Surveillance by means of a random sensor network:
a heterogeneous sensor approach
A. Farina, G. Golino
A. Capponi
C. Pilotto
Selex Sistemi Integrati
Via Tiburtina, km12,400
00131 Rome
Italy
California Institute of Technology
Computer Science
1200 E. California Boulevard,
MC 256-80 Pasadena,
CA 91125
USA
University of Rome “La Sapienza”
Computer Science
Via Salaria 113
00198 Rome
Italy
[email protected]
[email protected]
[email protected]
[email protected]
Abstract – A distributed approach to the surveillance is
presented. A clustering architecture is modelled and the
behaviour of the corresponding heterogeneous random
network with self-organizing capability is investigated.
Two types of sensors, simple and complex, spread out
over the surveillance area. Simple sensors can only
compute binary information (yes or no detection);
complex sensors, instead, are able to form a target track.
A two-way efficient local communication among sensors
is hypothesized. From it, a global coherent behaviour of
the network emerges, and the resulting network is able to
track the moving objects. Benefits and drawbacks of our
solution are analysed by means of Monte Carlo
simulations.
Keywords: target tracking, distributed estimation,
random network of sensors, self-organizing network.
1. Introduction
Automatic surveillance is a process of monitoring the
behaviour of selected objects (targets) inside a specific
area by means of sensors. Sensors typically perform the
following functions:
• detection of a target inside the surveillance
area;
• estimation of target position (localization);
• monitoring of the target kinematic behaviours
(tracking);
• classification and/or recognition of the targets.
The classical approach to surveillance of wide areas
(e.g. over 100 Km 2 ) is based on the use of a single or few
sensors with long range capabilities. The signal received
by the single sensor is processed by means of suitable
digital signal processing subsystems. In this case the
sensors are costly, with adequate computation and
communication capabilities. Sensors are normally
located in properly selected sites, to mitigate terrain
masking problems; nevertheless, they provide different
performance depending on the location of target inside
0-7803-9286-8/05/$20.00 © 2005 IEEE
the surveillance area. Typical sensors are radars [1],
infrared or TV cameras [2], seismic or acoustical
sensors.
Nowadays, a novel approach to the automatic
surveillance has been adopted; it is based on the use of
many sensors with short range capabilities. In this case,
sensors are cheap and have limited computation and
communication capabilities [3]. They can be randomly
distributed inside the surveillance area and if the
number of sensors is high, the performance of the
surveillance system can be considered independent of
the location of the targets. The signal received by each
sensor is processed using the computational capabilities
of a sub-portion of the sensor system. This process is
called Collaborative Signal and Information Processing
(CSIP) [4].
The CSIP has three levels of applications:
• First level: each sensor provides only
detection information; there is a central unit
which receives and processes the data from the
sensors optimising detection and performing
the localization and tracking functions.
• Second level: each sensor provides detection
and localization information; there is a central
unit which receives and processes the data
from the sensors optimising detection and
localization
and
performing
tracking
functions.
• Third level: each sensor provides detection,
localization and tracking information; there is
a central unit which receives and processes the
data from the sensors optimising the detection,
localization and tracking functions.
The different levels correspond to different single
sensor complexities:
• First level: sensors with small sensing and
communication capabilities; the sensor should
detect targets in its coverage area; the sensor
has no resolution capabilities, thus it cannot
discriminate between the presence of one or
more targets [5].
1
•
Second level: sensors with medium sensing and
communication capabilities; the sensor should
detect the targets in its coverage area; it can also
determine the range and/or bearing of the
targets; the sensor has resolution capabilities.
• Third level: sensors with complex sensing,
processing and communication capabilities; the
sensor should detect the targets in its coverage
area; it determines the range and bearing angles
of the targets; it can also track the targets and it
has resolution capabilities [1], [6], [7] and [8].
The next figure portrays a typical scheme of a sensor
network with the three mentioned levels of nesting
complexity. Possible applications are environmental
monitoring, industrial sensing, infrastructure integrity,
surveillance for defence, battlefield and homeland
security.
