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USC Computer Science Technical Reports, no. 729 (2000)

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USC Computer Science Technical Reports, no. 729 (2000)

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Content 1
GPS-less Low Cost Outdoor Localization For
Very Small Devices
Nirupama Bulusu, John Heidemann, Deborah Estrin
USC/Information Sciences Institute
bulusu, johnh, estrin@isi.edu
Abstract— Instrumenting the physical world through
large networks of wireless sensor nodes, particularly for ap-
plications like marine biology, requires that these nodes be
very small, light, un-tethered and unobtrusive, imposing sub-
stantial restrictions on the amount of additional hardware
that can be placed at each node. Practical considerations
such as the small size, form factor, cost and power con-
straints of nodes preclude the use of GPS(Global Position-
ing System) for all nodes in these networks. The problem of
localization, i.e., determining where a given node is physi-
cally located in a network is a challenging one, and yet ex-
tremely crucial for many applications of very large device
networks. It needs to be solved in the absence of GPS on all
the nodes in outdoor environments. In this paper, we propose
a simple connectivity-metric based method for localization
in outdoor environments that makes use of the inherent radio-
frequency(RF) communications capabilities of these devices.
A fixed number of reference points in the network transmit
periodic beacon signals. Nodes use a simple connectivity
metric to infer proximity to a given subset of these reference
points and then localize themselves to the centroid of the lat-
ter. The accuracy of localization is then dependent on the
separation distance between two adjacent reference points
and the transmission range of these reference points. Initial
experimental results show that the accuracy for 90% of our
data points is within one-third of the separation distance.
Keywords—localization, radio, wireless, GPS-less, con-
nectivity, sensor networks.
I. INTRODUCTION
W
I reless networks of sensors greatly extend our
ability to monitor and control the physical envi-
ronment from remote locations. Networked sensors can
collaborate, aggregate the huge amount of sensed data
to provide a rich, multi-dimensional view of the physi-
cal environment. However, instrumenting the physical
world, particularly for applications such as marine biol-
ogy, requires that the devices we use as sensor nodes be
small, light, unobtrusive and un-tethered. This imposes
substantial restrictions on the amount of hardware that
can be placed on these devices.
In these large sensor network systems, however, we
need nodes to be able to locate themselves in various
environments, and on different distance scales. This
problem, which we refer to as localization
1
, is a chal-
lenging one, and yet extremely crucial for many appli-
cations of very large networks of devices.
GPS [8] solves the problem of localization in outdoor
environments for PC class nodes. However, for large
networks of very small, cheap and low power devices,
practical considerations such as size, form factor, cost
and power constraints of the nodes preclude the use of
GPS on all nodes.
In this paper, we address the problem of localization
for such devices, under the following constraints.
RF-based: We assume small nodes will be con-
nected with some kind of short-range radio. Our pri-
mary goal is to leverage this radio for localization,
thereby eliminating the cost, power and size require-
ments of a GPS receiver.
Ad hoc: In addition, we desire a solution that does
not require pre-planning or extensive infrastructure.
Responsiveness: We need to be able to localize
within a fairly low response time.
Cost: We desire to minimize computation and mes-
sage costs to reduce power consumption.
Receiver-based: In order to scale well to large dis-
tributed networks, the responsibility for localization
must lie with the receiver node that needs to be local-
ized and not with the reference points.
Adaptive Fidelity: In addition, we wanted our al-
gorithms to be adaptable to the granularity of available
reference points.
This paper proposes an idealized radio model and a
simple connectivity based localization method for such
devices in unconstrained outdoor environments, that
We borrow the term localization from robotics, where it refers to
the problem of determining the position of a mobile robot in some
coordinate system.
2
makes use of the inherent radio-frequency RF commu-
nications capabilities of these devices. A fixed number
of nodes in the network serve as reference points and
transmit periodic beacon signals. Nodes use a simple
connectivity metric to infer proximity to a given sub-
set of these reference points and then localize them-
selves to the centroid of the selected(proximate) refer-
ence points.
The paper makes the following key contributions.
It presents a detailed and systematic exploration and
classification of the design space and work done in the
area of localization.
