case.
The accuracy of initiation point detection can be improved if lane marking data is
augmented with visual data on driver’s gaze status. In this case, the initiation point could
be marked when the driver returns his/her gaze to the forward view upon glancing at the
mirrors or side windows before initiating the maneuver.
The end point is not as important as the initiation point in terms of safety analysis,
but when wrongly detected it distorts the information about the completion time and the
shape of the maneuver. By analogy to the initiation point, we say that the lane change
ends when the lateral vehicle position in the adjacent lane stabilizes with respect to the
lane.
We utilize the data of surrounding vehicles as a factor that affects a driver’s
behavior. We use longitudinal projection of the relative distance between the subject and
another vehicle of interest (we denote it as D
X
) in order to characterize the relative
positions of the vehicles. In addition, we use the longitudinal projection of the relative
speed between the subject and the vehicle of interest (V
r
). The relative speed is defined as
positive when the relative distance between the vehicles is decreasing.

51

B. Longitudinal adjustment
If the gap in the destination lane is not acceptable for the driver to start the maneuver
then he/she might perform longitudinal adjustment. There are two strategies to adjust the
position: slow down with respect to the vehicles in the destination lane in order to move
in behind them, or speed up with respect to these vehicles in order to find a spot ahead of
them.
In order to analyze longitudinal adjustment, other studies [91] assume that
surrounding vehicles are at a constant speed. This assumption is not appropriate for a
system that will provide recommendations to the driver in real world situations. Absolute
values of longitudinal speed are not as important as their relation to the speed of the
vehicles in the destination lane.
We characterize the way the driver performs longitudinal adjustment with three
parameters. The first two describe a portion of the adjustments and their direction with
respect to the overall number of lane changes:

(3.1)

where n
+
– number of positive longitudinal adjustments before the lane change
maneuver, n
–
– number of negative longitudinal adjustments before the lane change
maneuver, N – total number of lane change maneuvers. The coefficient α describes how
often a driver performs a longitudinal adjustment before the maneuver, while β shows
which direction of adjustment is more preferable to the driver.
,
 
 
 





n n
n n
N
n n


52

The third parameter is the relative speed with respect to the vehicle in the destination
lane, with respect to which driver performs longitudinal adjustment. We store the peak
value of the relative speed for every longitudinal adjustment before the maneuver. From
collected speed values we construct distribution curves (Figure 3.2) for a particular driver
that, along with coefficients in (3.1), can be used to provide personalized longitudinal
adjustment recommendations before the lane change maneuver.
C. Gap Acceptance
The driver initiates the maneuver at the moment when he/she feels the positions of
the surrounding vehicles are acceptable for his/her comfort and safety standards. The gap
acceptance depends on personal preferences, current speed, urgency for changing lanes,
direction of the maneuver (left or right), and other factors.
To model gap acceptance for an individual driver, we take into account three
surrounding vehicles that affect a driver’s decision on adjusting his longitudinal position
and initiating lane change (Figure 3.3): the leading vehicle in the origin lane (L
O
), the
leading vehicle in the destination lane (L
D
) and the following vehicle in the destination
lane (F
D
). The latter two gaps are critical variables that affect a driver’s decision to
initiate lane change [53], while information on the gap acceptance to the leading vehicle

(a) negative adjustment (b) positive adjustment

Figure 3.2: Example of distribution curves of the peak relative speed
during longitudinal adjustments
-1.4 -1 -0.6 -0.2 0 0 0.4 0.8 1.2 1.6 2
53

in the origin lane is important for providing personalized longitudinal adjustment
recommendation to find the gap in the destination lane. The critical gaps are assumed to
have a log-normal distribution [53], while the gap to the leading vehicle in the origin lane
has a normal distribution as a non-critical variable. These assumptions are based on
analysis of real time data not included in this work.
In order to initiate the maneuver, the driver must evaluate the surrounding traffic
environment. Judgment is made based on factors such as relative distance and relative
speed with respect to the surrounding vehicles [54]. In our model we use the longitudinal
projection of the relative distance D
X
between the subject and one of the three vehicles of
interest as a dependent variable. That is, we aim to model the distance that is accepted by
the driver depending on independent variables – factors that might affect the driver’s
decision. One of such factors is the relative speed between the subject and the vehicles of
interest. A driver might prefer to keep a larger gap between his/her vehicle and another if
the other vehicle is closing the gap between them. Similar to the relative distance, we use
the longitudinal projection of the relative speed V
r
between the subject and one of the
three vehicles of interest. The subject speed V also affects the gap acceptance – drivers
usually accept smaller gaps when the traffic density is high and the speeds are low [52].

Figure 3.3: Pre-lane change trafic configuration
L
O

L
D
F
D

54

Direction of lane change (left or right) is another parameter that we take into account
in the model. A driver might demonstrate different gap acceptance behavior depending
on whether he/she is changing lanes to the left or to the right lane [92].
Another important factor that affects gap acceptance is whether the lane change is
mandatory or discretionary. Drivers are ready to tolerate lower gaps for mandatory lane
changes than for discretionary ones [93].
It is hard to recognize in advance which type of lane change a driver is about to
perform. We propose an idea that the blinker status might be considered as a reliable
indicator of lane change type. Its usage in advance is correlated with the urgency of the
lane change maneuver [92]. That is, when the driver switches on the blinker in advance
before the lane change, there is a high chance that he/she has a strong need to perform the
maneuver. NHTSA reports that blinkers are used in no more than 45% of lane changes
[94]. Moreover, some drivers have a habit of switching the blinker on when the maneuver
has already been initiated [92]. Therefore, in majority of cases if the blinker is activated
in advance it shows forethought demonstrating a stronger desire to change lanes. The lane
change assist system can address this need by relaxing the threshold conditions associated
with a driver’s comfort zone for the lane change maneuver in order to find an empty spot
in the destination lane as soon as possible.
We take into account the above described factors in order to develop the appropriate
models for each driver/vehicle system. We view the acceptance gap separately for the
three surrounding vehicles of interest and model them in the form of a linear regression
with independent variables of the subject speed V, the relative speed V
r
, and two
additional dichotomous (categorical) variables: blinker status b (0 – off, 1 – on) and
55

direction of the lane change d (0 – left, 1 – right). The critical gaps for the leading and the
following vehicles in the destination lane are assumed to have a lognormal distribution
[93]. We establish the regression model for the vehicles in the destination lane as follows:

d b V V V D
r r X
θ η ) , 0 min( ζ ) , 0 max( ε δ γ ) ln(      

(3.2)

The parameter γ represents the y -intercept term – it is the gap acceptance value when
all explanatory variables are set to be zero. The values of η and θ are the differential
intercept coefficients that represent the effect of blinker status and direction of the lane
change on the gap acceptance. The value of δ characterizes the gap acceptance
dependence on the subject speed. Coefficients ε and ζ represent the slopes corresponding
to the gap acceptance dependence on positive and negative relative speed V
r
respectively.
We split the relative speed term into positive and negative intervals because the
magnitude of its effect on the gap acceptance is different depending on the sign. For
instance, other studies indicate that for the lead vehicle in the destination lane the
influence of the relative speed on the gap acceptance is strongest when the vehicle is
faster than the subject vehicle [53].
The necessary assumptions for applying the linear regression such as
homoscedasticity (constant variance) and small correlation between the predictions are
satisfied for all three gaps. The expression (3.2) can be written in vector form as:

  ψ, ln x D
X


(3.3)

56

where x = (1, V, max(0,V
r
), –min(0,V
r
), –b, –d) is a vector of independent variables and ψ
= (γ, δ, ε, ζ, η, θ)
T
is the parameter vector. If n data samples are available, we can
combine them into a matrix X = (x
1
T
, x
2
T
,…, x
n
T
)
T
. The corresponding measurement
vector of gap acceptance is represented as Y = (ln(D
X1
), ln(D
X2
),…, ln( D
Xn
)). We use the
least squares method to determine the coefficients of the regression model as:

, ) ( ψ
1
^
Y X X X
T T 
 (3.4)

In order to establish a similar regression model for the lead vehicle in the origin lane,
we take into account the fact that the corresponding gap is a non-critical variable [93].
Therefore, we assume its distribution to be normal and omit the direction variable in the
model in order to obtain:

b V V V D
r r X
η ) , 0 min( ζ ) , 0 max( ε δ γ     

(3.5)

We use the estimated mean of acceptable gaps for the particular driver along with
the estimation of the variance to assess if the actual gaps are acceptable for the driver to
change lanes. The acceptance probability of a gap is calculated as a probability that the
actual distance D
actual
to the vehicle is greater than the preferred gap D
preferred
. We view
gap acceptance separately for the vehicles of interest. Consequently, the probability that
the driver will find the gaps to the vehicles in the destination lane acceptable to initiate
the maneuver is given as a product of acceptance probabilities for the separate vehicles
[53]:
57

] [ ] [
) ( ) ( ) (
preferred
XF
actual
XF
preferred
XL
actual
XL
D D
D D D D
D D P D D P
F accept P L accept P change P
  
  
(3.6)

During the course of a drive, the system collects data on the gaps at the initiation
point of lane change maneuvers in order to estimate the parameters of the linear
regression. Until the system collects enough data to establish the corresponding
coefficients, we use the mean and variance of the gaps disregarding their dependence on
speed, relative speed, blinker status, and lane change direction. This scheme allows for a
quick initial style evaluation, with accuracy improvement when the linear regression
results are generated.
The knowledge of a driver’s acceptance gaps and the way he/she performs
longitudinal adjustment before the maneuver can be used to provide personalized
recommendations. For instance, an optimization problem can be formulated to determine
an appropriate longitudinal adjustment in order to find an opening in the destination lane
[95].

3.3. MODELING OF LANE CHANGE KINEMATICS

In addition to the way a driver performs longitudinal adjustment before the lane
change maneuver and his/her gap acceptance at the maneuver initiation point, it is
important to know the way a driver performs the maneuver itself. We propose a two-
layer model structure that combines both stochastic and kinematic modeling techniques
(Figure 3.4). The lower layer describes the lane change maneuver in the form of a
58

kinematic model. The higher layer reflects the kinematic model parameter’s dependence
on a particular driver’s style and the surrounding traffic. Such a structure provides model
adaptation and, at the same time, contains physically meaningful parameters.
We choose GMM and sinusoidal lane change models as the stochastic and kinematic
counterparts respectively. The GMM was chosen because it demonstrated its
effectiveness in modeling other driving tasks [96, 97]. The sinusoidal lane change model
is selected because of its simplicity (only two parameters) and yet adequate
representation of the lane change. The small number of model parameters results in a low
computational cost, which is important when implementing the system in real-time.
A. Sinusoidal lane change model
The sinusoidal lane change kinematic model establishes a relationship between time
and lateral acceleration during the maneuver:









 t
t t
H
t a
lat lat
lat
  2
sin
2
) (
2
, (3.7)

Figure 3.4: Two-layer model structure

59

where a
lat
– lateral acceleration, t – time from the beginning of the maneuver, H – final
lateral displacement, t
lat
– time needed to complete the lane change maneuver. The
parameter t
lat
characterizes the driver’s style. The lateral acceleration in ( 3.7) is
associated only with the lane change maneuver. That is, if performed on a curvy road, the
total lateral acceleration of the car consists of two components: lateral acceleration
associated with the lane change maneuver and the centrifugal acceleration. In addition,
uneven road surfaces might introduce another component of acceleration. The profile of
the lateral acceleration associated with the lane change is estimated using the vehicle
position relative to the lane markings. We note that the lane change behavior of the driver
in a straight line lane may be different than that in a curvy lane. For instance, during a
lane change to the left on left-curved road, the driver may prefer to have a long small
amplitude steer to the left and a short right steer afterwards in order to minimize the
lateral acceleration. In our work we don’t consider the modeling of the lane changing
behavior on curvy roads. We believe however that the same methodology can be applied
to obtain personalized models that take into account the curvature of the road.
We choose the sinusoidal model rather than the polynomial one because data of the
initiation and end points of the maneuver are sufficient for calculating the parameters of
the sinusoidal model. Knowledge of the initiation and end points allow us to calculate the
duration and total lateral displacement. That is, we avoid relying on the car’s lateral
acceleration curve which might be corrupted by components not related to the lane
change maneuver. Lateral acceleration associated solely with the lane change maneuver
can be obtained as a second derivative of the lateral position with respect to lanes.
60

However, a second derivative is not a desirable estimation either. Hence, we prefer the
sinusoidal model that doesn’t require the knowledge of the acceleration curve to
determine its parameters.
When the model coefficients are calculated, one can estimate the curves of the lateral
acceleration, speed, and position trajectory associated with a lane change. This
information can be used to evaluate whether the conditions are safe and appropriate for
the driver’s style, and this in return can be used to provide recommendations to the
driver.
We calculate the parameters t
lat
and H for each particular instance of lane change.
They are stored in a data vector along with the subject vehicle speed and the distances to
the leading vehicle in the origin lane, the leading vehicle in the destination lane, and the
following vehicle in the destination lane. These values are captured at the time point of
the lane change initiation. We later use a set of such vectors to train the Gaussian Mixture
Model (GMM).
B. GMM
We use GMM to adjust the kinematic model parameters in (3.7) to a particular
driver’s style and to establish their dependence on surrounding traffic environment. We
define the vector of 4 x 1 size that contains the parameters that affect the duration of the
lane change maneuver as:

