Tracking Multiple Targets Using Binary Proximity Sensors ¤
Jaspreet Singh
Upamanyu Madhow
Electrical and Computer
Engineering, University of
California, Santa Barbara
CA 93106 USA
f jsingh , madhow g
@ece.ucsb.edu
Rajesh Kumar
Subhash Suri
Computer Science
University of California
Santa Barbara
CA 93106 USA
f rajesh , suri g
@cs.ucsb.edu
Richard Cagley
Toyon Research Corporation
Goleta, CA 93117, USA
rcagley@toyon.com
ABSTRACT
Recent work has shown that, despite the minimal informa-
tion provided by a binary proximity sensor, a network of
such sensors can provide remarkably good target tracking
performance. In this paper, we examine the performance
of such a sensor network for tracking multiple targets. We
begin with geometric arguments that address the problem
of counting the number of distinct targets, given a snapshot
of the sensor readings. We provide necessary and su±cient
criteria for an accurate target count in a one-dimensional
setting, and provide a greedy algorithm that determines the
minimum number of targets that is consistent with the sen-
sor readings. While these combinatorial arguments bring
out the di±culty of target counting based on sensor read-
ings at a given time, they leave open the possibility of ac-
curate counting and tracking by exploiting the evolution of
the sensor readings across time. To this end, we develop a
particle ¯ltering algorithm based on a cost function that pe-
nalizes changes in velocity. An extensive set of simulations,
as well as experiments with passive infrared sensors, are re-
ported. We conclude that, despite the combinatorial com-
plexity of target counting, probabilistic approaches based on
fairly generic models for the trajectories yield respectable
tracking performance.
Categories and Subject Descriptors: I.4.8 [Scene Anal-
ysis] Tracking, Sensor fusion; G.2 [Discrete Mathematics]
Counting Problems; G.3 [Probability And Statistics] Prob-
abilistic algorithms; General Terms: Algorithms, Theory,
¤This work was supported by the National Science Foun-
dation under grants CCF-0431205, CNS-0520335, CNS-
0626954 and CCF-0514738, by the O±ce of Naval Research
under grants N00014-06-1-0066 and N00014-06-M-0260, and
by the Institute for Collaborative Biotechnologies under
grant DAAD19-03-D-0004 from the US Army Research Of-
¯ce.
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IPSN’07, April 25-27, 2007, Cambridge, Massachusetts, USA.
Copyright 2007 ACM 978-1-59593-638-7/07/0004 ...$5.00.
Experimentation; Keywords: Target Tracking, Sensor Net-
works, Binary Sensing, Counting Resolution, Particle Filters
1. INTRODUCTION
We investigate the problem of tracking targets using a
network of binary proximity sensors. Each sensor produces
a single bit of output, which is 1 when one or more targets
are in its sensing range and 0 otherwise. These sensors are
not able to distinguish individual targets, decide how many
distinct targets are in the range, or provide any location-
speci¯c information. Despite the minimal information pro-
vided by a single binary sensor, a collaborative network of
binary sensors has been shown in prior work [18] to yield re-
spectable tracking performance: the resolution with which
a target can be localized is inversely proportional to ½Rd¡1,
where ½ is the sensor density, R is the sensing range, and
d is the dimension of the space. In this paper, we extend
the work of [18], which considered a single target, and in-
vestigate the problem of tracking multiple targets, without
a priori knowledge of the number of targets.
We have chosen to focus on the simple and minimalistic
setting of binary sensors because the cost and power con-
sumption of sensor nodes is a severe constraint in large-scale
deployments, and both can be signi¯cantly reduced by re-
stricting the nodes to provide binary detection. Thus, by
constraining ourselves to a binary sensing model, we can
work with low-power, low-cost sensor nodes that can form
the basis for a highly scalable architecture for wide area
surveillance. This information can, of course, be augmented
by a small number of more capable sensors (e.g., cameras),
although we do not explore such enhancements in this paper.
Examples of sensor modalities that are suitable for low-
cost nodes include [1] Seismic, Acoustic, Passive infrared
(PIR), Active infrared, Ultra wide band radar imaging, Mil-
limeter wave radar, Magnetometer and Ultrasonic. For many
types of sensors, it is possible to use simple thresholding to
get a binary reading or perform onboard signal processing
for rough classi¯cation. The former option requires drasti-
cally reduced processing, and leads to signi¯cant power sav-
ings. As an example, for acoustic sensing (e.g., the Knowles
EA-21842 sensor) and magnetometer sensing (e.g., the Hon-
eywell HMC1002 sensor), the power consumption can be
reduced ¯ve-fold by using binary mode rather than classi¯-
cation mode. In our lab-scale experiments, we employ PIR

sensors due to their good performance, low cost, and ease of
systems integration [11].
As shown in [18], the binary sensing model is analogous to
coarse-grained analog-to-digital conversion that ¯lters out
rapid variations in the target's trajectory. This motivates
algorithms that attempt to track only \lowpass" versions of
the trajectory. For multiple targets, however, we encounter
signi¯cant additional di±culties, since we cannot tell how
many targets are within a sensor's range when it outputs a 1.