It proposes a method for coarse-grained localization
based on an idealized radio model and demonstrates its
validity and applicability in outdoor unconstrained en-
vironments.
It describes a simple implementation of the model
and presents initial results.
II. RELATED WORK
Essentially any method for localization relies on two
features, reference points (either fixed or moving but
whose positions are known at any given instant) and
communication (unidirectional or bidirectional, single
or multiple modalities of communication) between the
reference points and the node to be localized.
We classify the approaches in two categories, based
on the information inferred during the communication.
Approaches which infer fine grained information such
as distance to a reference point based on signal strength
or timing measurements fall into the category of fine
grained localization and those that infer coarse grained
information such as proximity or the presence of con-
nectivity to a given reference point are categorized as
coarse grained localization methods.
We discuss the techniques and work that has been
done so far in each of these categories, and classify
them further.
A. Fine-grained localization
Fine-grained localization methods can be further
classified into range-finding and directionality based
methods, depending on whether ranges or angles to ref-
erence points are being inferred.
A.1 Range-finding
The range(distance) of the mobile node to several
reference points is determined by one of the several
techniques enumerated below. The position of the mo-
bile node can be computed based on trilateration or
multilateration.
Timing: The distances from the mobile host to the
reference points can be inferred from the times-of-flight
of their respective communication signals.
The time-of-flight, again, may be calculated using the
timing advance technique which measures the amount
that the timing of the mobile has to be advanced in or-
der for the received signal to fit into the correct time
slot. This technique is used in GPS [8] and Pinpoint’s
Local Positioning System(LPS) [7]. GPS measures
one-way flight time whereas LPS measures round-trip-
time(thereby eliminating the need for time synchro-
nization).
GPS [8] is a wide-area radio positioning system. In
GPS each satellite transmits a unique code, a copy of
which is created in real time in the user-set receiver
by the internal electronics. The receiver then gradually
time shifts its internal clock till it corresponds to the re-
ceived code: an event called lock-on. Once locked-on
to satellite, the receiver can determine the exact timing
of the received signal in reference to its own internal
clock. If that clock were perfectly synchronized with
the satellite’s atomic clocks, the distance to each satel-
lite could be determined by subtracting a known trans-
mission time from the calculated receive time. In real
GPS receivers, the internal clock is not quite accurate
enough. An inaccuracy of a mere microsecond corre-
sponds to a 300-meter error.
Pinpoint’s 3D-iD system [7] is a Local Positioning Sys-
tem(LPS) that covers an entire three-dimensional in-
door space and is capable of determining the 3-D loca-
tion of items within that space. The LPS subdivides the
interior of the building into cell areas that vary in size
with the desired level of coverage. The cells are each
handled by a cell controller which is attached by a coax-
ial cable to up to 16 antennas. It provides an accuracy
of 10 meters for most indoor applications, though some
may require accuracy of 2 meters. The main drawback
of this system is that it is centralized, and requires a lot
of infrastructural set up effort.
3
Alternately, the time of flight can be calculated by mak-
ing explicit time-of-arrival measurements based on two
distinct modalities of communication, ultrasound and
radio, as in the Active Bat [6]. These two different
modalities travel at vastly different speeds( ms
and
ms
) , enabling the radio signal to be
used for synchronization between the transmitter and
the receiver, and the ultrasound signal to be used for
ranging. The Active Bat system however requires sig-
nificant effort for deployment indoors. Ultrasound sys-
tems cannot be used outdoors because they all use a sin-
gle transmission frequence( kH z) and hence there is
a high probability of interference from other ultrasound
sources.
Signal Strength: In their recent paper [5], Bahl et.al.,
suggest estimating distance based on signal propaga-
tion characteristics in indoor environments. They com-
pute distance from measured signal strength by apply-
ing a Wall Attenuation Factor(WAF) based signal prop-
agation model. Their approach is effective indoors, un-
like ours, but it requires extensive pre-planning, making
it unsuitable for rapid or ad hoc deployment.
A.2 Directionality
Another way of estimating location is to compute the
angle of each of the reference points with respect to the
mobile node in some reference frame. The position of
the mobile node can then be computed using triangula-
tion methods.
