Journal of Robotics, Networking and Artificial Life, Vol. 3, No. 2 (September 2016), 128-131

Global sensor selection for maneuvering target tracking in clutter

Wenling LiThe Seventh Research Division, Beihang University
37 Xueyuan Road, Haidian District, Beijing, 100191, China
Yingmin Jia

The Seventh Research Division, Beihang University
37 Xueyuan Road, Haidian District, Beijing, 100191, China
E-mail: lwlmath@buaa.edu.cn, ymjia@buaa.edu.cn

Abstract
This paper studies the problem of sensor selection for maneuvering target tracking in the cluttered environment. Bymodeling the target dynamics as jump Markov linear systems, a decentralized tracking algorithm is developed byapplying the extended Kalman filter and the probabilistic data association technique. A cost function that minimizes
the expected filtered mean square position error is utilized and a sensor selection scheme is proposed. A numericalexample is provided to illustrate the effectiveness of the proposed approach.
Keywords: Sensor selection, Jump Markov system, Extended Kalman filter, Maneuvering target tracking, Clutter

1. Introduction
Sensor or node selection has been found a wide range ofapplications in diverse civilian and military areas such1
as sensor placement for structures, chemical plant2
3,4control and wireless networks. In recent years theproblem of sensor selection for target tracking has been
investigated. As pointed out in Ref. 5, the main idea
beyond sensor selection is to optimize a cost functionthat represents the localization accuracy constrained by
the number of active sensors. A cost function thatminimizes the geometrical dilution of precision (GDOP)
is used to derive the sensor selection scheme where thebest three sensors are selected. Based on the GDOPmeasure, an adaptive sensor selection strategy has been
proposed in which the signal power measurements areused. By combining with the prior information, which is
not accounted for the GDOP measure, global sensor

selection method that minimizes the expected filteredmean square position error have been studied forbearing-only tracking. Especially, two strategies
including the `add one sensor node at a time' and the`simplex' have been developed for selecting the best
subset of active sensors.6 These results are extended topropose local sensor selection schemes which do not
require the knowledge of all the sensors locations in thenetworks.
In the target tracking community, the single model
approach is used mainly for targets with fixed kinematic
behaviors while for targets with multiple kinematics
behaviors (i.e., maneuvering targets), the multiple
model tracking algorithm is preferred.7 The problem of
sensor selection for maneuvering target tracking has
been investigated in Ref. 8 and 9. To our knowledge,
little research has been done to deal with the problem of

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Wenling Li, Yingmin Jia

sensor selection for target tracking in the clutteredenvironment.
In this paper, we consider the problem of sensor
selection for maneuvering target tracking in thecluttered environment. By using the global knowledgeof all sensors locations, a cost function that minimizes
the expected filtered mean square localization error isdeveloped to select a given number of active sensors. As
the cost function is derived based on the decentralizedstructure, we investigate how to derive the decentralized
fusion formula by applying the basic extended Kalmanfilter (EKF) and the PDA technique so that the clutter
information can be combined into the cost function.
Meanwhile, we have to circumvent the difficulty
encountered in multiple model decentralized fusion.10
By minimizing the cost function, a sensor selection
scheme is proposed based on the `add one sensor node
at a time' strategy. Simulations are provided to illustrate
the effectiveness of the proposed algorithm.

originated power measurement from sensor s can bemodeled in a logarithmic formz k , s = K − 10η log10 (rk , s ) + vk , srk , s = ( xk − xs ) 2 + ( yk − ys ) 2，s = 1,2,  , N

where K and η ∈ [ 2,5] denote the transmission power
and the path loss exponent, respectively. They are
dependent on the radio environment, the antennacharacteristics and so on. ( xs , ys ) represents the positionof sensor s and rk , s is the relative distance between
sensor s and the target. N is the number of sensors.

vk , s is zero-mean white Gaussian with variance Rk , s .