T
Fd Ld
Dx Dx H V s ] , , , [  , (3.8)

61

where V – the subject vehicle speed, H – total lateral displacement during the lane change
maneuver, D
X
– longitudinal projection of the relative distance between the subject and
another vehicle of interest. The combined model layout and its signals are depicted in
Figure 3.5. We do not consider the distance to the leading vehicle in the origin lane. Data
analysis indicates that this parameter is non-critical as it does not affect the duration of
the lane change maneuver. This shows that when initiating the maneuver, the driver’s
attention switches solely to the vehicles in the destination lane. Another parameter that
might affect the duration of the lane change is the road curvature. For instance, on a left-
curved road it might take the driver more time to perform the lane change to the left due
to centrifugal acceleration already applied to the car. If the measurement of the road
curvature is available it should be added to the model. Since our experimental vehicle
doesn’t provide the road curvature measurements, we omit the parameter in this work.
We define an augmented vector of 5 x 1 size to also contain the time required for the
driver to complete the lane change maneuver as:

(3.9)

We represent the joint probability density function between the prediction vector
(3.8) and the duration of the maneuver t
lat
in the form of the multivariate Gaussian
T
lat
t s r ] , [ 
GMM
t
lat

Figure 3.5: Lane change kinematic model layout

Sinusoidal
Model
a
lat
(t)












Fd
Ld
Dx
Dx
H
V
62

distribution functions described in (2.5) and (2.6).
We can estimate the model parameters given a data set for multiple lane change
maneuvers in the form of the vector (3.9). In order to perform accurate GMM training we
use sample entries where the leading and the following vehicles in the destination lane
(L
D
, F
D
) are present when the maneuver is initiated.
Given a set of dynamic data for a particular driver/vehicle, the GMM parameters θ
can be estimated using the Expectation Maximization (EM) described in (2.10) – (2.14).
C. Maneuver shape prediction
After the model is trained, it can be used to predict lane change duration t
lat
, given
the prediction vector (3.8). We approximate the total lateral displacement parameter H as
the width of the lane the subject vehicle is currently in. If the width cannot be estimated
because of a lack of right or left lane markings, then we assign it to be 3.7 meters, which
is a standardized lane width according to the U.S. Highway Interstate System.
We perform an initial maneuver feasibility check by assessing the longitudinal
distance D
X
to the leading and the following vehicles in the destination lane in order to
determine if there is enough space to fit the subject vehicle. If the check is passed, we
determine the expected lane change duration as the one that maximizes the GMM
probability density function:

), θ ; , ( max arg

lat
t
lat
t s p t
lat
 (3.10)

where is a vector of the estimated model parameters. 

63

If one or more of the two surrounding vehicles (L
D
, F
D
) are absent, then we
substitute their corresponding entries with fictitious far-distanced vehicles. In this case,
we assign the relative distance D
X
to be a large number (100 meters).
The GMM is used to establish dependence between lane change trajectory
parameters and traffic environment for a particular driver. However, it requires a large
number of samples for its training. Until there is enough data to train the GMM, we
establish probability density functions of the kinematic parameters associated with lane
changing without assuming any dependency between them. This allows rough, but quick
insight into a driver’s style, so the corresponding ADAS can be supported with some
individual driver characteristics as soon as possible. When available, the GMM will
replace the rough estimates with more precise ones in order to provide a more accurate,
personalized description of a driver’s style. The expected maneuver duration is then
substituted to (3.7) to predict the lane change acceleration curve, which in turn can be
integrated to obtain lateral velocity and trajectory with respect to the lanes.
The gap acceptance, longitudinal adjustment and maneuver kinematics models can
be used as a kernel of a personalized ADAS. The system should evaluate the surrounding
traffic environment in real time and provide the driver with recommendations if it’s
reasonable to initiate the maneuver. If the gaps are not acceptable, the system should
provide longitudinal adjustment recommendations to the driver to find the gap in the
destination lane.
In addition to driver’s acceptance, the system can perform supplementary safety
evaluation of the maneuver. The duration and shape of the maneuver can be assessed by
ADAS with respect to their feasibility and safety in order to provide appropriate
64

recommendations to the driver. For instance, when the expected duration of the lane
change is abnormally small or the peak lateral acceleration value is too large for a
particular driver, the maneuver may be considered not desirable. In addition, the gaps in
the destination lane can also be assessed from a safety perspective [91]. The design of
ADAS however is outside the scope of this work and is part of future work.

3.4. EXPERIMENTS

We used a customized vehicle to run experiments and collect on-road data. The
vehicle is pre-equipped from the factory with sensors to measure the values of speed, lane
markings, and blinker status. The data is accessed through a CAN (controller area
network) bus for real-time data processing and storage. In addition, the vehicle is
equipped with side-facing radars as well as front and rear-facing lidars (sensors that
measure distance by illuminating objects with a laser). These sensors provide 360º
coverage of object detection (Figure 3.6) in a vicinity of up to 50 meters and allow

Figure 3.6: Layout of the vehicle’s sensors
Radar
Radar
Lidar Lidar
65

measurement of the relative distance, speed and angle to the surrounding vehicles.
The presented modeling framework is implemented as a real-time application on the
vehicle built-in PC with the following configuration: Intel Core i5-2300 CPU at 2.80GHz
with 6GB of RAM. Three drivers participated in the experiments. They were of similar
age (27, 28, and 31 years old), same gender (male), similar driving experience (4, 5, and
6 years), and identical education level (PhD students). Prior to data collection, they had
an opportunity to perform casual daily trips for several months without any restrictions or
requirements to the trips. That is, the participants were given time to adapt to the vehicle
and feel comfortable demonstrating their natural driving behavior. For the data collection,
the drivers were asked to drive near the downtown area of Los Angeles and Palo Alto on
arterial streets and urban highways. The drivers were not restricted to a particular route
and were not given any restrictions, including the duration of the journeys. The drivers
performed 97 trips in total with the average duration of a trip lasting 51 minute. During
driving, the on-board PC recorded collected data with a frequency of 30 Hz and stored it
in a data file that was later processed off-line. The process of data acquisition and
recording was hidden from the drivers, so the system did not intrude on the driving in any
way or affect natural driving behavior. We should note that the use of three drivers was
just to demonstrate that our method can easily distinguish between different driving
styles. The number three is not used for any statistical inference or analysis. For each
driver however we collected a large number of data to train and validate the models.
A. Data processing
We used the collected lane change data to determine the lane change initiation and
end points. By assessing the video signal from a camera, we established that the overall
66

portion of lane changes performed without detected lane markings was only 12%. Part of
this missing data was reconstructed by performing lane signal interpolation for the cases
where data was missing for less than 3 seconds. We detected lane change maneuvers in a
set of data by first searching points where the vehicle crossed a lane (Figure 3.7). A jump
in the vehicle lateral position with respect to one of the lanes at the moment when the
vehicle crosses a lane can be explained by switching in what is considered to be the
neighboring lanes of the vehicle. When the crossing point was detected, in its proximity
we looked for the two extremum points of the lateral position with respect to the lanes:
the one that occurs before the lane crossing specifies the initiation point, while the one
after indicates the end of the maneuver. We used additional filtering techniques to avoid
classifying changing more than one lane at a time or interpreting turning as a lane change.
In order to distinguish the L
O
, L
D
and F
D
vehicles from all the vehicles detected by
radar (Figure 3.8), we used their relative position and their location with respect to the
lane markings. By doing so we detected the closest vehicles in the current and
neighboring lanes which corresponded to the position of the L
O
, L
D
and F
D
vehicles.
After a lane change maneuver was performed and the end point detected, we referred to

Figure 3.7: Vehicle’s lateral position with respect to lanes and lane change detection
0
2
-2
meters
1
3
-1
-3
65 70 60 seconds
67

the traffic configuration at the initiation point. We stored the relative speeds and distances
from the subject vehicle to the lead vehicle in the origin lane, the following vehicle in the
destination lane, and the lead vehicle in the destination lane.
The parameters associated with gap acceptance regression and GMM were estimated
in quasi-real time. Chunks of driving data were processed every fixed period of time after
which we updated the model parameters. We performed GMM training when there were
enough lane change sample points. We set the minimum number of data to be 100. We
find this number to be reasonable for establishing a well-trained model and avoiding ill-
conditioning.
We perform lane change shape prediction and gap acceptance estimation in real
time. That is, when the associated models are trained, at every moment in time we
calculate the gap acceptable to the driver and the expected lane change kinematic
parameters of the potential maneuvers to the left and right. The system is implemented as
a C++ application and is able to provide online prediction with 30 Hz frequency.

Figure 3.8: Object detection from the radar data
68

B. General data analysis
On average it took 11.6 hours to collect 100 lane changes – the number we specified
to be the minimum for GMM training after which the system can start providing reliable
personalized lane change duration prediction. Before this number is reached, the system
can provide personalized assistance based on the duration probability density function
that can be constructed with a smaller number of samples.
Table 3.1 gives a summary of the collected data. Overall we collected 717 lane
changes for the three drivers. There are slightly more lane changes to the right than the
left: 388 versus 329.
We classify the driver indicating the desire to change lanes in advance when he
switches the blinker on at least 3 seconds before the maneuver. The amount of samples
when the blinker was used in advanced is small – only 78. The overall portion of such
lane changes is 10.8% for the three drivers.
C. Longitudinal adjustment and gap acceptance
Table 3.2 presents parameters described in (1) that characterize the drivers’ habits of
adjusting their longitudinal position before the maneuver. The data indicates that a
majority of the lane changes were not preceded by longitudinal adjustment. If there was
an adjustment then it was in the positive direction.
Table 3.3 provides information on the mean values of lane change parameters for all
of the collected data. The distributions of all the parameters presented in the table are
normal, except for the relative distance to the lead and following vehicles in the
destination lane which had a lognormal distribution. This indicates that the relative
69

distance to the following and the preceding vehicles in the destination lane are the two
critical parameters that affect a driver’s decision to initiate a lane change.
Table 3.4 presents the values and significance of the linear regression models’
coefficients for Driver 1. Coefficients related to the lead vehicle in the destination lane
(L
D
) and the following vehicle in the destination lane (F
D
) correspond to the expression
(3.2). The coefficients related to the lead vehicle in the origin lane correspond to the
Direction Blinker Driver 1 Driver 2 Driver 3 All
Left
On 15 2 20 37
Off 183 67 42 292
Right
On 18 6 17 41
Off 252 62 33 347
All 468 137 112 717
Table 3.1: Contingency table of the data – number of samples

Parameter Driver 1 Driver 2 Driver 3 All
Number of positive
adjustments (n
+
)
51 9 2 62
Number of negative
adjustments (n
–
)
19 6 7 32
Total number of
lane changes (N)
468 137 112 717
α 0.15 0.11 0.08 0.13
β 0.46 0.2 -0.56 0.32
Mean of relative
speed peak, km/h
7.2 5.3 4.6 5.7
Table 3.2: Longitudinal adjustment of the drivers

Dx
LO
,
m
Dx
LD
,
m
Dx
FD
,
m
Vr
LO
,
m/s
Vr
LD
,
m/s
Vr
FD
,
m/s
Left 20.1 16.1 18.0 0.63 0.52 -0.23
Right 22.7 15.1 17.4 0.65 0.67 0.12
All 21.4 15.8 17.7 0.64 0.60 -0.05

Table 3.3: Mean values of lane change parameters for all available data
70

expression (3.5). All associated significance values are less than 0.1 which indicates that
their respective terms are important predictors.
The sign of the coefficients indicate that Driver 1 needs larger gaps when driving at
higher speeds, when the relative speed between his/her vehicle and the surrounding
vehicles is high, and when he performs maneuvers to the right as opposed to the left. In
general, Driver 1 accepts smaller gaps for maneuvers when he switched on the blinker
signal in advance. A small standard error, significance values of zero, and substantial R
2
values (Table 3.5) support the effectiveness of the constructed model. The regression
coefficients for the other two drivers indicate that they have different gap acceptance
preference. For instance, Driver 3 prefers larger gaps and there is no strong dependence
between blinker usage and gap acceptance.
D. Lane change kinematics
We trained the GMM by using only samples that contained the leading and the
following vehicles in the destination lane. The amount of such data for driver 1 is 45% of
the overall amount (210 samples). We used 80% of this data as a training set and 20% as
γ δ ε ζ η θ
L
O

Value 9.38 0.11 1.68 0.9 1.16 -
Signif. 0.00 0.00 0.00 0.05 0.10 -
L
D

Value 2.11 0.03 0.42 0.11 0.45 0.50
Signif. 0.00 0.04 0.02 0.00 0.08 0.09
F
D

Value 2.23 0.02 0.35 0.06 0.67 0.73
Signif. 0.00 0.05 0.07 0.09 0.03 0.04
Table 3.4: Linear regression coefficients and their significance

R
2
Significance Std. error
L
O
0.33 0.00 3.25
L
D
0.48 0.00 0.64
F
D
0.52 0.00 0.54
Table 3.5: Linear regression model characteristics

71

a raw data set to perform the model evaluation. We measured the accuracy of the model
by assessing the difference between the actual and expected lane change duration. An
increase in the number of the GMM components M improves the accuracy of the model
(Table 3.6). However, an increase in components also increases the computational cost.
We set this number to be 4 in order to balance the accuracy-computation cost for the real-
time application. The GMM outperforms the baseline model, which uses the average
maneuver duration as a guess: the 4-component GMM mean prediction error for the raw
set is 0.84 seconds, while the baseline model’s error is 1.44 seconds on the same data set.
Therefore, we can conclude that the proposed framework is effective. The baseline model
can be used up to the point when there is enough data to train the GMM which gives a
more accurate prediction.
Another indicator of the effectiveness of the model is its ability to capture a driver’s
personal style. If the model is trained on the set of one driver and used to predict lane
change duration on a raw data set belonging to another driver, then we observe a
deterioration in the accuracy of the predictions: the mean prediction error increases from
0.84 to 1.82 seconds when the Driver 1 model was applied to the Driver 3 data set. The
results indicate that the model is able to distinguish between the drivers of very similar
backgrounds.
Table 3.7 presents the kinematic parameters of the lane changes for Driver 1. The
distributions of the parameters are normal. The sinusoidal model adequately describes the
lane change lateral acceleration with respect to the lanes. The mean error between the
lateral position obtained by integrating (3.7) with parameters established by the GMM
72

and the actual lateral displacement in time for the maneuvers is 0.35m for Driver 1. This
indicates that the kinematic model represents lateral displacement reasonably well.