One such technique used in cellular networks, is
known as small aperture direction finding. It requires a
complex antenna array at each of the cell site locations.
The antenna arrays can in principle work together to
determine the angle(relative to the cell site) from which
the cellular signal originated. When several cell sites
can determine their respective angles of arrival, the cell
phone location can be estimated from the intersection
of projected lines drawn out from the cell site at the an-
gle corresponding to the signals origin. There are two
drawbacks of this approach. The cost of the complex
antenna array implies that it can be placed only at the
cell sites. Secondly the cell sites are responsible for de-
termining the location of the mobile node which will
not scale well when we have a large number of such
nodes. This approach too, cannot be used in indoor en-
vironments.
Another example of directionality based systems are
the VOR/VORTAC stations [10], which were used for
long distance aviation navigation prior to GPS. The
VOR station transmits a unique omnidirectional signal
that allows an aircraft aloft to determine its bearing rel-
ative to the VOR station. The VOR signal is electrically
phased so that the received signal is different in various
parts of the 360 degree circle. By determining which of
the 360 different radials it is receiving, the aircraft can
determine the direction of each VOR station relative to
its current position.
B. Coarse Grained Localization
Our work is perhaps most similar to earlier work
done in coarse-grained localization using Infra Red(IR)
technology.
In the Active Badge system [1] system, a badge worn
by a person emits a unique IR signal every 10 seconds.
Sensors are placed at fixed positions within a building
and as they receive the unique identifiers, the location
manager software is able to provide information about
the person’s location to the requesting services and ap-
plications. While the performance of this system is
quite good, a major drawback is that the range of the
IR system is fairly small, and consequently the build-
ing has to be wired up with a significant number of sen-
sors. In the few places where such systems have been
deployed, sensors have been physically wired in every
room of the building. Such a system scales poorly, and
incurs significant installation, configuration and main-
tenance cost.
Another system that is based on IR technology is de-
scribed in [3]. This system requires IR transmitters to
be located at fixed positions inside the ceiling of the
building. An optical sensor sitting on a head mounted
unit senses the IR beacons and system software deter-
mines the position of the person. This system suffers
form similar drawbacks as the Active Badge system.
IR tends to perform poorly in the presence of direct
sunlight and hence cannot be used outdoors.
4
III. IDEALIZED RADIO MODEL AND
LOCALIZATION ALGORITHM
A. Idealized Radio Model
We have found an idealized radio model useful for
predicting bounds on the quality of localization. This
section presents this idealized model. To our surprise,
this model compares quite well to outdoor radio propa-
gation as we explore in Section IV.
We make two assumptions in our idealized model:
Perfect spherical radio propagation.
Identical transmission range(power) for all radios.
B. Localization Algorithm
Multiple nodes in the network serve as reference
points(named R
to R
n
). They are situated at known
positions( X
Y
to X
n
Y
n
), that form a regular
mesh and transmit periodic beacon signals(period = T )
containing their respective positions. We assume that
the reference points can be synchronized so that their
beacon signal transmissions of neighboring reference
points do not overlap in time. Furthermore, in any
time interval T , each of the reference points would have
transmitted exactly one beacon signal.
First, we define a few terms.
d Separation distance between adjacent reference
points
R Transmission range of the reference point
T Time interval between two successive beacon sig-
nals transmitted by a reference point
t Receiver sampling or data collection time
Nsent i t Number of beacons that have been sent by
R
i
in time t
Nrecv i t Number of beacons sent by R
i
that have
been received in time t
CM Connectivity metric
S Sample size for connectivity metric
C M thr esh Threshold for CM
X
est
Y
est
Estimated Location of the receiver
X
a
Y
a
Actual Location of the receiver
Each mobile node listens for a fixed time period t
and collects all the beacon signals that it receives from
various reference points.
We characterize the information per reference point
R
i
by a connectivity metric(CM
i
), defined as
CM
i
Nrecv i Nsent i
.
In order to improve the reliability of our connectivity
metric, we would like to base our metric on a sample of
at least S packets, where S is the sample size, a tunable
parameter of our method( i.e., N sent i S). Since
we know T to be the time period between two succes-
sive beacon signal transmissions, we can set t, the re-
ceiver’s sampling time as:
t S T From the beacon signals that it receives, the re-