1 ………… n
sensor head
Rx
receiver
Rx
thresholding
First level
Plot
plot extraction
Plot
Second level
Track
tracking
Track
Third level
to communication link and processing centre
Figure 1. A sensor network with the three levels.
In a hybrid approach to CSIP, the network consists of
different kinds of sensors, first level sensors and third
level sensors, spread out randomly over the surveillance
area. The number of first level sensors exceeds the
number of third level sensors. Close sensors exchange
data. From local interactions, sensors form an efficient
system that follows the target, i.e. local communication
leads to a self-organizing network. A similar approach is
described in [15], where a distributed solution for the
tracking problem in wireless and ad-hoc sensor network
is described as well.
Self-organization and emerging behaviour are novel
areas of investigation. Researchers associated with the
Santa Fe Institute in New Mexico play an active role in
this field (see www.santafe.edu). Applications of this
theory can be found in the area of surveillance problems,
environmental monitoring [9], and homeland security
[4].
The paper is organized as follows:
• section 2 briefly recalls results concerning the
theory of self-organizing systems and the
theory of random graphs;
• section 3 provides the description of our
approach;
•
•
section 4 explains our experimental results;
section 5 gives conclusions.
2. Basic concepts
Our approach to the distributed target detection,
localization and tracking aims to combine the theory of
random graphs with the theory of self-organizing
systems. This section summarizes the basic concepts
and definitions of the two fields.
Self-organization can be defined as the spontaneous
creation of a globally coherent pattern out of local
interactions among initially independent components
[10]. Flocks of birds, shoals of fish, swarms of bees are
examples of self-organizing systems; they move
together in an elegantly synchronized manner without a
leader which coordinates them and decides movement.
Characteristics of self-organizing systems are:
global order from local interactions, distributed
control, robustness and resilience, organization and
emergent properties [10]. In a self-organized system,
its elements affect only close elements; distant parts of
the system are basically independent. The control is
distributed, i.e. all the elements contribute to the
fulfilment of the task. The system is relatively
insensitive to perturbations or errors, and have a strong
capacity to restore itself. Initially independent
components form a coherent whole able to fulfil
efficiently a particular function.
Several engineered systems have been described as
self-organizing systems, for example, self-organizing
neural networks, swarm intelligence and selfconfiguring and adaptive sensor networks; for an
overview see [11].
The most natural way to approach random network
topology is by means of the theory of random graphs
[12], [13]. Using the theory of random graphs, an upper
bound to the estimated number of active sensors at each
time step is computed.
A graph G is a pair G = (V (G ), E (G )) of finite
sets with the following relationship:
⎛V (G) ⎞
⎟⎟
E (G) ⊆ ⎜⎜
⎝ 2 ⎠
where
⎛V(G)⎞
⎟⎟
⎜⎜
⎝ 2 ⎠
(1)
denotes all subsets of V (G ) containing
exactly two elements. The elements of V (G ) are called
vertices of the graph G and the elements of E (G ) are
called edges of G .
Two vertices v and w are said to be adjacent if
{v, w} is an edge of G . The neighbourhood of a vertex
v in G is the set of vertices that are adjacent to v . The
degree of the vertex v in G , denoted by d G (v ) , is the
cardinality of the neighbourhood of v in G . A set
2
W ⊆ V (G ) is a clique of G if any two vertices of W
are adjacent. In the next figure, a graph is visualized.
c
a
d
b
future work.
We suppose that the number of simple sensors is
large compared to the number of complex ones. In the
next figure it is shown an instance of our network
architecture; each complex sensor (large circle) is the
centre of a star sub-network whose elements are simple
sensors (small circle).
Figure 2. A graph G with vertex set V (G ) = {a, b, c, d }
and edge set E (G ) = {{a, b}, {a, c}, {b, c}{a, d }} .