3.5. CONCLUSION

In this chapter we developed a methodology that models how a driver changes lanes
with a particular vehicle. The methodology combines advantages of stochastic and
kinematic modeling techniques in order to come up with models that can run in real time
with the capability of adjusting their parameters as new data are received for better
accuracy. The models capture the behavior that involves adjusting longitudinal position
and speed before the lane change maneuver, gap acceptance to initiate the maneuver, and
the kinematics of the maneuver. This modeling framework can be used to develop a lane
change driver assistance system as part of ADAS in order to provide appropriate and

Number of GMM
components
Mean difference between actual and
expected lane change duration, s

Training set Raw set
2 0.75 1.03
3 0.56 0.91
4 0.50 0.84
5 0.48 0.82
7 0.46 0.81
10 0.45 0.81
Table 3.6: Fit accuracy versus number of GMM components

H, m t, s a
max
, m/s
2

Mean 3.32 6.52 0.61
Std. Dev. 0.39 1.52 0.32
Table 3.7: Kinematic Characteristics of Lane Changes

73

desirable recommendations to the driver that are personalized to his/her driving
characteristics and dynamics.
We used experimental data to train the proposed models and validate them. The
experimental results demonstrate the effectiveness of the approach. In addition we
demonstrated that the models are indeed personalized by applying the methodology to
three different drivers and showing that the corresponding three models differ enough for
the system to identify who the driver is.
74

4. VEHICLE LATERAL POSITION PREDICTION

4.1. INTRODUCTION

As production vehicles are being outfitted with more and more advanced sensors
such as GPS/IMU, camera, LiDAR, radar, etc., it is increasingly desirable from a safety
standpoint to utilize the trove of sensor data to develop Comprehensive Risk Assessment
Systems (CRAS) that will assess any potential risks that might arise in the immediate
driving environment and beyond (Figure 4.1). Since risk can evolve as a function of a
cavalcade of structural (e.g., road topology), environmental (e.g., traffic density, weather,
time of day), and human factors (e.g., fatigue, distraction), a CRAS may require
advanced forewarning subsystems operating on different sources of information;
information from localized components of the immediate environment to real-time traffic
information from online or V2V communication. In order for a CRAS to select the best
remedial strategy for an impending risk, it is crucial to have an accurate index of
prediction accuracy, conversely error tolerance, at different forecast lengths for the
different subsystems.

Figure 4.1: Traffic environment forecasting
75

In this chapter we took the initial steps toward evaluating the prediction accuracies at
different forecast lengths of a specific instantiation of Time Lagged Feedforward Neural
Networks (TLFNN), namely Multi-Layered Perceptron with a sliding input window
(MLP-sw), with respect to lane change and overtaking maneuvers. We chose a Neural
Network technique because of its demonstrated power in time series forecasting [98-102].
We chose lane change and overtaking maneuvers because they are amongst the few
principal driving behaviors, along with lane keeping and car following that occur
frequently on a daily basis, and because they are among the core use cases in the
development of ADAS, either as standalone systems or potential subsystems of a CRAS.
This chapter is organized as follows. Section 4.2 briefly describes Neural Network
modeling methodology. Section 4.3 defines the problem and our approach. Section 4.3
contains experimental results. Section 4.4 presents conclusions.

4.2. ARTIFICIAL NEURAL NETWORKS

A. Advantages and Pitfalls
MLP-sw belongs to a general class of statistical modeling tools called Artificial
Neural Networks (ANNs). ANNs are composed of parallel adaptive nonlinear elements
that operate, in principle, as that of human neurons. Their power of lies in the fact that
they are universal function approximators [103, 104], and can be treated as a data-driven
multivariate nonlinear nonparametric statistical modeling method that makes very little a
priori assumptions with respect to the nature of the data involved [105].
76

ANNs are quite attractive because they can be used to model complex input-output
relationships, especially when the precise nature of the relationship is unknown or too
complex to implement by hand. They offer a practical and, often one of a few
appropriate, means of solving many real-world problems that have a lot of observations,
but very little theoretical knowledge regarding the structure of the system to which those
observations arose [103]. They have provided superior results compared to traditional
modeling techniques, and saw extensive use in applications such as optimization, pattern
classification, signal processing, and forecasting.
Yet, their flexibility also masks their greatest pitfall – the temptation to apply it
without understanding the details of the model. This is compounded by the fact that many
applications of ANNs are published with relatively sparse details about essential features
and methodology. The lack of transparency hinders easy understanding and replication,
which often contribute to an overestimation of the powers of ANNs and underestimation
of their potential limitations. Thus, it is crucial to have a clearer understanding of the
advantages and limitations of various models and techniques [106], including, but not
limited to MLP-sw.
B. Time Lagged Feedforward Neural Networks
The MLP-sw explored in this study is a specific case of Time Lagged Feedforward
Neural Networks (TLFNN). TLFNN are adaptations of one of the most influential classes
of ANNs, namely, Multi-Layered Perceptrons (MLP). They have the same basic structure
as MLPs, which are typically composed of an input layer, an output layer, and one or
more intermediated layers called hidden layers (Figure 4.2).
77

What separates TLFNNs from the typical MLPs is simply the nature of their
respective inputs. For typical MLPs, the input is comprised of n independent variables
and the output corresponds to a single or a set of dependent variables. Thus, the
functional relationship estimated by a typical MLP can be written as y = f (x
1
, x
2
,…,x
n
),
where x
1
– x
n
are n independent predictors and y is the corresponding predicted
variable(s), which is equivalent to a nonlinear multivariate regression problem. However,
the input to TLFNNs may contain time lagged (past) values of one or more data series.
For example, if the past values are those of the predicted variable y, i.e., y = f (y
t
, y
t-1
,…,
y
t-n
), then the functional relation modeled by a TLFNN would simply amount to a time
series auto-regressive problem. When a TLFNN incorporates both the predictor variables
and time lagged observations of the predicted variable as input, the functional relation
would be that of a general transfer function; which has wide application in control
systems [103].

Figure 4.2: A typical Time Lagged Feedforward Neural Network (TLFNN)

78

The MLP-sw employed in the current study falls in the latter category, in that it
incorporates predictor variables such as speed, steering wheel angle, etc., as well as past
trajectory values, as parts of the input. What differentiates MLP-sw from other forms of
TLFNN, such as Focused Time Delayed Neural Networks (FTDNN), is that no tapped
delay line [107] is employed. The temporal slice, X(t), simply becomes X(t-1) in the next
input vector. In this respect, the input is simply a sliding window that consists of n-
temporal slices (Figure 4.2).

4.3. LATERAL TRAJECTORY MODELING AND PREDICTION

Two major contributing factors accounting for roughly 75% of the Lane Change and
Merging (LCM) accidents are the failure to detect the presence or correctly estimate the
trajectory of the other vehicle in the adjacent lane. A significant portion of LCM
accidents can be avoided by an ADAS that monitors the driver’s blind spots and actively
predicts the trajectories of the object vehicle and the surrounding vehicles to forewarn
any potential impending risk of collision; and if necessary, assume active control to
execute safe avoidance maneuvers. Note that NHTSA reports that it takes an average of
1.5s from the initiation of the lane change maneuver to cross into an adjacent lane [50], a
point where the typical LCM accident occurs. If an ADAS can offer advanced
forewarnings that will span the entirety or a significant portion of that period, it can
adaptively select the best and least intrusive remedial strategy.
However, in order for such ADAS to be effective, the forecast accuracy and optimal,
or even maximally tolerable, forecast length of the specific forewarning system it
employs must be fully indexed. Thus, the current study takes the initial steps of
79

evaluating a forerunning candidate, namely MLP-sw, for incorporation into such a
forewarning system.
A. Forcasting and Dynamic Time Series
A time series is a collection of data recorded over a period of time. For automotive
needs, the time periods to which time series data may be collected can vary from seconds,
minutes, weeks, to even longer depending on the nature of the information and intended
application. Regardless, a critical assumption in time series analysis is that a reliable
pattern or sets of patterns can be identified. And based on the temporal order of the
identified pattern a future value can be inferred from past values. Thus, prediction
accuracy is contingent on the following factors:
• The number of identifiable patterns.
• Correct identification of a specific pattern.
• Accurate temporal placement of the past values.
Accurate temporal placement of past values usually is not a big problem for time
series forecasting because most applications only deal with a single general pattern. As
long as past values can be matched to a unique juncture, accurate forecasts can be made
at very large prediction horizons. In this case, time series forecasting is essentially a
nonlinear regression problem because the first two points above are not an a priori issue.
However, if the time series is a dynamic composition of different sub-patterns that have
no single general pattern, accurate temporal placement can be a huge problem. To
illustrate this point, we only need to think about what occurs during a typical drive. A
driver can decide to go straight for a long period of time or change lanes (left or right)
80

multiple times. The precise paths we take to and from the same locations can be quite
different each time.
These kinds of dynamic variations are problematic for advance forecasting and
require a careful formulation. Since vehicle paths are dynamic compositions of many
maneuvers, an ADAS with advanced forewarning must take on the dual roles of
identification and forecasting. That is, it has to make forecasts based on the identified
maneuver. Moreover, it has to take into consideration the following issues:
• How quickly it can recognize a specific maneuver.
• How quickly it can adjust its predictions to match.
• The precise tolerable prediction horizon.
All of which are contingent on the diversity of the maneuvers involved and their
respective temporal progression. Thus, any candidate system under consideration for
incorporation into an ADAS has to be evaluated with respect to these issues accordingly.
At the same time, we should keep in mind that the maximal prediction horizon for any
dynamic time series is inherently constrained by the minimal duration of the shortest
maneuver involved.
B. MLP-sw and Memory Length
For MLP-sw, the additional issue of the optimal memory length that will balance
between prediction accuracy and processing cost need to be kept in mind. If a system
does not have enough memory for correct temporal placement, prediction accuracy can
be severely impacted, even when a specific pattern is identified; especially if the input is
noisy or contain measurement errors. This is particularly so for systems that depends on a
limited sliding window to act as a buffer for history.
81

This issue is easily illustrated in Figure 4.3. If the history captured in the sliding
window is a relatively homogenous stretch (e.g., A, D), even within a particular
maneuver (e.g., B, C), accurate temporal placement becomes rather problematic because
it would be difficult to differentiate one homogenous stretch from another (e.g., A from C
or D). Although this problem can be solved by increasing the memory length to include
disambiguating information, it comes at an added processing cost. For every additional
temporal slice added to the input vector, an additional 1/n processing cost is incurred; n
being the previous number of temporal slices. Thus, it is critical for any potential
commercial application of these kinds of predictive systems to determine the optimal
memory length that will balance between prediction accuracy and processing cost. This is
one of the core issues investigated in the current study.
C. The Current Approach
Note that a large number of factors, including network structure, training method and
sample data may affect the forecast ability of the networks. Thus, it is imperative for us to
investigate what is the nature of the input that will give the best result with a wider range
of maneuvers involved, while keeping the methodology relatively homogeneous in order

Figure 4.3: Homogenous stretches with respect to lane keeping, overtaking from the
right, and the left
Lateral position
Time
C A B D
82

to keep in contact with the research reported in the literature.
This is important given that a number of researchers [98-100] have used an MLP-sw
to model and predict lane change maneuvers on different data sets and reported
discrepant predictive capabilities. For example, [98] used an MLP-sw to predict lane
change behavior with respect to the Next Generation Simulation (NGSIM) data and
found that prediction is piecemeal accurate, while [100] utilized a similar network to
predict lane change behaviors in a two lane road with great forecast accuracy over a long
period of time. [98]’s result might be reflective of the fact that they included a larger
number of different maneuvers in their simulation, while [100] simply focused on a
single use case of lane change and overtaking from the left. At the same time, [100] noted
that the NGSIM data may be coarse and contained inherent measurement errors. The
differences in the reported predictive capabilities of MLP-sw succinctly highlights that
(a) different data sets and input variables, (b) the number of maneuvers involved, and (c)
data fidelity can all have an impact, even when similar networks are used.
Thus, in order for an MLP-sw to be incorporated into an ADAS or a CRAS, we need
to fully understand its predictive capabilities with the type of input and range of
maneuvers that will suit our specific goals and needs. Accordingly, we employed a
similar MLP-sw as [98-100] in modeling lane change and overtaking maneuvers in a
much more flexible situation of driving on a multi-lane highway, where the maneuvers
involved include periods of steady driving, lane change and overtaking on the right and
the left. Our current assessment focused on situations where the lane change and
overtaking maneuvers are made when there is only a single vehicle that precedes the
object car.
83

The driving environment is formalized as an egocentric Cartesian coordinate system
(Figure 4.4), with the object vehicle being the center of the sensor feed and data
parameters calibrated according to its relative position and speed. The lane change and
overtaking maneuvers are operationalized as simple lateral movements at different speeds
to minimize the need to model longitudinal movements. This way, the object vehicle is
the active observer similar to the driver. Thus, the output of the network and potential
mitigation strategies implemented by an ADAS are based on an analogous, albeit much
more expanded, perspective as the driver.