ceiver node infers connectivity to a collection of ref-
erence points for which the respective connectivity
metric exceeds a certain threshold, C M thr esh(say
90%). We denote the collection of reference points by
R
i
R
i
R
i
k
. The receiver localizes itself to the
region which coincides to the intersection of the con-
nectivity regions of this set of reference points, which
is defined by the centroid of these reference points.
X
est
Y
est
X
i
X
i
k
k
Y
i
Y
i
k
k
We characterize the accuracy of the estimate by the
error distance ED defined as,
ED q
X
est
X
a
Y
est
Y
a
By increasing the density of beacons that populate
the grid (i.e increasing
R
d
, the granularity of the local-
ization regions becomes finer, and hence the accuracy
of the location estimate improves. This is illustrated in
figure 1.
IV. VALIDATION
Since our localization model is dependent on the
spherical radio propagation assumption, described in
the previous section; we checked the validity of our as-
sumption in both outdoor and indoor environments.
Outdoors: In an empty parking lot; we did a system-
atic traversal of about 121 grid points in a 10m*10m
grid with the radio transmitter placed at . There
were no holes or non-linearities in the transmission. We
calculate the range sample as the distance between the
transmitter and the farthest point from it along
each X ISO-line(points with same X coordinate value)
5
3*2 Grid of Beacons
FEWER AND LARGER LOCALIZATION REGIONS
4*3 Grid of Beacons
MORE and SMALLER LOCALIZATION REGIONS
THE SHADED AREA REFLECTS ONE SUCH LOCALIZATION
REGION
Fig. 1. Granularity of Localization Regions vs. Grid Density
whose CM exceeds C M thr esh, yielding 11 range
samples in all. The maximum variance in the range
with CM thresh was 2 meters, as can be seen
in figure 2. The median range was 8.94m, which is used
to plot the theoretical range in the graph. Among the 78
data points that appear in the graph, there is a mismatch
at 10 points and match at 68 points between theory and
experimental values, i.e., there is an 87% correlation
between the two.
Indoors: We conducted a similar experiment in-
doors. The range with a 90% connectivity metric var-
ied from about 73 feet(in a corridor with direct Line Of
Sight) to about less than 15 feet(with walls in between).
Hence the idealized radio model may be considered
valid for outdoor unconstrained environments only.
V. EXPERIMENTAL RESULTS
A. Experimental Testbed
Our experimental testbed consisted of 4 reference
points, located at the corner of a 10m*10m grid. This
grid was further subdivided into 100 1m*1m smaller
grids and we collected data at each of the 121 small
grid corners.
The transmitters at each reference point and the re-
ceiver are the Radiometrix-RPC 418(radio packet con-
troller) modules connected to Toshiba Librettos running
RedHat Linux 6.0. A 3 inch antenna is used for the ex-
0
2
4
6
8
10
0 2 4 6 8 10
Y (in m)
X (in m)
Expt
Theory
Median range
Fig. 2. 90% connectivity ranges for the reference point (0,0)
perimental purposes. We used about 5 RPC modules in
all(including 1 for the receiver).
A.1 Software
The software was written for the Radiometrix RPC-
418 modules and consists of two components.
1. Beacon: The reference point periodically transmits
a packet (every 2 seconds in our experiment) containing
its ID and position.
2. Receiver: The receiver obtains its current measured
position based on an input from the user. For each
measured position, it samples for a time period t de-
termined by the sample size S, and logs the set of ref-
erence points it hears from and its current localization
estimate.
There are several implementation issues that our soft-
ware did not address, since we were interested in an
empirical study rather than actual deployment. These
issues are mentioned below, and discussed more fully
in Section VI.
Collision Avoidance: Multiple reference points must
transmit their beacon signals periodically without col-
lision or with minimum collision. This is acutely tied
to time synchronization. Currently we start the trans-
mission at the reference points in a linear sequence to
achieve this, which will clearly not scale when we have
larger numbers of reference points.
Power Consumption: Packet reception is expensive
power wise and we want our receivers to ideally sample
6
0
2
4
6
8
10
0 2 4 6 8 10
Y (in m)
X (in m)
Ref.(0,0)
Ref. (10,0)
Ref. (10, 10)
Ref. (0, 10)
Fig. 3. Experimental 90% connectivity ranges for the 4 ref-
erence points
for a small period of time. We plan to conduct further
experiments to determine an optimal sample size.
B. Results
In this section, we discuss the experimental results
based on our implementation. Our experimental param-
eters are T = 2 seconds, S=20, t=41.9seconds.
2
.
In figure 3, we see the areas of connectivity of the 4
reference points in the grid. We collected data at 121
points in all, wherein adjacent points are separated by
1m each. We see several distinct regions in the grid,
based on the areas of overlap. Each distinct region con-
stitutes an equivalence class, defined by the centroid of