Our ¯rst task in this paper, therefore, is to understand how
well we can count the number of targets, given a snapshot
of the sensor readings. We employ geometric arguments to
characterize when an accurate count is possible, and provide
a lower bound on the number of targets, based on a greedy
algorithm for explaining the sensor's observations with the
minimum number of targets. While these arguments bring
out the di±culty of target counting based on a snapshot,
they do not preclude the possibility of accurate counting
and tracking when we account for the evolution of the sen-
sor readings in time, using a model for the targets' behavior.
To this end, we develop a particle ¯ltering algorithm which
employs a cost function penalizing changes in velocity. It
is shown by simulations that the particle ¯lter algorithm
is e®ective in tracking targets even when their trajectories
have signi¯cant overlap. The algorithm is general enough to
incorporate a simple model for non-ideal sensing, and pro-
vides acceptable tracking performance for our experimental
system with PIR sensors even when one of the sensors fails.
We restrict attention to one-dimensional systems through-
out this paper. This enables us to gain fundamental in-
sight, as well as to easily display multiple trajectories on
two-dimensional space-time plots. However, both our geo-
metric target counting arguments and the particle ¯ltering
algorithm generalize to higher dimensions.
Our focus in this paper is on the e±cacy of collaborative
tracking rather on the communication protocols used by the
sensor nodes. Thus, we assume that all of the sensor read-
ings are available at a centralized processor, which can then
estimate the targets' locations and trajectories. Distributed
implementations of our algorithms, in which neighbors col-
laborate to estimate segments of trajectories, are possible,
but are not considered here. We note that the binary sens-
ing model has minimal communication requirements, hence
this assumption of centralized processing is quite practical:
a sensor need only convey the intervals at which it switches
\on" and \o®" (assuming that the readings are averaged
so as to remain reasonably steady, this is far more e±cient
than sending a sample of the sensor's readings at regular
intervals).
The rest of the paper is organized as follows. Section 2
discusses the problem of target counting based on a snap-
shot of the sensor readings. In Section 3, we describe our
particle ¯ltering algorithm. Section 4 provides simulation
results, while Section 5 describes our experimental set-up
and results. We end with the conclusions in Section 6.
Related Work
The problem of tracking multiple targets using sensor net-
works has been explored by many prior references [15, 16, 13,
5, 19, 9, 17]. Owing to its simplicity and minimal commu-
nication requirements, the speci¯c use of binary proximity
sensors for tracking applications has also drawn consider-
able attention of late. However, most of the work related
to binary sensing has been applied to the case of tracking a
single target [3, 8, 18]. The tracking techniques employed in
the large-scale deployment in [2] can be loosely interpreted
in terms of a binary sensing model, even though a variety of
sensing modalities and a variety of targets are considered.
Reference [12] contains a distributed tracking algorithm for a
binary sensor network, but assumes perfect knowledge about
the number of targets and their identities, unlike the present
work.
In our work, we investigate both target counting and track-
ing. Prior work on counting targets includes [14], but it
assumes more detailed sensing capabilities than our simple
binary model. The classical framework for tracking is based
on Kalman ¯ltering, with Gaussian assumptions for the sen-
sor readings; for example, [10] investigates the use of Kalman
¯ltering for distributed tracking. In recent years, the use of
particle ¯lters, which can handle more general observation
models, has become popular. However, most prior work on
the use of particle ¯lters for tracking in sensor networks [4,
6, 7] assumes a richer sensing model than the binary model
we consider. An exception is our own prior work in [18] on
the use of particle ¯lters for tracking a single target using
non-ideal binary sensing. In this paper, we build on these
ideas to develop particle ¯lters for tracking multiple targets.
2. TARGET COUNTABILITY
In order to develop fundamental geometric insights, we
restrict attention in this section to an idealized model in
which each sensor's coverage area is a circular disk of radius
R: each sensor detects a target without fail if it falls within
this disk, and does not produce false positives or negatives.
While we develop our basic ideas and theorems in one di-
mension, we comment on their relevance and extensions to
higher dimensions as appropriate.
We want to understand and articulate the conditions un-
der which an algorithm can track multiple targets with prov-
able guarantees. A ¯rst step for any tracking algorithm must
deduce how many distinct targets are present in the ¯eld,
and so we begin our investigation by asking under what cir-
cumstances an algorithm can reliably determine the number
of distinct targets in the ¯eld, given a snapshot of the sen-
sor readings. This is a worst-case model which applies, for
example, when the rate at which the sensors report their
readings is low compared to the rates at which the targets
cross the boundaries of the sensors' coverage areas. Put an-
other way, this section addresses the most general scenario,
in which we have no model for the targets' trajectories. As
we shall see in Section 3, when we do employ a plausible
model corresponding to a scenario in which the sensor read-
ings are available at a \high enough" rate, then it is indeed
possible to do better than what is promised by the worst-
case model considered in this section.
2.1 Target Counting with Binary Sensing
Some spatial separation among the targets is clearly a
necessary precondition for accurately disambiguating among
di®erent targets, but what does that mean, and how much
separation is enough? For instance, is the following simple
condition adequate: each target moves su±ciently (arbitrar-
ily) far from the remaining targets at some point during the
motion. Let us call this the condition of individual separa-
tion. Unfortunately, as the following simple result shows,