4.4. EXPERIMENTS

A. Data Collection and Description
The data used in the current experiment were collected from a driving simulator with
three customizable displays that offered a wide viewing angle of the surrounding
environment and traffic as well as realistic sound. The driver cabin is adopted from a
production Audi A7, with a force-feedback steering wheel, gas and brake pedals, and a

Figure 4.4: Sensor data formalized as a Cartesian coordinate system
Object Vehicle
Flow
84

fully functional dashboard. The simulator is programmed with a realistic vehicle dynamic
model as a production Audi A7. Thus, the data collected have a very high degree of
fidelity.
We focused on the behaviors of a single driver. The driver was given time to adapt
to the simulated environment, so his driving behaviors would mirror those in a natural
environment. We collected 2 hours of driving data that contained periods of steady
driving (i.e., lane keeping) and 100+ lane change and overtaking maneuvers on the left
and right. The data were recorded at 0.075s sampling interval and processed offline in
Matlab. The entire data set was split into 80/20 portions for training and validation,
respectively.
The following variables were measured (Figure 4.5):
• Vehicle speed.
• Steering wheel angle.
• Inverse of lane curvature radius.
• Lateral position with respect to road center.
To predict the future lateral position value y of the object vehicle we use speed V,
steering wheel angle α, lane curvature c along with their historical samples, and historical
samples of the past lateral position values as input. Specifically, the input vector to the
system at the discrete time instance i is x(i)= (V(i), V(i-1),…, V(i-h), α( i), α( i-1),…, α( i-
h), c(i), c(i-1),…, c(i-h), y(i), y(i-1),…,y(i-h)), where h is the width of the historical
window, and the output is the future lateral position value y(i+k) at prediction horizon k.
85

B. Network Architecture and Parameter Tuning
The MLP-sw used in the current study consists of an input layer, a single hidden
layer, and single output unit (Figure 4.6). The activation function of the hidden layer is
sigmoidal while the output layer is linear. The signal weights are denoted by , the bias
terms by b, the number of hidden units by N. The parameters N, k and h are tuned to
determine the balance between prediction accuracy and processing cost.

Figure 4.5: Model signals: predictors (solid blue), prediction (dashed red)
Speed, mph
Steering wheel angle, rad
Lane curvature
-1
, 1/m x10
-4
Lateral position with respect to the middle of the road, m
50

40

30

20
0.5

0

-0.5
10

5

0

-5
0

-5

-10

-15
Time, s
100 110 120 130 140 150

Figure 4.6: The architecture of MLP-sw used in the current study
y(i+k)
1:h
1:h ω
ω
b
Output layer
x(i)
y(i)
ω
b
N
Hidden layer
86

Model training is carried out using a Levenberg-Marquardt back propagation
algorithm [108], which relies on Hessian matrix approximation to provide fast parameter
estimation. The model was trained for 100 epochs, where at every epoch we injected
white Gaussian noise into the input vectors. Training with noise not only ensures that a
global minimum will be reached during training, but also it increases model robustness
and tolerance to variations and noisiness in the input signals [109]. The standard
deviation of the added noise was proportional to the observed MSE (mean squared error)
during training, and decreased linearly at each subsequent epoch so that at the very last
epoch the level of injected noise was zero. The initial standard deviation of the noise was
set at 1m and then at 80% of the observed MSE at the end of the first iteration; after
which it was reduced linearly to 0% at the 100
th
epoch.
Model tuning was carried out by varying one of the three model parameters above
while keeping the other two fixed. Figure 4.7 shows the model performances at different
window sizes. The model performance plateaus at 1.5s and does not show any significant
decreases in MSE with larger window sizes. Similarly, hidden unit tuning shows that

Figure 4.7: Prediction accuracies for
different window sizes: training set
(solid blue), validation set (dashed red)
0.5

0.4

0.3

0.2

0.1

0
MSE, m
0.5 1 1.5 2 2.5
Historical window width, s

Figure 4.8: Prediction accuracies for
different number of hidden units: training
set (solid blue), validation set (dashed red)
0.5

0.4

0.3

0.2

0.1

0
MSE, m
5 10 15 20 25
Number of hidden units
87

performance is asymptotic at 10 hidden units, with no significant MSE decreases with
larger numbers (Figure 4.8). Accordingly, the optimal balance between performance and
processing cost was set at a memory length of 1.5s and 10 hidden units.
C. Prediction Horizon and Error Tolerance
Assessments of prediction accuracies at different horizons was carried out based on
the tuned model above. We gradually increased the prediction horizon at 0.5s increments.
Table 4.1 shows the prediction accuracies in terms of MSE at different horizons. The
prediction accuracy of the model deteriorates as prediction horizon increases. To
illustrate the deviation in prediction at different horizons, the predicted lateral trajectories
of one lane change and overtaking maneuver from the validation set at horizons of 0, 1
and 2s are depicted in Figure 4.9. Panel (a) shows the predicted trajectories with respect
to the actual trajectory, and panel (b) shows the prediction errors in terms of deviations
from the actual trajectory.
Both panels clearly show that prediction accuracy decreases as the prediction
horizon increases. Moreover, they show that prediction is very accurate for the steady
state periods of the maneuver, while large prediction errors tend to occur during the
transition intervals; specifically, the beginning of the maneuver, its apex, the initiation
back to the original lane, and the end of the maneuver.
Prediction
horizon, s
Prediction MSE, m
Training set Validation set
0.5 0.034 0.051
1 0.082 0.112
1.5 0.151 0.214
2 0.239 0.322
2.5 0.394 0.511
3 0.518 0.706

Table 4.1: Accuracy dependence on prediction horizon
88

These results provide support for [98]’s conclusion that prediction under such a
system is piecemeal accurate. One reason might be that when a larger amount of
maneuvers is involved, it becomes increasingly difficult for the system to disambiguate
among multiple dependencies as the prediction horizon become larger.
Nonetheless, from a safety standpoint, what is important is not the overall prediction
error of the system captured in the MSE, but rather the maximal tolerable deviation in
prediction. As we can see in panel (b) of Figure 4.9, that the maximum deviation in
prediction at the horizon of 1s is about 0.25m, and at 2s is 1m.

(a) lateral position prediction (meters)

(b) deviations in prediction (meters)

Figure 4.9: Vehicle lateral position prediction: actual (solid bold black),
estimation–0s (dashed green), 1s (dash-dot blue), 2s (solid red)
5

4

3

2

1

0
95 100 105 110 115
Time, s

1

0.5

0

-0.5

-1

89

The overall distribution of deviations in prediction at 1 and 2s for the validation set
are depicted in the histograms shown in Figure 4.10. Although the maximal prediction
error at the 1s horizon is well within the tolerable range, this does not mean that
prediction horizons of 2s and beyond are unusable. One can pick the precise horizon
depending on his prediction goals and accuracy specifications; it is simply the case that
the maximal prediction errors at the different horizons need to be kept in mind, and
whether or not the prediction accuracies can be augmented by other means.
One way of improving prediction accuracies is through output smoothing. By
eliminating the spikes in prediction error, prediction accuracies at longer horizons can

(a) 1s prediction horizon

(b) 2s prediction horizon

Fig. 4.10: Histogram of the deviations in prediction
at the prediction horizons of 1 and 2 seconds
-1 -0.5 0 0.5 1.0
0.2

0.1

0

-1 -0.5 0 0.5 1.0
Density Density
Prediction deviation (meters)
Prediction deviation (meters)
0.2

0.1

0

90

potentially be brought to within tolerable range. Another way is to introduce methods that
can narrow down the number of maneuvers that have to be distinguished by the system.
One such method is the estimation of driver intention based on the analysis of a driver’s
in cabin behaviors prior to the different maneuvers [110]. Another method is the
estimation of the empirical probabilities of different maneuvers for different scenarios.
Ultimately, the precise method(s) to augment the prediction accuracies at longer
prediction horizons depend on the precise nature and specifications of the ADAS that
different OEMs choose to develop.

4.5. CONCLUSIONS

In this chapter, we described a method of modeling and predicting a vehicle’s lateral
position using an MLP-sw. The model was trained and tuned on data of a single driver
from a high fidelity simulator. The model’s performance on the validation set showed
that the maximal prediction error at a prediction horizon of 1s is well within tolerable
range. A prediction horizon of 2s or more can potentially be brought into tolerable range
with output smoothing and other means.
Although the system described here shows great potential for possible incorporation
into a standalone ADAS or a subsystem of a CRAS, more work can be done to improve
and augment its abilities. In particular, one can extend the application to include
behaviors of more drivers as well as data from real world driving scenarios to improve
generality. We should also note that the system described here can be easily ported with
respect to modeling and predicting the trajectories of other vehicles in the driving
91

environment. Thus, the current application can be further augmented by encompassing
the trajectories of surrounding vehicles in addition to that of the object vehicle. Another
way to augment the system is to incorporate variables that reflect driver status (head
positions, gaze direction, etc.) that will improve the prediction accuracies of the object
vehicle at longer horizons.
These improvements have the potential of increasing the feasibility of a CRAS that
will evaluate the likelihood of potential collisions and other driving hazards to provide
the best and least intrusive remedial strategy accordingly. We should also note that the
applications of a CRAS are not limited to driver controlled vehicles; it can also be
applied to autonomous vehicles to augment situation awareness when a driver resumes
control.

92

5. PERSONALIZED DRIVER ASSISTANCE FOR
SIGNALIZED INTERSECTIONS USING V2I
COMMUNICATION

5.1. INTRODUCTION

Maneuvering through intersections is an unavoidable routine in daily driving (Fig.
5.1). It can be stressful and even risky due to the presence of cars moving in multiple
directions, misinterpreting the right-of-way rules and traffic light signals, and due to
human error on the part of the other driver. According to the NHTSA (National Highway
Traffic Safety Administration), intersection-related crashes amount to about 40% of the
all crashes – the largest portion among all accident types [111] and contributes to 22% of
all fatal crashes occurring in the United States [112] – the second fatality cause after run-
off-road crashes [113]. These numbers suggest that intersection maneuvers are one of the
most dangerous driving tasks. In addition intersection maneuvers add stress especially
when the driver is in a hurry and has to stop at a red traffic light [114].