the reference points in the region. These can be con-
trasted with the theoretically predicted overlap regions,
seen in figure 4.
The location estimate at each grid point is the cen-
troid. We use the error-distance metric defined in Sec-
tion III to characterize the performance.
In figure 5, the error-distance is plotted as a function
of the position. Clearly, the error-distance is lowest at
the the position corresponding to the centroid of the re-
gion and increases towards the edges of the region. The
average error-distance was 1.83m and the standard de-
Although our experimental parameter values for T , and hence
t are high, we can substantially scale them down without violating
the integrity of the experiment
0
2
4
6
8
10
0 2 4 6 8 10
Y (in m)
X (in m)
(0,0)
(10,0)
(10, 10)
(0, 10)
Fig. 4. Theoretical 90% connectivity ranges for the 4 refer-
ence points
viation was 1.07m. The mimimum error was 0m and
the maximum error was 4.12 across 121 error-distance
samples.
Figure 6 shows the cumulative error-distance distri-
bution across all the grid points. For over 90% of the
data points, the error-distance falls within 3.0 meters i.e
within 30% of the separation-distance between two ad-
jacent reference points. This result is based on 4 refer-
ence points only. Since we observed a high correlation
between our model and experiment, improved granular-
ity can be expected with a higher density of reference
points.
Figure 7 presents a simulation based scaling result
of the error-distance behavior. We present it to predict
how the granularity of localization can be expected to
vary when the density of reference points is increased.
In our simulation, we assume an infinite two-
dimensional mesh of reference points, with any two ad-
jacent reference points spaced a distance d apart and
transmission range R. Our coordinate system is cen-
tered at one such reference point, which is assumed to
be at .
The localization estimate of any point X Y in the
mesh can be obtained in two steps.
Step 1: Determine all the reference points which are
7
4 ref.
3.66
3.2
2.75
2.29
1.83
1.37
0.916
0.458
0
5
10
0
5
10
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
X(in m)
Y(in m)
Error-Distance(in m)
Fig. 5. Position Error Graph
within range R of X Y , by considering all the refer-
ence points between X R Y R and X R Y R .
Step 2: Localize X Y to the centroid of the selected
reference points and compute the corresponding error-
distance.
Foragiven d, we increase Rd from 1 to 4. We
consider the average and maximum error-distances of
the localization estimates for 10201 uniformly spaced
points within one grid in the mesh, for each Rd value.
Although the maximum and average error do not de-
crease monotonically, non-trivial increments to Rd ,
(for instance, an increment of 1) lead to lower maxi-
mum and average error-distances on the whole.
In particular, the maximum error-distance experi-
ences a substantial drop(from 0.5d to 0.25d) when the
density Rd is increased from 1 to 4.
VI. DISCUSSION AND FUTURE WORK
In this section, we will discuss some general prob-
lems that arise in deploying our localization method and
present some of our ideas on solving them.
Collision Avoidance or Reference
Point Synchronization
In order for our method to work well, reference points
must be synchronized so that their beacon signal trans-
missions do not overlap in time. This synchronization
0
20
40
60
80
100
0 0.5 1 1.5 2 2.5 3 3.5 4
Cumulative probability
Error Distance(in m)
"4refpoints"
Fig. 6. Cumulative Error-Distance Distribution
needs to be local and not necessarily global. This syn-
chronization can be achieved by using some kind of a
randomized back-off scheme, wherein the time inter-
val T is subdivided into several smaller slots and each
reference point randomly picks a slot to transmit or by
applying a hash function on its node(reference point)
ID, if available. Of the two alternatives, the former
seems more attractive since it eliminates the need for
node IDs.
Reference Point Configuration
We have left the issue of how the reference point coor-
dinates are configured and how they are deployed open.
This could be achieved through limited human inter-
vention. The reference points themselves could use
GPS since they do not have the same constraints as
other nodes. If the number of reference points is too
large, then we need to develop some self-configuration
schemes in future work.
Placement Heterogeneity of Reference
points
Our localization method assumes that the reference
points are placed at the intersections of a regular mesh.
We controlled the placement, to bound the quality of
localization. However it may not always be feasible
to control the reference point placement with such uni-
formity. Preliminary analysis with a 1D model(linear
placement of reference points with non-uniform dis-
tances of separation) seems to suggest that it does
not impact the localization accuracy too adversely,
8
0
0.1
0.2
0.3
0.4
0.5
0.6
1 1.5 2 2.5 3 3.5 4
error(as a fraction of d)
R/d
Variation of Error with density R/d
avg-err
"max-err"