Our aim is to find the set of active sensors that
optimizes the cost function. As the clutter is considered,
we should investigate how to combine the clutter
information into the cost function.
3. Sensor election for Maneuvering Target
Tracking in Clutter

2. Problem formulation

Decentralized fusion of EKF-PDA

In this paper, we consider a two-dimensional (2-D)
target-observer scenario. The target dynamics ismodeled as the following coordinated turn model

Assume that the target dynamics
measurement model can be represented bysin(ωT )1 0− 1−cos(ω ωT ) ωsin(ωT ) 0 1 1−cos(ω ωT )
ωx +w
xk +1k0 0 cos(ωT ) sin(ωT )  k
0 0 sin(ωT )T cos(ωT ) 
where xk = ( xk , yk , x k , y k ) denotes the target state.
( xk , yk ) and ( x k , y k ) represent the target position andvelocity components, respectively. ω denotes the turnrate and T is the sampling time period. ω k is zero-mean
white Gaussian noise with covariance Q k .
To formulate the target dynamics into the frameworkof jump Markov systems, we assume that at any time
the target motion obeys one of M dynamic behavior
models, which can be described by the above
coordinated turn model with different turn rate. The
switching between models is governed by a timehomogeneous first-order Markov chain rk with known

π ijtransition probability=P=
rk −1 i} .
{rk j=A radio receiver that provides the signal power
measurement is used throughout this paper. The target-andthexk +1 = Φ k xk + wk
z k , s = hs ( xk ) + vk , s , s = 1,2,  , N

where Φ k and the covariance ∑ k of wk are derived by
the best-fitting Gaussian approximation. hs is thenonlinear measurement function of sensor s . By
combining the EKF and the PDA technique, a single
forward run of the tracking algorithm proceeds asfollows for each sensor s.
First of all, the predicted mean and covariance are
obtained by using a standard Kalman filterxˆks|k −1 = Φ k −1 xˆks −1|k −1

Pks|k −1 = Φ k −1 Pks−1|k −1Φ Tk −1 + Σ k −1
Then, the predicted measurement and the innovation
covariance can be derived aszˆks|k −1 = hs ( xˆks|k −1 )vki , s = z ki , s − zˆki |k −1
S k , s = H k , s Pks|k −1 H kT, s + Rk , swhere H k , s is the Jacobian matrix of the nonlinear
function hs evaluated at xˆ k −1|k −1 .

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129sGlobal sensor selection for~S k , s = ( S k-,1s - S k-,1s Bk , s S k-,1s ) -1

i

After receiving the measurements Z k , s by sensor s, z k , s= S k , s - S k , s S k-,1s ( S k-,1s S k , s S k-,1s - Bk-,1s ) -1 S k-,1s S k , s

is validated if[ z ki , s − zˆks|k −1 ]T S k−,1s [ z ki , s − zˆks|k −1 ] < γ

where γ is the gate threshold.
By assuming that the number of clutter in the validated
region is assumed to be Poisson distributed, aparametric PDA technique is used to generate theassociation event probability
b k0, s =b ki , s =Wherebk , sbk , s + ∑ j =1 dmk , 2bk , sbk , s + ∑ j =1 dmk , 2jk ,s= S k , s + ( Bk-,1s - S k-,1s ) -1

Therefore,On the other hand, we have~
K k , s vk , s − K k , s ( ~z k , s − zˆks|k −1 ) = 0

which leads to~z k , s = [ I + ( Bk−,1s − S k−,1s ) −1 S k−,1s ]vk , s + zˆks|k −1

jk ,s, i = 1,  , mk , sd ki , s = exp(−0.5[vki , s ]T S k−,1s vki , s )1 − PD PG
PDPD is the detection probability, PG is the probability thatbk , s = λ | 2πS k , s |1/ 2

the measurement originated from the target falls into thevalidated region, and λ is the spatial density of clutter.
Finally, the updated estimates can be computed byxˆks|k = xˆks|k −1 + K k , s vk , s

Based on the above EKF-PDA tracking algorithm, we
can obtain the decentralized fusion formula. We assume
that each sensor knows its position and they share thecommon prior information. Suppose each active sensor
have obtained estimates xˆ k −1|k −1 and Pk −1|k −1 at time
step k-1, the filtered estimates can be derived by eachsensor via communicating with other active sensorsxˆk |k −1 = Φ k −1 xˆk −1|k −1xˆk |kPk |k −1 = Φ k Pk −1|k −1Φ Tk + Σ k −1~
H T R −1 [ ~z − h ( xˆ
= P [ P −1 xˆ+k |ki =1