Figure 5.1: A chain of traffic lights
93

Intersection delays result in fuel wasting and increase of emissions. Some estimates
suggest that idling fuel loss can cost hundreds of thousands of dollars per intersection per
year [115, 116]. One way of reducing travel time, fuel consumption and emissions is to
focus on improving traffic light control. That is, to provide adjustments to the traffic on
the macroscopic level. There have been considerable research efforts on adaptive signal
control techniques whose main objective is to reduce the traffic jams and average traffic
light waiting time [117-119]. However, these efforts do not take into account the
individual driver characteristics and offer no guarantees that every driver will be satisfied
with the trip.
In our work we focus on another approach, – we look at the problem on the
microscopic (individual) level assuming that we can’t manage the traffic lights. Drivers
can achieve reduction of fuel consumption and emissions by following principles of eco-
driving. Eco-driving is a set of driving methods that promotes energy efficiency,
environmental awareness, and the use of technological advancements in motor vehicles to
increase fuel economy, road safety, and pollution reduction [120]. However, eco-driving
techniques must be applied by the driver thoughtfully and in appropriate situations, since
their incorrect usage might bring negative results [121, 122]. Recent trends among car
manufacturers is to equip vehicles with assist systems that help drivers follow eco-driving
principles in order to reduce fuel consumption and emission [123].
A driver assistance system can be specifically aimed at helping drivers with
intersection maneuvering in order to increase driver’s comfort, economy and safety at
intersections. The key component of such a system is V2I communication, which allows
accessing information on the location and timing of traffic lights at the intersections that
94

are relevant to the driver’s route. The assistance system would then perform data analysis
to find the optimal driving pace that minimizes unnecessary accelerations and
decelerations. The optimization algorithm usually aims at minimizing a cost function that
contains fuel consumption, traveling time and emissions. The system’s goal is to provide
driver with pace recommendations, following which will result in smooth driving,
minimizing waiting at intersections, which in turn allows reducing fuel consumption and
emissions [124-127].
However, not all drivers will be willing to follow the recommendations of such a
system if it doesn’t consider their preferences. A system that r elies on the average driver
characteristics may be found too conservative by an aggressive driver and too aggressive
by a passive more cautious driver. Studies show significant differences in driving
characteristics at approaching and crossing intersections among different drivers. These
characteristics are acceleration [128], stopping behavior [129, 130], choice of top speed
and the way driver approaches intersections. In addition, different drivers might assign
different priorities between time of arrival and fuel economy. A driver assistance system
is more acceptable if it knows the driver’s preferences and takes them into account when
providing recommendations.
In this chapter we present a personalized pace optimization methodology that uses
driver’s cha racteristics and preferences when approaching and crossing an intersection to
optimize driving pace on a route. This methodology can be used in an ADAS that
provides the driver with personalized assistance on approaching and passing
intersections. We assume that the following information is available through V2I:
• traffic lights location and timing data for each one of them on the route.
95

• traffic flow speed.
We use the traffic flow speed to evaluate the maximum speed on the route intervals
in order to avoid providing speed recommendations that are impossible to follow due to
slowly moving preceding vehicles.
The developed system calculates an appropriate driving pace at which to approach
and pass the intersections on the route in order to maintain desirable by the driver balance
between eco-driving parameters and time of arrival. In our work we consider only
signalized intersections. Our methodology can be generalized to include any type of
intersection with minor changes.
This chapter is organized as follows. Section 5.2 describes the traffic light operations
and vehicle energy models. Section 5.3 presents our approach on learning driver’s
preferences, optimization problem formulation and its solution. The results of the
experiments and simulations are given in Section 5.4 and conclusions are presented in
Section 5.5.

5.2. VEHICLE AND TRAFFIC LIGHT MODELS

In order to define a cost function for optimization, we need to formulate fuel
consumption and traffic lights operation models. In our work we assume that the fuel
consumption is proportional to energy that is consumed by a vehicle. We assume that the
vehicle is petrol operated and is not equipped with advanced energy recovery systems
such as KERS (Kinetic Energy Recovery System). We note that our pace optimization
methodology can be applied to any vehicle type and configuration. One can easily modify
96

and extend the presented model to accommodate other classes of vehicles such as electric
vehicles or vehicles with energy saving and recovery systems.
A. Vehicle energy model
The vehicle energy consumption on a particular segment of the road can be
estimated from forces applied to the vehicle. We assume that the vehicle moves in the
longitudinal direction on a flat road. The longitudinal vehicle dynamic model is
represented as [131]:

, (5.1)

where F
t
– the traction force at the wheels, F
aero
– the aerodynamic resistance force,
F
friction
– the rolling resistance force. We assume there is no slip at wheels and there is no
mechanical energy dissipation involved in the drivetrain. Then model (5.1) can be
expressed as:

mg c V A c x m F
r a d t
  
2
ρ
2
1
 
, (5.2)

where c
d
– the aerodynamic drag coefficient, A – the vehicle frontal area, ρ
a
– the air
density, V – the vehicle speed, c
r
– the rolling resistance coefficient, m – mass of the
vehicle, g – gravitational acceleration.
At every moment in time the power required from the engine is expressed as
follows:
friction aero t
F F x m F   
 
97

, (5.3)

where P
0
is the power required from the engine while idling.
The vehicle energy consumption on a specific road segment corresponding to a time
interval [0, T] can be calculated as:

(5.4)

We approximate each traveling path with the following segments: idling, travelling
with constant speed, decelerating and accelerating. We assume that the vehicle is not
equipped with energy saving or recuperating system that allows recovering energy from
braking. Hence, energy consumed during deceleration is equal to the idling energy for the
time of the segment:

(5.5)

For road segments of constant speed the energy consumption is expressed as:

mgVT c T V A c T P Pdt W
r a d
T
   

3
0
0
ρ
2
1
(5.6)

) 0 , max(
0
V F P P   
dt V F T P Pdt W
T T
 
   
0 0
0
) 0 , max(
T P W
0

98

In order to find the energy consumption for the segments where the vehicle is
accelerating, we need to specify the acceleration profile applied to the vehicle. Since the
acceleration profile is very much dependent on how a particular driver responds, we use a
personalized acceleration curve, which the system learns in real time as described in the
personalization section of the chapter.
B. Traffic light operations
In our work, we focus on individual driving pace optimization, as opposed to the
problem of centralized traffic management. The key component of the pace planning
algorithm is the knowledge of the traffic lights location, signal phase and timing. We
assume that the traffic lights timing is available in advance through V2I communication
and doesn’t change during the course of driving. We express the status of traffic lights at
time t by the expression:

, (2.7)

where s
i
(t) – status of the i
th
traffic light (1 – green, 0 – red), T
i
0
– the cycles phase time of
the i
th
traffic light, T
i
– the cycle duration for the i
th
traffic light, T
i
G
– the duration of the
green light for the i
th
traffic light, k = 0, 1, 2, etc. – cycle number. In addition, we denote
distance to the traffic lights from the initial vehicle position as d
i
.
For safety precautions, we consider the yellow phase of the traffic light to be
undesirable for intersection passing. For this reason we combine the yellow and red



     
    

i i
G
i i i
G
i i i i i
i
T k T t T kT T
T kT T t kT T
t s
) 1 ( , 0
, 1
) (
0 0
0 0
99

traffic lights phases and refer to them as the red traffic light phase. As a result, our
algorithm won’t advise the driver to pass the intersection during the yellow light phase.

5.3. OPTIMIZATION PROBLEM AND PERSONALIZATION

The goal of the proposed algorithm is to provide the driver with recommendations
that will improve the journey quality depending on his/her preferences. We aim to find a
driving pace that optimizes fuel consumption, time of arrival and yet doesn’t compromise
driver’s comfort. The knowledge of traffic light locations and their timing along the route
can be used together with traffic characteristics to synchronize the speed of the vehicle in
order to pass the upcoming intersections in effective way.
An example of a trivial straight route with three upcoming traffic lights is presented
in Figure 5.2. The green dashed lines represent time intervals when the corresponding
traffic light is green. Possible driving paces that allow crossing the intersections on the
green are shown on the graph. We mark the intersection crossing nodes on the graph by
numbers. Then all available pace choices can be presented in a form of a decision tree
(Figure 5.3). In order to optimize the driving pace the algorithm has to compare all
possible paces and pick the one with the lowest cost function. Such a decision however
needs to take into account the way the driver responds at intersection crossings otherwise
any recommendation that deviates from the driver’s style considerably will affect
compliance in a very negative way.
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In our work we take into account personal driver’s preferences and driving style. For
instance, a driver can prefer arriving at destination as soon as possible, regardless of fuel-
consumption as opposed to an eco-friendly driver who aims to save fuel and prefers
smooth accelerations. Our algorithm learns driver’s habits and uses this knowledge to
calculate a pace that optimizes time of arrival (TOA) and fuel consumption in a manner
that is more likely to be acceptable to the individual driver.
A. Personalization
In our work we assume that the driver might be willing to compromise between the
time of arrival and fuel economy. We denote coefficients associated with these

Figure 5.2: Sample graph of available paths to cross intersections on the green
distance

3

4
5

6

7
1

2
time

0

Figure 5.3: Decision tree of possible paths to cross intersections on the green
0
1 2
3 3 4
5 6 5 6 6 7
101

parameters as α and β respectively. We assign their values to belong to the interval [0, 1],
with 1 representing the highest significance, and their sum to be equal to 1.
By default, the weights are set to be equal to 0.5. The ADAS can explicitly ask the
driver to specify the coefficient values. That is, the driver is requested to select the level
of eco-mode from 0 to 1 indicating a tradeoff value between time of arrival and eco-
driving. The alternative approach is to estimate the tradeoff based on the choices the
driver makes from the list of suggested driving paces corresponding to different
coefficients. If the algorithm is used to optimize a driving pace of transportation trucks,
commercial or delivery vehicles one can follow the approach used in aviation [132]
where the coefficients are assigned based on a tradeoff between fuel cost and expenses
associated with delays. In addition, we take into personal driving habits: top speed,
acceleration and deceleration preferences, and the way driver approaches and turns at
intersections. These parameters are used in the optimization algorithm to generate and
evaluate paces that reflect the personal driving style.
Some drivers might find the speed limit to be too high for comfortable and safe
driving, so they prefer to drive with smaller speeds. We incorporate the acceptable top
speed value V
top
in our algorithm in order to avoid providing pace recommendations that
are not acceptable or desirable by the driver. The value V
top
can be determined by
observing the vehicle speed that the driver finds acceptable while driving on an empty
road. We note that the assigned value should always be less than or equal to the speed
limit. We focus our work on urban driving; therefore we assume the speed limit to be
35mph.
102

In order to model driver’s acceleration profile, we assume that vehi cle acceleration a
linearly decreases with speed:

V a a γ
0
  , (5.8)

where a
0
– maximum acceleration, γ – speed dependence coefficient, V – vehicle’s speed.
One can assume a more complicated relationship, such as a second order polynomial.
However, on-road data indicates that the expression (5.8) describes acceleration profiles
reasonably well. In addition, its simplicity allows us to obtain closed-form solutions for
energy consumption, which result in low computational cost.
Assuming that acceleration is performed on a time interval [0, t] and the initial speed
is V
0
, we obtain expressions for the speed V and acceleration a at time t by integrating the
expression (5.8):

   
0 0
γ
0
γ
γ
1
) ( V a e a t V
t
  

(5.9)

 
0 0
γ ) ( V a e t a
t
 
 

(5.10)

An example of the acceleration profile and its matching speed curve are depicted in
Figure 5.4. The corresponding acceleration profile parameters in (5.8) are a
0
= 2m/s
2
, γ =
0.1s
-1
. In addition, by integrating the expression (5.9) we obtain the distance covered by
time t during acceleration:

103


















  

) 1 (
γ γ
1
γ
0
0
0
t
e V
a
t a d (5.11)

Assuming that the vehicle accelerates as described in (5.8) with an initial speed V
0

we can calculate the energy consumption on the time interval [0, T] by substituting (5.9)
and (5.10) into (5.4). We don’t present the expression because it is too lengthy.
In contrast to the acceleration curve, we model deceleration as a fixed value a
dec
.
This shape describes drivers’ behavior reasonably well. We assign the parameters a
0
, γ
and a
dec
so the modeled acceleration and deceleration curves resemble the habits of a
particular driver. We present experimental data that supports our approach on modeling
the acceleration and deceleration profiles in the experimental section of the chapter.
We also take into account the way the driver prefers to approach intersections. In
general case, when the driver approaches the intersection on the green, he/she prefers to
cautiously slow down in order to turn left, right or to proceed straight. To take it into
account, we denote as V
left
, V
right
, V
straight
, the speed values that the driver prefers to slow
down to in order to turn left, right or proceed straight respectively. In this work we
assume that these values depend on personal driving habits only. When applying our
time, s

(a) acceleration profile

(b) speed profile

Figure 5.4: Example of acceleration profile and its corresponding speed curve
acceleration, m/s
2

0 10 20 30 35
2

1

35
30

20

10

speed, mph
0 5 10 15 20
speed, mph
104

methodology to a real route, one should also consider adding a parameter of intersection
configuration and geometry in order to estimate the speed reduction values more
accurately.
We use the limiting speed values V
top
, V
left
, V
right
, V
straight
, expressions (5.9)-(5.11)
along with the expressions for energy consumption in order to formulate and solve the
optimization problem.
B. Green windows search
In order to find an optimal driving pace we need to evaluate all feasible intersection
crossing time windows. We perform a search of possible crossing times for the upcoming
intersections based on the initial subject vehicle speed, traffic lights location, phase and
lights duration described by the model (5.7). We measure the distances to the traffic
lights d
i
from the initial vehicle position and their time phases from the point in time
when the algorithm is executed. We perform a recursive search by applying Algorithm 1
to every intersection one by one starting from the closest one.
Algorithm 1 Search of possible intersection
crossing time windows

1:
;
2:
;
3:
next instance after t
fast
, when light switches to
red;
4: ;
5:
;
6: while < do
7:
;
8: ;

9: ;

10: end while

min
1
max
1





i
i i
fast
t
V
d d
t
1  j

max
, j i
t
) , max(
max
,
min
,
G
j i fast j i
i
T t t t  
max
1
min
1





i
i i
slow
t
V
d d
t
i j i
T t 
min
,
( )
slow
t
1   j j
i j i j i
T t t  

min
1 ,
min
,
) , min(
min
,
max
, slow
G
i j i j i
t T t t  
105

The output of the algorithm is a set of j feasible crossing time windows

for the i
th
intersection. The windows for the i
th
intersection are used as inputs in the
crossing window search algorithm for the (i+1)
th
intersection. The algorithm searches for
green windows on the interval