A random graph G is a graph G with a probability
distribution over its edges. Given two vertices i and j
in V (G ) , an edge between v and w occurs with
probability p , where p is a fixed value in the closed
interval [0,1] . In a random graph, each pair of vertices
i, j defines a binary random variable which can assume
value 0 and 1 as follows:
⎧1
X i, j = ⎨
⎩0
if {i,j} ∈ E(G)
(2)
otherwise
All the random variables
X i , j follow the same
Pr{ X i , j = 1} = p and
Pr{ X i , j = 0} = 1 − p and the random variables are
independent.
probability distribution,
i.e.
Figure 3. Network architecture.
3. Model of Surveillance System
Sensors are randomly spread out over a two dimensional
and squared surveillance area. It is reasonable to assume
that they will be uniformly distributed over it.
Our network consists of two types of sensors, simple
and complex. As in [5], simple sensors have only the
capability of sensing their coverage area, compute binary
information and transmit data to complex sensors.
Binary information is encoded by a 1 if sensor detects
something crossing its coverage area and by a 0
otherwise. Complex sensors, instead, have computation
capabilities, they are able to locate the target by applying
the maximum likelihood estimation algorithm described
in [5]. In our analysis, however, a modification to the
original approach in [5] has been done. In particular, the
sensor detection probability is not an exponential decay
function but, rather, a quadratic function to emulate the
wave propagation by spherical waves. Once the target
location has been estimated it is processed by a classical
Kalman filter algorithm to form a target track [7], [8].
Sensors exchange information only if they are close, i.e.
if the overlapping of their coverage areas is greater than
a fixed constant (strong overlapping). Simple sensors
communicate with complex sensors and complex sensors
with both simple and complex ones. A two-way efficient
local communication among sensors is hypothesised.
Details on the communication protocol are object of
A clustering architecture has been implemented:
simple sensors are the elements of the clusters and
complex ones are the heads of the clusters. Since
sensors are randomly deployed, it is possible that some
simple sensor does not belong to any cluster, i.e. no
complex sensor is inside the sensor coverage area.
These sensors are useless, because the information they
compute cannot be processed by any complex sensor.
This is a limitation of our model and the problem will
be the object of future research.
We investigate the case when only one target is
crossing within the surveillance area. It is assumed that
initially the target is outside the surveillance area. Our
objective is to detect and track the target, minimizing
the tracking error and the power consumption of the
sensors in the network.
Being sensors provided with a limited amount of
energy, an asleep-awake mechanism for sensors has
been implemented. Principles of design sensors are
such that they are asleep for most of the time, their
wakeup is very fast in the sense that they start
processing quickly and they minimize the work while
awake, see [14].
Our approach is similar to the one in [9] called
“Frisbee model”. Sensors which are far from the
current target position are turned off since they are not
needed. When the target track estimation is carried out,
only a limited zone of the network that is close to the
target is kept in its fully active state. The active zone is
3
centred at the predicted location of the target that is
being tracked and the zone moves through the network
along with the target. To make the estimation of target
track more accurate, in addition to the active zone
around the predicted target location at the current time
step, there is another zone of active sensors centred
around the prediction of target track at the previous
recursive step. We call this approach “Frisbee model
with memory”. Sensors which are not in the two abovementioned zones are in an asleep state and they do not
contribute to the target track estimation at the current
time step.
Because the target location algorithm of [5] requires
the knowledge of the position of the single sensors, we
assume that complex sensors are able to compute and
store the positions of close simple sensors. To evaluate
their positions, multilateration technique can be used; to
this end, complex sensors compute the delay of simple
sensors’ replies to a broadcast message.
Simple sensors monitor their coverage area, awake
close complex sensors, transmit their binary information
to them and fall asleep. Complex sensors collect data
from simple sensors, process their information as in [5]
and compute the estimated position of the target. At this
stage complex sensors choose which simple sensors will
be used to detect the target at next step. Sensors that are
in the area centred in the current estimated position of
the target and ones centred in the previous estimated
position of the target are awaken.
Applying the theory of random graphs, the expected
number of active sensors at each time step and the
correspondent standard deviation are computed in
Appendices 1 and 2. These parameters can be very
useful in the analysis of the performance of the network.