H S−1
k ,smk , 2

Bk , s = β k0, s S k , s + ∑ β ki , s vki , s [vki , s ]T − vk , s vkT, si =1

In order to develop the decentralized fusion formula, wewould like to rewrite the updated mean and covarianceas the same form of the usual Kalman filter, i.e.,~+ K k ,s (~xˆ = xˆz k , s − zˆks|k −1 )~ ~ ~Pks|k = Pks|k −1 − K k , s S k , s K kT, ssk |ks
k |k −1~~
K k , s = Pks|k −1 H kT, s S k−,1s~~
S k , s = H k , s Pks|k −1 H kT, s − Rk , sk ,sk ,ssk |k −1) + H k , s xˆk |k −1 ]]~~ ~ ~K k , s S k , s K kT, s = Pks|k −1 H kT, s S k−,1s H k , s Pks|k −1~= K k , s S k , s S k−,1s S k , s K kT, s

When the signal power measurement is applied, theupdated covariance for the decentralized fusion of EKFPDA can be rewritten as J ,0Jf = Jp + 0,0 −1−1

Where J f = Pk |k , J p = Pk |k −1 andcos 2 φk , s , sin φk , s cos φk , s ~J = (10η log10 e) 2 ∑ Rk−,1s rk−, s2 2s∈N asin φk , s cos φk , s , sin φk , s 
Note that[H k , s = −10η log10 e rk−,1s cos φk , s , rk−,1s sin φk , s ,0,0]

where ( rk , s , φk , s ) is the position of sensor s relative toIt can be observed that our aim is to define ~z k , s and~Rk , s .To this end, we have

k ,sSensor selection

mk , 2vk , s = ∑ β ki , s vki , sK k ,s = P∑s∈N as∈N awhereTk ,sk |k −1 k |k −1~
Pk−|k1 = Pk−|k1−1 + ∑ H k−,1s Rk−,1s H k , sPˆks|k = Pˆks|k −1 − K k , s ( S k , s − Bk , s ) K kT, ssk |k −1~
Rk , s = Rk , s + ( Bk−,1s − S k−,1s ) −1

the predicted target position in polar coordinates.
The aim of sensor selection is to search for theminimum expected mean square posterior error which
can be expressed in terms of the posterior Fisher
information matrix. Specifically, the cost function to beminimized for sensor selection isρ ( N a ) = [ J −f 1 ]1,1 + [ J −f 1 ]2, 2

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Wenling Li, Yingmin Jia

Wheredenotes the (i,j)th element of the matrix A

where ‘tr’ represents the trace of the matrix, andA practical strategy called as ‘add one sensor node at atime’. For this strategy, an initial active set isestablished by using the exhaustive search, which
includes two active sensor nodes and requires
overconfigurations. Thenevaluating
the rest of sensor nodes are added to the initial active set
one at a time by minimizing.
4. Simulations
Three models corresponding to different turn rates areused. The sampling period is taken to be 1 s for target
motion model. The network consists of 30 sensors
randomly scattered over a field. The sensing range foreach sensor is 25 m. For the signal power measurements,
the transmission power is taken to be 9 dBm and thepath loss exponent is 3. The variance of themeasurement noise is 0.2 for all sensors. The detection
probability and the gate probability are set to 0.997 and0.999, respectively. The gate threshold is 16 and thespatial density of clutter is 0.1.
In the simulations, the root mean square error (RMSE)
in position is used for performance comparison. The
RMSE in position of the proposed algorithm withdifferent numbers of active sensors is shown in Fig.1. It
can be observed that the tracking performance isimproved as the number of active sensors is used andthe best performance is achieved when all the active
sensors in the sensing range are utilized.
5. Conclusion
In this paper, we propose a global sensor selection
scheme for tracking maneuvering target in the clutteredenvironment. A formulation of PDA for decentralized
fusion is derived which helps the definition of the costfunction for sensor selection. This is implemented bydeveloping novel measurement vector and noise
covariance matrix combining the clutter information.
Simulation results are provided to verify that theproposed algorithm.

Fig.1 RMSE in position of the proposed filter.

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