Fig. 7. Simulation based Variation of Error with den-
sity(R/d)
provided the maximum degree of non-uniformity is
bounded. This is an area for future work.
Robustness
Since the success of our localization method depends
on the node reliably inferring connectivity, and hence
proximity to its neighbouring reference points, it must
be tolerant of reference point failures. Reference
points should monitor themselves and fail-stop when
their battery power drops down. Some amount of re-
dundancy(additional nodes that can serve as reference
points, if need be) should be incorporated into the sys-
tem to tolerate reference point failures.
Efficiency and Parameter Tuning
In order to avoid collisions, we need T to be high. In
order to ensure the consistency of our connectivity met-
ric, we need S to be high. However, in order to reduce
power consumption at the receiver, we need to reduce
t i.e., we would like to use smaller values of S and
T . Since, we use the connectivity metric as a coarse-
grained measure, our experience seems to suggest that a
small value of S, such as 10 would suffice. The value of
T would be determined by the reference point density
Rd and the efficacy of the collision avoidance scheme.
VII. CONCLUDING REMARKS
This paper addresses localization in unconstrained,
outdoor environments for networks of low-cost, very
small devices where GPS is not available on all nodes.
We suggested a connectivity-metric based localization
method based on an idealized radio model where the
receiver localizes itself with high confidence to the cen-
troid of a set of reference points. In outdoor envi-
ronments, our model correlated very well with reality
(87%).
Our approach is simple, adaptive to the granularity
of reference points available and lends itself easily to
a distributed implementation, and is hence scalable to
large, distributed networks of devices. Initial experi-
mentation has shown promising results, with our simple
scheme, for a small number of reference points. Simu-
lation suggests that the granularity of error-distance can
be improved by further increasing the density of refer-
ence points.
We also outlined some general problems which need
to be tackled for large scale deployment and presented
our ideas for solving them.
ACKNOWLEDGMENTS
The authors would like to thank Lewis Girod and
Jeremy Elson for their suggestions and feedback.
REFERENCES
[1] A. Harter and A. Hopper, A Distributed Location System for
the Active Office, IEEE Network, January 1994
[2] http://www.ascension-tech.com
[3] R. Azuma, Tracking Requirements for Augmented Real-
ity, Communications of the ACM,V ol. 36, No.7,pp:50-51,July
1993
[4] T.S. Rappaport, Wireless Communications - Principles and
Practice, IEEE Press, 1996.
[5] Paramvir Bahl and Venkata N. Padmanabhan, User Location
and Tracking in an In-Building Radio Network, Technical Re-
port MSR-TR-99-12, Microsoft Research, 1999.
[6] A.Ward, A. Jones, A. Hopper A New Location Technique for
the Active Office ORL Technical Report newblock Composable
Ad Hoc Mobile Services for Universal Interaction, In Proceed-
ings of Mobicom ’97, September 1997.
[7] J. Werb, C. Lanzl, Designing a positioning system for finding
things and people indoors, IEEE Spectrum, September 1998.
[8] B. Hofmann-Wellenhof, H. Lichtenegger, J.Collins, Global
Positioning System: Theory and Practice, Second Edition,
Springer-Verlag, 1992.
[9] P. Enge and P. Misra, Special Issue on GPS: The Global Po-
sitioning System, Proceedings of the IEEE, pp.3-172, January
1999.
[10] http://www.arundel.net/xplane/html/vor.html

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Description

Nirupama Bulusu, John Heidemann, Deborah Estrin. "GPS-less low cost outdoor localization for very small devices." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 729 (2000).

Asset Metadata

Creator Bulusu, Nirupama (author), Estrin, Deborah (author), Heidemann, John (author)

Core Title USC Computer Science Technical Reports, no. 729 (2000)

Alternative Title GPS-less low cost outdoor localization for very small devices (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

Tag OAI-PMH Harvest

Format 8 pages (extent), technical reports (aat)

Language English

Unique identifier UC16269712

Identifier 00-729 GPS-less Low Cost Outdoor Localization For Very Small Devices (filename)

Legacy Identifier usc-cstr-00-729

Format 8 pages (extent),technical reports (aat)

Rights Department of Computer Science (University of Southern California) and the author(s).

Internet Media Type application/pdf

Source 20180426-rozan-cstechreports-shoaf (batch), Computer Science Technical Report Archive (collection), University of Southern California. Department of Computer Science. Technical Reports (series)

Access Conditions The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Repository Email csdept@usc.edu

Inherited Values

Title Computer Science Technical Report Archive

Description Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017.

Coverage Temporal 1991/2017

Repository Email csdept@usc.edu

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)