If many simple sensors are activated, then the estimation
will be very accurate. On the other hand, being sensors
provided with a limited amount of prime energy, a
reduction of the network life will be reported.
The implemented system is an adaptive selfconfiguring system, i.e. a self-organizing system. It
consists of a collection of independent randomly located
sensors that, carrying ahead local interactions, estimate
the position of the target without a centralized control
unit that coordinates their communication. It is fault
tolerant and adapts to changing conditions. Furthermore,
it is able to self-configuring, i.e. there is not an external
entity that configures the network. Finally, the task is
performed efficiently, i.e. it guarantees both a reasonably
long network life good target tracking performances as
shown in Section 4.
4. Case Study
In this section we illustrate the results obtained by a
Monte Carlo simulation program that has been prepared
to emulate a random network for target detection and
tracking. The network of sensors that has been emulated
is depicted in figure 4; in particular, the circles represent
the position of the sensors in an x-y Cartesian plane, the
dashed lines the connections between simple sensors
and complex sensors, the solid lines the connection
between complex sensors. The surveillance area is
squared and the number of dispersed sensors is N=100,
of which 80 are simple sensors and 20 are complex.
The sensors are uniformly distributed over the
surveillance area; the location of each sensor is
supposed to be known. The extension of the
surveillance area is 20m by 20m in the example; but it
can be also, say, 20km by 20km, and the corresponding
tracking performance will be degraded accordingly.
Figure 5 shows with stars the successive position of a
target that moves along two straight lines of different
headings; the number of target positions is 49 in the
numerical example that follows. In this example, there
is at least one active complex sensor that performs the
following calculations:
i.
ii.
iii.
iv.
estimation of the target location on the
basis of the detections achieved by the
sensors in the Frisbee model with memory;
calculation of the accuracy of target
position measurements via the Cramer-Rao
lower bound (CRLB);
application of the tracking algorithm to the
sequence of target measurements; a
standard Kalman filter with four-state
components (target position in xcoordinate, target position in y-coordinate,
target speed in x-coordinate, target speed
in y-coordinate) has been adopted; the
covariance
matrix
of
the
target
measurements has been determined on the
basis of the CRLB analysis of point ii;
determination of the position of the Frisbee
model with memory; in the numerical
example that follows each Frisbee is a
circle with a radius of 4.5m: this number is
related to the sensor coverage which is 3m
in this example.
The number of independent Monte Carlo simulation
runs is 100. The average number of active sensors as
the target proceeds along its 49 successive positions is
displayed in figure 6; the figure contains two curves:
the one with “+” refers to the Monte Carlo simulation,
while the other with dots represents the analytical result
calculate on the basis of the theory described in
Appendices 1 and 2. it is noted that just about 15% of
the total number of sensors is active while the majority
of sensors is asleep.
The performance of target tracking algorithm is
summarised in the next four figures: figure 7 to 10. In
particular, figures 7 and 8 refer to the tracking position
error along x-coordinate, while figures 9 and 10 relate
to the tracking position error along y-coordinate.
Figures 7 and 9 show the estimation bias (in m), while
figures 8 and 10 give the estimation error standard
deviation (in m). Each figure displays four curves: the
curves labelled with “+” refer to the measurement of
4
target position as obtained by applying the algorithm in
[5] using only the sensors awaken by the “Frisbee model
with memory” (we refer to this as self-organized
network of sensors), while the curves labelled with
circles relate to the corresponding estimation smoothed
by the tracking filter; the curves labelled with a cross are
pertinent to the measured position of the target of the
whole network (i.e.: all the 100 sensors are used to
estimate the target track), and the curve labelled with
squares concern with the corresponding estimation
smoothed by the tracking filter. By a close look to the
achieved simulation results, it appears that,
notwithstanding the limited number of active sensors
(15% of the total number), the bias and error standard
deviation favourably compare with the performance that
would be offered by the whole network. Also the
comparison between the measurement and the estimation
curves shows the benefit achieved by the tracking filter
with the self-organizing network.