. The interval bounds are respectively the
fastest and the slowest times the driver can reach the next intersection based on the
knowledge of the crossing window of the previous intersection

, minimum
V
min
and maximum speeds V
max
allowed on the interval. The value V
max
is the smallest of
V
top
and the traffic flow speed on the interval V
flow
. In addition to the maximum allowed
speed, we define the minimum speed limit V
min
because it’s illegal to drive too slowly,
since it might lead to traffic impedance [133] and can increase the chances of an accident
[134]. We set up the minimum speed limit V
min
to be 20 mph. We note that the choices of
the speed limit and the minimum speed limit values are made without loss of generality
as the specific values can be changed without affecting the proposed methodology. If
there are right turns on the route, in addition to the green window search we perform
additional iterations of the Algorithm 1 in order to find the potential paces that allow
turning right on the red. In order to do that, we replace the green traffic light windows at
corresponding intersections by the red windows.
When the Algorithm 1 is applied to several intersections, its outputs form a decision
tree (Figure 5.3), whose nodes are intersections crossing time intervals. The decision tree
is expanding exponentially and therefore the computation time increases exponentially as
well [135]. Therefore, one should set the number of intersections to be such that the
system is able to calculate travelling pace and provide recommendations to the driver in
real time without significant delays. The green windows search is performed either to a
106

specified number of intersections ahead or it halts at intersection for which there is no
feasible crossing window is found. In the former case the assistance system should
provide smooth stop recommendations at the intersection where waiting at the red light is
inevitable.
C. Optimization problem
We formulate an optimization problem in order to compare all feasible paces to find
the one that minimizes travel time, fuel consumption and addresses driver’s preferences.
The goal of the optimization algorithm is to minimize a cost function that incorporates
time of arrival and fuel consumption:

, β α kT W C   (5.12)

where α and β – driver’s preference parameters associated respectively with fuel
consumption (replaced by energy W) and time of arrival T, k – parameter that equalizes
the significance and values range of the fuel consumption and time of arrival. If we
denote upcoming intersections by index i, then the cost function can be presented as a
sum of the cost functions associated with the separate intervals between the intersections:

 


 
n
i
i i
kT W C
1
β α (5.13)

In the previous section we defined the maximum and minimum speed boundaries for
an interval to be V
max
and V
min
respectively. As the result, for i
th
interval we have a speed
107

window [

,

] to vary the driving pace. When there is a room for speed variations,
a fixed distance interval can be covered in a fixed amount of time by applying different
speed profiles. We adopt pace profiles with only one acceleration or deceleration on an
interval, since a recommendation with two or more changes of speed in the range of the
same interval is not efficient from fuel economy point of view and might be confusing to
the driver. Figure 5.5 shows an example of possible speed profiles with one acceleration
interval to cover 230 meters in 20 seconds with an initial speed of 20mph. We assume
acceleration profile with parameters a
0
= 2m/s
2
, γ = 0.1s
-1
. The two speed profiles
pictured in bold depict two extreme cases: acceleration at the very beginning of the
interval (bright blue line) and the very late acceleration (dark blue line). All other
possible speed profiles are bounded by these two curves.
Among the speed profiles depicted in Figure 5.5, the optimal curve from the fuel
economy point of view is the one with early acceleration. In this case, the vehicle reaches
a lower top speed which reduces drag losses. In addition, acceleration recommendations
at the beginning of intervals allow the driver to perform speed changes in advance, so
there is plenty of time to correct driver’s actions to reach the upcoming intersection at the

Figure 5.5: Possible speed profiles to cover a fixed interval in a fixed time
minimum speed
0 4 8 12 16 20
40
35
30
25
20
15
10
5

time, s
speed, mph
speed limit
108

desired time. Therefore, we remove the ambiguity by always picking the speed profile
with the earliest acceleration. As the result, a specified set of intersection crossing times
will correspond to one driving pace profile. In our optimization algorithm we use a
function that calculates the speed and acceleration profiles for the route intervals between
the intersections given the route configuration, the distances between the intersections,
intersections crossing times, traffic speed, acceleration and deceleration profiles, driver’s
preference in approaching the intersection and the initial vehicle speed at the beginning
of the first interval. We omit the algorithm description since it contains trivial logic of
intersection crossing cases (right, left, straight) and vehicle kinematics described by (5.8)-
(5.11).
Given the speed and acceleration profiles, we calculate the energy consumption (5.4)
and compute the cost function (5.13). We formulate an optimization problem as follows:





 







    

n
i
t
t
i i
n i t
dt t V t F t t k P C
i
i
i
1
1 0
: 1 ,
1
) 0 ), ( ) ( max( α ) )( β α ( min

(5.14)

Overall, the optimization problem is subject to the traffic lights model (5.7), driver
deceleration and acceleration profiles and the following relationships:








 
 
  
 
max min
0 0 0 0
1 ) ( when ) (
) ( , 0 , 0
,
V V V
t s d t x
V t V d t
V a d V
i i i i
 
(5.15)

109

The optimization is performed with respect to the intersection crossing times t
i
,
which are constrained by the possible intersection crossing intervals

, –
outputs of the Algorithm 1 that is iteratively applied to every intersection on the route.
The constraint is a set of possible crossing interval branches (Figure 5.2). This set
contains all feasible intersection crossing solutions, however not every solution belonging
to the set is feasible. This is, because the interval bounds reflect the slowest and fastest
possible speeds on the interval. One for example, can obtain an unfeasible solution by
connecting the slowest boundary of the possible crossing interval for an intersection with
the fastest boundary of the next intersection within the same solution branch. This case
will require vehicle speed that is greater than the maximum speed allowed on the interval
between the intersections. In addition, the Algorithm 1 doesn’t take into account the
acceleration and deceleration kinematics, therefore the resulting green window intervals
are a rough estimation for feasible intersection crossing times.
In order to solve an optimization problem, we need to avoid corrupted or missing
driving pace solutions for all possible crossing windows inputs. If an initial guess to the
optimization problem turns out to be unfeasible in the specified speed boundaries, we,
depending on the case, either increase the maximum or decrease the minimum speed
boundaries for the problematic interval, so the pace profile exists. The violation of the
upper or the lower boundaries of the speed is highly undesirable; therefore, we introduce
a penalty term to the cost function proportional to the speed violation values:

   ) ) ( η ) 0 ), ( ) ( max( α ) )( β α ( min
1
1
1 0
: 1 ,
dt t P t V t F t t k P C
i
i
i
t
t
n
i
i i
n i t



     



, (5.15)

110

where η – penalty term coefficient, P(t) – penalty term at time t which is defined as:






 
 

else
V t V if t V V
V t V if V t V
t P
i i
i i
, 0
) ( ), (
) ( , ) (
) (
min min
max max

(5.16)

We assign the cost function penalty coefficient η to be such that the penalty term has
a large value comparing to other terms. In this case the optimization will be primarily
aimed at reducing the speed limit mismatch until the penalty term vanishes (if possible).
This approach allows performing optimization without additional intersection crossing
windows feasibility check.
The described optimization problem (5.15) is non-convex, since the optimization
function is non-convex. Therefore, there is no guarantee to reach the global minimum due
to the presence of multiple local minimums. Since the boundary conditions in the form of
the crossing intervals are discontinuous, we apply optimization algorithm separately for
every branch in the crossing window set provided by Algorithm 1 and then compare
resulting costs to select the smallest one. In addition, we introduce a sub-optimal
approach for every path by formulating another simplified convex optimization problem
that provides an initial guess to the original problem. The simplified problem represents
the search of the intersection crossing times for a particular path based on a simplified
cost function formulation.
For the simplified optimization problem we neglect acceleration and deceleration
vehicle kinematics and corresponding energy costs. Consequently, the simplified problem
111

is convex and guarantees convergence to its global minimum. We use the solution as
initial guess for the original optimization problem (5.15).
We apply the Sequential Quadratic Programming (SQP) method to solve the
simplified and the original optimization problem. SQP method solves a set of
optimization subproblems, each of which optimizes a quadratic model of the objective
function [136].
The optimized values of intersection crossing times define a personalized driving
pace, which can be advised to the driver by the means of HMI.

5.4. SIMULATION RESULTS

We showcase our personalized pace optimization algorithm by applying different
drivers’ profiles to a specific route (Fig ure 5.6). The route configuration and the traffic
light operations are described in Table 5.1. We chose such configuration that provides
multiple green window opportunities.
We assume the speed limit and consequently the maximum flow speed to be 35mph.

Figure 5.6: Route configuration
Start
Finish
I II
III
IV V VI
25mp
h
30mp
h
112

We note that the intervals II-III and III-IV have reduced flow speed V
flow
: 25mph and
30mph respectively, while other intervals are not congested and allow driving with the
speed limit.
A. Personalization
Three drivers participated in the experimental part of the study. They were of similar
age (27, 28, and 31 years old), same gender (male), similar driving experience (4, 5, and
6 years), and identical education level (Ph.D. students). In order to establish driving
profiles, they performed data collection on a customized vehicle. The vehicle is pre-
equipped from the factory with sensors to measure the values of speed and acceleration.
We accessed the data through a CAN (controller area network) bus and stored it for
offline processing. In addition, we recorded front-facing camera video to parse the data.
Test drives were performed on urban roads in downtown area of Los Angeles, so the
drivers crossed numerous traffic light controlled intersection during their trips. As the
result, the collected data contained segments representing acceleration after the complete
stop and deceleration to the complete stop. We parse the data in order to extract segments
Traffic light
number
I II III IV V VI
Route
direction
Straight Left Straight Right Straight Straight
Distance, m 600 1200 1800 2400 3000 3600
Phase, s 20 5 10 10 20 10
Green phase
duration, s
15 8 25 15 15 20
Red phase
duration, s
15 20 18 25 15 25
Traffic flow
speed, mph
35 35 25 30 35 35

Table 5.1: Traffic light characteristics

113

that reflect unconstrained acceleration or deceleration segments, that is, when the drivers
didn’t experience constraints from the slowly preceding vehicles. We use the lea st
squares method to establish the parameters of acceleration and deceleration profiles.
Figure 5.7 demonstrates how the acceleration model fits the smoothed acceleration data
profiles established by the drivers. The deceleration data for the drivers is presented in
Figure 5.8. In contrast to the acceleration data, there is no uniformity in the deceleration

Figure 5.8: Deceleration data (solid) and its approximation (dashed):
Driver 1(red), Driver 2 (green), Driver 3 (blue)

acceleration, m/s
2

0

-0.5

-1

-1.5

-2.0

0 10 20 30 35
speed, mph

Figure 5.7: Acceleration data (solid) and its approximation (dashed):
Driver 1(red), Driver 2 (green), Driver 3 (blue)
acceleration, m/s
2

4

3

2

1

0

10 20 30 35
speed, mph
114

curve shapes between the drivers. Nevertheless, the fixed rate deceleration model
reasonably well approximates the curves.
The time of arrival versus fuel economy parameters α and β along with the
preferable speeds V
top
, V
left
, V
right
, V
straight
can be established by observing drivers’
performance. However, since our goal is to demonstrate how different driver preferences
result in different optimal paces, we assign these parameters by ourselves so they vary
from driver to driver. Table 5.2 presents the complete list of parameters associated with
the drivers’ habits and preferences that we used in the optimization algorithm.
B. Optimization
In this work we use the following simulation parameters associated with the vehicle:
P
0
= 250 J, m = 1500 kg, c
d
= 0.29, A = 2.13 m
2
, ρ
a
= 1.225 kg/m
3
, c
r
= 0.015. We assign
the penalty term coefficient η to be 10
5
and specify coefficient k in (5.15) that balances
significance of fuel consumption and time of arrival to be 1500. The former value was
assigned ad hoc, so optimization algorithm outputs are desirable to the three drivers
participated in the study. Ideally, the value of k should be tuned based on a series of
experiments involving a large population of drivers with different preferences.
The green window search algorithm generates 18 possible crossing windows for the
drivers. The possible crossing windows are depicted in Figure 5.9. The corresponding
α β
a
0
,
m/s
2

γ,
1/s
a
dec
,
m/s
2

V
top
,
mph
V
left
,
mph
V
right
,
mph
V
straight
,
mph
Driver 1 0.2 0.8 3.85 0.18 1.70 35 25 20 35
Driver 2 1.0 0 2.13 0.12 1.35 30 15 10 30
Driver 3 0.5 0.5 3.12 0.18 1.6 35 20 15 32

Table 5.2: Drivers Profile

115

numeration is presented in the Table 5.3. There are 17 crossing windows for Driver 1 and
Driver 3: 1 – 3, 5 – 18. Driver 2 has 12 windows: 3 – 8, 10 – 15. We explain the smaller
number of feasible green windows for Driver 2 to be a consequence of the lower
maximum speed value compared to the other two drivers: 30mph versus 35mph.