Figure 4. Network of sensors of the case study in
section 4; the sensor are indicated by circles; the
complex sensors are connected by the solid lines,
simple and complex sensor by dashed lines.
5. Conclusions and Future Work
In this paper we have sketched a clustering architecture
of a distributed network of sensors randomly dispersed in
the surveillance area. The sensors are much less costly
than conventional long range high quality sensors. The
network trades-off the simplicity of each sensor with the
large number of them. We have presented a surveillance
strategy which accounts for the simplicity of the sensors
and their random location. A Monte Carlo simulation has
evaluated the accuracy of tracking a target which moves
in the surveillance area. It is noted that a limited number
of sensors are awake and follow/anticipate the target
movement; thus, the network self-organizes to detect
and track the target. This surveillance function is
performed efficiently: i.e., with limited sensor prime
power and with a reduced number of sensors in the
whole network.
However, our work presents some limitations, such
as known sensor locations, two-way efficient local
communication, these will be addressed in the future. In
details, we will investigate the following points:
i.
ii.
iii.
iv.
v.
design of an efficient communication
protocol among sensors in the network,
design of an efficient asleep/awake sensor
mechanism,
design of target location estimation
algorithms with unknown sensor positions,
adoption of alternative sensor organization
in addition to the Frisbee model with
memory (for instance, sub sets of sensors
arranged as a star),
determination of upper bounds on the
number of useless simple sensors for any
fixed sensor probability distribution.
Figure 5. Trajectory of the target (crosses) and
position of the sensors (circles).
Figure 6. Average number of active sensors as
function of the step number of the algorithm;
simulation and theoretical values.
5
Figure 7. Bias of the estimation of the target xcoordinate.
Figure 9. Bias of the estimation of the target ycoordinate.
Figure 8. Standard deviation of the estimation of
target x-coordinate.
Figure 10. Standard deviation of the estimation of
the target y-coordinate.
6
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Appendix 1: The expected degree of a vertex in
a random graph
The objective is to give an estimation to the degree of a
vertex in a random graph G = (V (G ), E (G )) on n
vertices [12],[13]. This result will allow us to calculate
in Appendix 2 the expected number of sensors active at
each time step.
Given two vertices i and j in V (G ) , suppose p to
be the probability that an edge occurs between i and
j , where p is a fixed value in the closed interval
[0,1] . The correspondent random variable X i , j takes
the value 1 with probability p ( Pr{ X i , j = 1} = p ) and
the
value
0
with
( Pr{ X i , j = 0} = 1 − p ).
probability
1− p
The following random variable is defined
DG (v) = d G (v)
(A1)
We compute E[DG(v)], where E[X] denotes the
expected value of the random variable X. The random
variable DG(v) takes positive integer values in the
closed interval [0, n-1].
Lemma 1. The probability that a vertex v in G has k
neighbours, where k ∈ [0, n-1], is
⎛ n − 1⎞ k
⎟⎟ p (1 − p ) n−k −1
Pr{DG (v) = k} = ⎜⎜
⎝ k ⎠
(A2)
Proof.
The proof is divided in two steps. First, we compute the
value of the probability for a particular feasible
configuration of the graph, then, we extend the
calculation for all the possible feasible configurations.
Let E be defined as the event “vertex v is adjacent
only to the vertices v1 , v2 ,K, vk ”, i.e.
X v ,vi = 1 ∀ i = 1,..., k and
X v ,w = 0 ∀w ∈V (G ) − {v, v1 , v2 ,..., vk }
(A3)
Denoting V (G ) − {v, v1 , v2, ..., vk } by Wk , it is possible to
rewrite (A3) as
k
⎧
⎫
E = ⎧⎨ I X v ,vi = 1⎫⎬ ∩ ⎨ I X v ,w = 0⎬
⎩i =1
⎭ ⎩w∈Wk
⎭
(A4)
Since the random variables { X i , j }i ≠ j are pair-wise
independent, then
k
⎧
⎫
Pr{E} = Pr ⎧⎨ I X v,vi = 1⎫⎬ Pr ⎨ I X v ,w = 0⎬
⎩i =1
⎭ ⎩w∈Wk
⎭
(A5)
7
Appendix 2: The expected number of sensors
active at each time step
We have that
⎧k
⎫
Pr ⎨ I X v ,vi = 1⎬ = p k
⎩ j =1
⎭
(A6)
And
⎧
⎫
Pr ⎨ I X v ,w = 0⎬ = (1 − p ) n−k −1
w
∈
W
⎩ k
⎭
(A7)
Hence,
⎧
⎫
Pr ⎨ I X v ,w = 0⎬ = (1 − p ) n−k −1
⎩w∈Wk
⎭
(A8)
The event “ DG (v) = k ” can be described as the
union of the elementary events “vertex v is adjacent
only to k vertices in V (G ) ”. It is well know that the
number of these elementary events is
⎛ n − 1⎞
⎜⎜
⎟⎟
⎝ k ⎠
(A9)
Since these elementary events are pair-wise disjoint,
the conclusion is that
⎛ n − 1⎞ k
⎟⎟ p (1 − p ) n−k −1
Pr{DG (v) = k } = ⎜⎜
⎝ k ⎠
(A10)
The random variable, therefore, is a binomial random
variable, i.e. DG (v) ~ B(n − 1, p) .
Theorem 2. The expected degree of a vertex v is
n −1
⎛ n − 1⎞ k
⎟⎟ p (1 − p ) n − k −1 = (n − 1) p
E[ DG (v )] = ∑ k ⎜⎜
k
k =0 ⎝
⎠
(A11)
Proof.
If follows immediately from the computation of the
mean value of a binomial random variable.
Theorem 3. The variance of the degree of a vertex v is
Var[ DG (v )] = ( n − 1) p (1 − p )
(A12)
Proof.
If follows immediately from the computation of the
variance of a binomial random variable.
The results presented in Appendix 1, i.e. Theorems 2
and 3, are applied to the case study described in Section
4.
The random graph G consists of 100 vertices
uniformly distributed over the square area. Vertices of
the graph correspond to both simple and complex
sensors of the case study. In this analysis, we do not
distinguish between simple and complex sensors,
because in our case study complex sensors detect the
target as well. Two vertices of the graph G are adjacent
if the distance of their correspondent sensors is at most
3m, this value is related to the sensor coverage radius of
the case study.
In order to estimate the number of sensors in the area
of the Frisbee at each time step, the random graph H is
introduced. It has the same vertex set as G and
vertices are adjacent in H if the distance of their
correspondent sensors is at most 4.5m, this value
corresponds to the value of the Frisbee radius. The
expected degree of the closest sensor in H to the
estimated position of the target gives an estimation to
the number of sensors contained in the area of the
frisbee at each time step, since sensors are uniformly
distributed over the surveillance area.
From now on, only the graph H is considered. The
probability p that an edge occurs between two vertices
in H is 0.16, since sensors are uniformly distributed
over the surveillance area. Applying the results in
Appendix 1 we have that the expected number of
sensors contained in the area of the frisbee is 15.84 and
the deviation standard is 3.64.
In our approach, two areas are active at each time
step and in our case study the two areas overlap
significantly. The size ( sO ) of their overlapping area
can be computed using simple geometry arguments. Its
value is 58.68. Since sensors are distributed uniformly
over the surveillance area, the expected number of
sensors in the overlapping area can be computed as
follows:
14.62 = 15.84
so
sF
(A12)
where s F is the size of the area of the frisbee. Hence,
the expected number of sensors in the area of the
Frisbee which are not in the intersection is 1.22.
Therefore, the estimated number of active sensors at
each time step is 17.06 with a standard deviation of
3.64.
The mathematical model based on random graphs
can be used to describe networks with non-uniformly
sensor distributions as well. Fixing properly p , the
results presented in Appendix 1 remain valid for any
sensor distribution.
8