Figure 5.9: Green windows configuration and
possible crossings
400

350

300

250

time, s
I II
III IV
1
2

4

6
11
15

16
traffic light index
10
14

Window
Number
Window
Configuration
1 0-1-3-5-9-14-17
2 0-1-3-5-9-14-16
3 0-1-3-5-9-13-16
4 0-1-3-5-9-12-16
5 0-1-2-4-7-12-16
6 0-1-2-4-7-12-15
7 0-1-2-4-7-11-15
8 0-1-3-5-10-14-17
9 0-1-3-5-10-13-17
10 0-1-3-5-10-13-16
11 0-1-3-5-8-13-16
12 0-1-3-5-8-12-16
13 0-1-2-4-8-13-16
14 0-1-2-4-8-12-16
15 0-1-2-4-8-12-15
16 0-1-2-4-6-12-16
17 0-1-2-4-6-12-15
18 0-1-2-4-6-11-15

Table 5.3: Crossing Windows Configuration

116

We note that the possible crossing windows 8 – 18 contain the right turn on the red
at the intersection IV. We apply the optimization algorithm separately to every possible
window sequence. The corresponding cost functions associated with the possible
windows for the drivers are presented in Figure 5.10. The green bars depict the optimal
crossing sequence. The red bars represent eliminated crossing windows, – the

(a) Driver 1

(b) Driver 2

(c) Driver 3

Figure 5.10: Cost function for available crossing
windows: optimal (green), candidate (blue),
unrealistic (red)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18
6.5

6

x10
5

8

7.5

7

x10
5

6.5

6.3

6.1
x10
5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18
117

optimization algorithm was not able to find a solution without a penalty function, which
means that they don’t contain feasible solutions. The charts clearly indicate different
outcomes of the optimization algorithm for the drivers. Driver 2 and 3 are recommended
to follow slower window sequences as more conservative and fuel-economy oriented
drivers as opposed to a more aggressive and hurried Driver 1. One can notice that Drivers
2 and 3 are guided to avoid stopping at intersections while Driver 1 is offered to turn
right on the red at intersection IV in order to arrive faster.
We can estimate fuel economy by comparing energy consumptions for the optimized
and natural driving paces. We calculate the nature driving pace assuming that a driver
doesn’t anticipate traffic lights status. Comparison graphs between the paces are
presented in Figure 5.11. The green vertical bars depict the green windows for the
optimized path. For all the three drivers there is a significant fuel economy: 50% for
Driver 1, 53% for Driver 2, and 56% for Driver 3. We note that the optimized driving
pace for Driver 1 allows saving a significant amount of fuel and yet provides the smallest
time of arrival according to the preference indicated by the driver. The results clearly
indicate the effectiveness of the algorithm.
We evaluate the described suboptimal optimization approach by comparing reached
minimums of the cost functions with its corresponding global minimums. The global
minimums search is implemented by randomly varying initial conditions of the
optimization problem. In 54.34% of cases, the proposed suboptimal approach reached the
global minimum. In the rest of the cases the difference between the reached minimum
and the global minimum value was 0.0034%. These numbers support the effectiveness of
the proposed optimization approach.
118

The algorithm computational cost is low enough to utilize it in a real-time ADAS.
The proposed algorithm is implemented in Matlab and is evaluated on a PC with the
following configuration: Intel Core i5-3317U CPU at 1.70GHz with 4GB of RAM. The

(a) Driver 1

(b) Driver 2

(c) Driver 3

Figure 5.11: Optimized (blue) and natural (black)
driving paces

50 100 150 200 250 300
40

35

30

25

20

15

10

5

0
I II III IV V VI
traffic light index
time, s
I II III IV V VI
traffic light index
time, s
40

35

30

25

20

15

10

5

0
50 100 150 200 250 300 350 400
I II III IV V VI
traffic light index
time, s
40

35

30

25

20

15

10

5

0
50 100 150 200 250 300
350
speed, mph speed, mph
speed, mph
119

described route with 17 available green windows requires 1.83 seconds for optimization.
Moreover, the computational cost can be reduced by making a decision on the path
selection based on the values of the simplified cost function. In this case the original
computationally expensive optimization problem that considers acceleration and
deceleration preferences will be implemented only once to optimize the selected path.

5.5. CONCLUSION

In this chapter we presented a personalized pace optimization algorithm for
approaching and crossing intersections using V2I communication. It learns driver’s
preference on balancing fuel economy versus time of arrival, top speed, the way driver
approaches intersections, acceleration and deceleration profile and applies this knowledge
to optimize driving pace. In our work, we focused on signalized intersections only. The
methodology can be generalized by expanding the set of models to contain driver’s
behavior and intersection models for other intersection types.
We demonstrated the developed algorithm by applying it to a route with six traffic
lights. We used three drivers’ preferences and driving profiles that were established based
on experimental data collected on a customized vehicle. The results indicate that
recommendations vary based on the drivers’ preferences. The comparison of optimized
and natural driving paces indicates that the algorithm can potentially help to save up to
50% of fuel.
The algorithm computational cost is low enough, so the proposed methodology can
be used as a core for an ADAS that provides real-time recommendations to the driver.
120

6. AUTOPILOT PERSONALIZATION

6.1. INTRODUCTION

Autonomous cars (Figure 6.1) are perceived as a major technological breakthrough,
which is compared with the invention of the car itself [137]. The technology will reduce
the number of accidents and enhance driving comfort [138, 139].
The list of the companies and research institutes that are working on self-driving
vehicle projects is extensive: Audi, Ford, Toyota, Honda, GM, Mercedes-Benz, Cadillac,
Nissan, Volvo, BMW, Google, MIT, and so on. The time horizon of a completely
autonomous car being introduced to the market, is estimated on average to be the end of
the decade [138] due to the need to extensively test the technology and to establish the
legal base [138, 140]. Nevertheless, the 2015 top of the line models of BMW, Mercedes-
Benz and Volvo will be equipped with autopilot capabilities: autonomous braking,
acceleration, and lane guidance [141-143]. The number of self-driving functions in the
cars will be increasing year-by-year. In parallel, their work boundaries will be gradually
extended, so there will be less and less traffic situations that require driver to take over

Figure 6.1: Google self-driving car on a test track
121

control.
The direction for the development of the car that drives itself is relatively clear, – the
car autopilot technology is being gradually improved and showcased. However, one very
important component of the technology, namely the interaction between human and
autopilot, has not been established well yet, – its implementation is still quite vague and
contains multiple unanswered questions [139]. Surprisingly, however, it will play a
crucial role in the success of the driverless cars [144], since safety (actual and perceived)
and comfort is what will ultimately determine the success of the product. In order for the
technology to be useful and perceived as safe it has to satisfy the following conditions
[145]:
1) Efficiency – autopilot should perform more efficiently than human driver.
2) Limitations – autopilot should safely and reliably operate within specified limits,
and these limits should be clear to driver.
3) Responsibility – the transfer between driver and autopilot should be safe and
reliable, the driver should know when the autopilot is activated and what it does.
4) Dynamics – driving performance should be acceptable and predictable by human
driver.
The aspect of driver-autopilot interaction incorporates factors (2)-(4) from the above
list. If not properly addressed, they will provoke driver’s mistrust to the system, stress
and even potential danger in situations such as control transferring from the autopilot to
the driver. Moreover, these problems are tangled by the fact that every driver is different:
requirements to the autopilot, safety and comfort perception vary based on the personal
driving skills, habits and preferences.
122

The issue of mistrust is a natural users’ reaction to a technology that is new to them
and that is aimed to significantly change the system’s functionality and the way of
operation that users got used to [146]. In order to develop trust, the system’s behavior and
future intentions should be clear to the driver at every moment in time. Users need to be
assured that the car knows what it is doing and that it’s doing the right thing. For
example, in dealing with slower drivers on the road, most drivers notice the slower car
well in advance and instinctively change lanes before they get stuck behind the slowpoke.
The autopilot should similarly notify the user that the system recognized the slower car,
and it should display how and where it intends to change lanes to get around it. It is
crucial to persuade early users that driverless cars can perform with comfort and safety, –
users will not be forgiving of a system that does not guarantee passengers safety. If users
do not feel safe, they may avoid buying automatic cars altogether and instead, would
insist on driving as they did before – manually.
In this chapter we discuss the personalization technique that aims to enhance comfort
and increase transparency of the autopilot behavior and its operational limits for a
particular driver.
We follow the current set of laws related to autonomous vehicles. We must note that
the laws haven’t taken its final form and differ from country to country and from one
USA state to another and will evolve in the future. Regardless of how laws take shape,
responsibility will transfer from drivers to car manufacturers [140]. Consequently,
autopilot must be able to deal with the worst possible driving scenarios and inadequate
driver’s behavior. We assume the autonomous vehicle to be NHTSA level 3 of
automation – that is, the driver is occasionally requested to take over control [147]. We
123

assume that in autonomous mode the autopilot is totally in control, but the driver is alert
and paying attention to the environment [138, 139]. However, this doesn’t imply that
driver is 100% focused and completely aware of the current road situation [148].
The chapter is organized as follows. Section 6.2 describes the autopilot
personalization feature and its application to automatic vehicle. Section 6.3 presents the
experimental results. The conclusions are formulated in section 6.4.

6.2. PERSONALIZATION BASED ON MODELS

A. Motivation
As we discussed above, the autopilot driving performance should be perceived as
comfortable, its intentions and decisions should be transparent and understandable to
every driver. If the autopilot performance and behavior is not acceptable or
understandable, the driver will mistrust the system. Trust to the autopilot can be enhanced
in two ways: by adjusting the autopilot behavior, so it mimics particular driver’s
performance, which makes its behavior clear and intuitive to the driver; and by creating a
transparent interface. The question of autopilot interface is a rich field for discussions. In
this work, we assume that the vehicle is equipped with an effective interface such as
HUD (Figure 6.2) and the autopilot communicates to the driver all relevant information
with regards road situation and its intentions. In this chapter we focus our attention on
another counterpart of the solution - autopilot personalization.
Since drivers are different, there should be a way to tune the autopilot performance
to satisfy expectations of every particular driver. As we discussed before, the manual way
of complete tuning is undesirable – it’s only practical for minor performance corrections
124

and fine-tuning. The approach with a pre-specified list of possible autopilot behavior
configurations is also hardly applicable. This is due the fact that there is no conformity
between drivers’ preference. For instance, a driver might demonstrate conservative habits
during vehicle following and act aggressively when changing lanes [149, 150]. Therefore,
there is a need to develop a methodology to automatically adapt every aspect of the
autopilot behavior to match the driver’s habits and preferences.
B. General methodology
By analogy to human behavior, the autopilot is implemented as a collection of agents
that represent separate driving tasks (Figure 6.3). The autopilot operation is performed by
switching between the driving cases accordingly to the road situation and driving goals.
This architecture gives an opportunity to adjust autopilot features separately for every
driving task. For instance, the autopilot can choose the vehicle following behavior
accordingly to the personal preferences: following distance, inverse time to collision and
their relationship in the perceptual space [145]. We adopt the idea that for the driver it’s
easier to evaluate if the car behaves in the proper way when the autopilot performs in a
manner similar to the driver’s. It is shown that the mos t favorable supervision case is
when human and the autopilot operation domains of driving tasks are identical [145]. It

Figure 6.2: Head-up display concept
125

helps the driver to develop a reasonable sense of autopilot boundaries and behavior. In
addition, the autopilot decisions should be made at a rate which human driver can follow
even if it’s not the mos t efficient way of driving [144]. In this case driver knows exactly
when the system will fall out the automation region, switches between tasks or fails.
The autopilot aspects that are needed to be tuned to mimic the driver are:
 Actions order and their switching (in which sequence the autopilot implements
operations and maneuvers).
 Aggressiveness level and performance characteristics (choice of following
distance, speed selection, lane change behavior etc.).
When the autopilot mimics driver’s natural action sequence, it’s easier for the driver
to supervise its status. The autopilot must copy such aspects as whether the driver prefers
to adjust the longitudinal speed before the lane change maneuver or during it. A possible
sequence learning algorithm solution is an automatic scripting based on driver’s behavior
[151], – the system observes a sequence of driver’s actions and learns to mimic it.

Figure 6.3: Tactical level of driving task
Autopilot
Turning
Following
Lane Change
Free-flow
Intersection
etc.
126

Autopilot aggressiveness and performance can be adjusted by using knowledge in
the form of personal driving characteristics models. Numerous works demonstrate how
personal driving style can be captured. Driver’s habit learning techniques can rely on
such methods as machine learning or statistical methods [149, 150]. The autopilot learns
driver’s habits when the driver controls the car, and then applies the know ledge to mimic
the driver when in control (Figure 6.4).
We must note that the autopilot behavior should consist of a reliable control
algorithm which remains fixed for all drivers. Only a certain list of parameters should be
adjusted to a particular driver. In addition, these parameters must have limitations on the
both conservative and aggressiveness ends to guarantee reasonable values of acceleration,
speed and driving smoothness. This allows avoiding adopting unreasonable or unsafe
driver’s habits.
The system should create a driver’s performance profile based on a data moving
window since driver’s performance might evolve with time. For instance, the driver’s
performance will differ depending on the seasons: in snowy winter the driver might
prefer to be more cautious; performance will gradually change during the period of
adaptation to a new car. One can specify the data moving window to be from several
hours to days behind the wheel, – the window width should compromise requirements for

(a) autopilot training while
driver is in the loop
(b) autonomous driving
mode

Figure 6.4: Manual and automated driving modes
Driver
Autopilot
Road
Situation
Control
Road
Situation
Driver
Control
Autopilot
127

data amount and how up to date this data is. In addition to the profile based on data
collected during many trips, the system should also establish a driver’s performance
profile for current trip. The need for such a profile is motivated by the fact that driver’s
performance and desires might evolve based on the mood and urgency to arrive. Hence,
the system should detect this trends and apply them in personalization. We determine the
trip coefficient

for some performance parameter p to be a ratio between the
performance parameter stored in the driver’s profile and its value during the current trip:

current
profile p
t
p
p
k  (6.1)

This parameter can be used to map a change for one performance parameter to
another. For instance, the system detects that during a trip the driver prefers the vehicle
following spacing policy with a parameter that is 1.2 smaller than the one stored in the
profile, but the system doesn’t have information on driver’s behavior alteration for lane
change because the driver didn’t change lanes before he/she engaged the autopilot. In this
case the system should use a mapping for the trip coefficient from one parameter p to
another parameter q:

) (
p
t
q
t
k f k  , (6.2)

where f is some function. The function must be specified based on experimental data.
128

When the autopilot exactly mimics driver’s performance, the driver might be
unsatisfied with some settings. For instance, when in autopilot mode, the driver might
tend to accept smaller values of accelerations and decelerations than when the driver
himself is in control. This is due to the fact that the driver cannot always anticipate what
the system will do, as opposed to when the driver himself is in control. This leaves the
driver vulnerable to being unpleasantly surprised by any sudden acceleration the autopilot
makes even if the driver applies such values when he controls the car. Therefore, the
driver should be able to manually fine-tune the autopilot performance after its parameters
are automatically adjusted. The system should compare the performance parameter p
value stored in the driver’s profile with the value the driver specified manu ally. We
define an acceptance coefficient for parameter p as:

specified
profile p
a
p
p
k  (6.3)

The trip and acceptance coefficients should be applied together to determine
appropriate performance level (Figure 6.5). When combined, the parameter p desired
value is specified as follows:

profile
p
a
p
t e appropriat
p k k p  (6.4)

We demonstrate the autopilot personalization on an example of Adaptive Cruise
Control (ACC).
129

C. Adaptive cruise control
We adopt the conventional ACC scheme, – the system regulates the vehicle speed V
towards the speed of the preceding vehicle V
P
and keeps the inter-vehicle spacing X
R

close to the desired spacing S
D
(Figure 2.2). That is, the control objective is expressed as
follows:

V
R
→ 0, δ → 0 as t → ∞, (6.5)

where V
R
= V
P
– V, δ = X
R
– S
D
. We assume the quadratic spacing policy [152], so the
desired following distance is expressed as:

S
D
= h
0
+ h
1
∙V + h
2
∙V
2
, (6.6)

where h
0
is an inter-vehicle spacing when the vehicle speed is zero, h
1
and h
2
are the first
and second order term coefficients. We don’t restrict the term coefficients to be positive
or negative since drivers might show different habits in choosing the following distance.

Figure 6.5 : Application of current performance and manual tuning
Current
Performance
Driver’s
Performance
Profile
Manual
Tuning
Determine
Trip
Coefficient
Determine
Acceptance
Coefficient
Determine
Appropriate
Performance
Level
k t
k a
130

In addition to proper spacing control, in order to satisfy driver’s comfort requirements,
the system must meet the following constraints:







 
max
max min

a a
a a a
(6.7)

where a – vehicle acceleration, a
min
and a
max
are acceleration limitations, ̇ max
–
maximum allowed jerk (acceleration derivative) value. In order to protect the vehicle
from responding to inconsistent or unsmooth performance of the preceding vehicle, one
can apply an acceleration filter or a limiter. Figure 6.6 depicts a candidate for the
acceleration limiter, – it eliminates erratic or sudden changes in the speed of the
preceding vehicle V
P
. In order to satisfy the small jerk condition, one can add a similar
filter for the jerk or a low pass filter on the acceleration signal to attenuate high-
frequency fluctuations.
The open-loop gain coefficient β, the spacing constants h
i
, the acceleration bounds
a
min
and a
max
should be specified based on driver’s preferences and acceleration
acceptance coefficient. For instance, for spacing policy (6.6) the desired following
distance for a particular trip is expressed as follows:

S
D
=

h
0
+

h
1
∙V +

∙V
2
(6.7)

Figure 6.6: Acceleration limiter
β 𝟎
Ṽ
p

a min
–
V
p

+
a max
131

The system should collect data and calculate the parameters that suit driver’s style.
After the parameters are tuned, the system can use the personalized control law for
longitudinal vehicle control in automatic mode during vehicle following. We provide a
numerical example in the experimental section.
We note that the specified control scheme, objectives and spacing model are
assumed for the sake of example, and one can adapt different control schemes, objectives
and a spacing model.

6.3. EXPERIMENTS

We used a customized experimental vehicle to collect on-road data. The vehicle is
equipped with sensors to measure speed. In addition, the vehicle is equipped with side-
facing radars as well as front and rear-facing lidars (sensors that measure distance by
illuminating objects with a laser). These sensors provide 360º coverage of object
detection in a vicinity of up to 50 meters and allow measurement of the relative distance,
speed and angle to the surrounding vehicles.
We demonstrate our personalization methodology on an example of a particular
driver. The driver is of 27 years old, male, with 4 years of driving experience. Prior to
data collection, he had an opportunity to perform casual daily trips for several months
without any restrictions or requirements to the trips. That is, the participant was given
time to adapt to the vehicle and feel comfortable demonstrating his natural driving
behavior. For the data collection, the driver was asked to drive near the downtown area of
Los Angeles and Palo Alto on arterial streets and urban highways. The driver was not
132

restricted to a particular route and was not given any restrictions, including the duration
of the journeys. The driver performed 11 trips in total with the average duration of a trip
lasting 35 minute. During driving, the on-board PC recorded collected data with a
frequency of 30 Hz and stored it in a data file that was later processed off-line. The
process of data acquisition and recording was hidden from the driver, so the system did
not intrude on the driving in any way or affect natural driving behavior.
We used the collected data to evaluate following distance policy the driver applies.
We use the least-squares estimation algorithm to determine the coefficients in (6.6) that
fit the data. Figure 6.7 shows how the quadratic model fits the data. The corresponding
coefficients have the following values: h
0
=3.25m, h
1
=1.11s, h
2
=-0.016s
2
/m. The model
fits data reasonably well, – the root mean squared error is 4.32m.
We pick data for a trip where the driver showed different performance. We calculate
coefficients to determine trip performance profile (Figure 6.7). The curve shows that the
driver performs more cautiously by choosing larger following distances. The ratio for
curves should be used to determine coefficient (6.1) in order to project this change to
other driving tasks like lane changing.

Figure 6.7: Spacing model curves: solid – fitted into all data (blue), dashed – fitted into
particular trip data (red), dash-dot – curve that takes into account acceptance coefficient
Following distance, m
40

30

20

10

0
Speed, mph
10 20 30 40 50 60 70 80
133

For demonstration purpose, we assume that the driver specified that he prefers the
autopilot to be more conservative than he is. He sets up an acceptance coefficient to have
a value of 1.2. We use expression (6.7) in order to calculate desired spacing policy. The
dash-dot curve in the Fig. 6.7 depicts the recommended spacing policy that the autopilot
should follow in order to satisfy the driver.
6.4. CONCLUSION

In this chapter we briefly reviewed the current state of the self-driving car
technology and motivated the need for autopilot personalization. The personalization is
aimed to alter autopilot performance so it mimics driver’s habits. It allows increasing
autopilot driving performance acceptance and simplifying the supervision task to the
driver by making the autopilot behavior more transparent and intuitive.
We demonstrate how this feature can be applied on examples of adaptive cruise with
supporting experimental data.

134

7. CONCLUDING REMARKS AND PROPOSED
RESEARCH DIRECTIONS

In this work we developed methodology that can be used to personalize ADAS in
order to improve driver’s safety and comfort. In particular, we developed:
 personalized models for vehicle following, lane changing and intersection
crossing driving tasks.
 diagnostic techniques that can be used to assess driver/vehicle status and evaluate
driver’s style .
 optimization algorithm for personalized intersection assistance.
 autopilot personalization technique.
We support the proposed models and methodologies with experimental data
collected on a customized vehicle.
There are three main directions future research could expand to include: outward,
upward, or downward. Expanding outward, this research could lead to developments in
other driving tasks such turning, overtaking, parking etc. Going upwards would involve
explaining exactly how to use this kernel we have developed to design a personalized
ADAS. Delving downwards would mean researching deeper into the specific modeling
areas which we have worked on here. A few of these new research areas are discussed
below.

135

A. Further Development of the Models
One can begin to take into account additional factors that affect a driver’s behavior
such as exhaustion due to long drives, a need to arrive at a certain destination more
quickly, unfamiliarity with the roads or route, etc. One can try to apply different types of
models to these same driving tasks and evaluate whether they give more accurate results.
Our models can indicate what the driver desires. However this does not look at the
objective safeness of their driving. Once can augment the models of the driver with
proper rule-based safety algorithm. This could allow informing the driver of adjustments
from a safety perspective as well as a personalized one. For instance, one can use
following distances that are correlated with safer driving techniques which can warn the
driver to slow down when he or she is following a vehicle too closely, whereas now we
only compare the following distance to a driver’s usual behavior.
B. Further Development of the Diagnostic Techniques
One can expand the diagnostics techniques presented in Chapter 2 for vehicle
following case. More sophisticated and flexible thresholds can be designed and applied in
order to improve accuracy of driver/vehicle status evaluation.
The vehicle status prediction approach described in Chapter 4 is very promising in
improving traffic safety. The approach can be used a kernel to create a monitoring system
that will forecast potentially dangerous situations. For this purpose, one should:
 Improve technique accuracy by injecting addition prediction variables.
 Apply the methodology for all parameters of the surrounding vehicles that might
affect the subject vehicle safety.
 Develop a methodology to evaluate potential risks and how to avoid it.
136

C. Human-Machine Interaction (HMI)
ADAS will not be useful unless they can present information to the human driver in
an effective manner. Research into good HMI can supplement driving assistance systems.
It is important to interact with the driver in non-intrusive, but still comprehensive and
informative ways. One sub-problem is to determine how users interact with an ADAS in
terms of preferences between audible or visual cues, warning frequency, etc. For
example, research in this area could lead to developments in heads-up displays used for
driving assistance such as those depicted in Figure 6.2.

137

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Abstract (if available)

Abstract Driving, while a necessary and sometimes enjoyable experience, can become stressful and often challenging in city environments due to congestion, difficult environmental conditions, and the mistakes of other drivers. The latest trend of improving the urban driving experience is equipping cars with Advanced Driver Assistance Systems (ADAS). These systems aim to make driving safer and more comfortable. They can advise the driver when performing certain maneuvers is safe and even assist the driver in performing these maneuvers. An ADAS can also monitor driver and vehicle response in order to detect and avoid potentially dangerous situations by comparing current values of parameters with expected ones. In addition, an ADAS can assume control of the vehicle. ❧ The assistance system can be effective only if it captures personal driving style as well as the dynamics of the driver/vehicle system. However, the conventional way of manually adjusting car systems to tailor them to a driver’s personal desires is hardly appropriate for an ADAS. This type of performance requires a large number of parameters that would need to be manually adjusted by the driver over many iterations of trial and error before driving begins. Most ADAS are designed having the average driver’s characteristics in mind. This may lead to a system that aggressive drivers find annoying and passive drivers find too aggressive. Consequently, by adding stress and disappointment, this could dissuade drivers from using the very system that is supposed to make driving easier and more joyful. ❧ In this work we present modeling techniques that allow extracting knowledge of driver/vehicle behavior for the most stressful and accident-provoking driving tasks: vehicle following, lane change and intersection crossing. The models capture the personal characteristics associated to a particular driver and vehicle. The models, along with the corresponding parameter learning techniques, recommendation personalization algorithms and diagnostics methodology can be used as a kernel for a system that can provide personalized driving assistance and behavior monitoring. In addition, the presence of skewed model parameters can be used to evaluate a driver’s level of aggression. ❧ We demonstrate the effectiveness of the proposed techniques by applying the methods to experimental data collected on a customized vehicle. The results demonstrate that the models are able to capture personal habits (such as following distance and lane change duration) and distinguish between different drivers. In addition, we show that the developed intersection assistance algorithm that takes into account driver’s habits and preferences helps to reduce fuel consumption.

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Asset Metadata

Creator Butakov, Vadim (author)

Core Title Personalized driver assistance systems based on driver/vehicle models

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 10/15/2014

Defense Date 10/08/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag car,machine learning,Modeling,OAI-PMH Harvest,Safety,self-driving cars,vehicle

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ioannou, Petros (committee chair), Bogdan, Paul (committee member), Savla, Ketan (committee member)

Creator Email butakov@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-507252

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Legacy Identifier etd-ButakovVad-3017.pdf

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Document Type Dissertation

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