2
the threshold is not an easy task in general. In [12], a
probability framework based on Gaussian mixture models
(GMMs) for fusing location estimates, which may be biased
and insistent, is presented. The exact probability that local
sensors are biased is needed to construct the Gaussian
component of the mixture model. When the prior information
is unknown exactly, the performance of the method may
experience an evident degradation. In [13], to fuse incoherent
local estimates, a fast and fault-tolerant fusion algorithm
(IT-FFGCC) is proposed by introducing an
estimate-dependent adaptive parameter, which can obtain
robust fusion and the degree of robustness varies with that of
incoherency between estimates to be fused.
This paper addresses the problem of estimation fusion in
sensor network, in the presence of possible biased local
estimates. A sensor selection-based optimization model is
presented to deal with this problem. Sensor selection [14-17]
is one of the major tasks of sensor resource management
(SRM) in target tracking. Generally, the motivation of
selecting sensors rather than utilizing all
N sensors lies in
two aspects: computational efficiency of parameter estimation
and energy consumption of sensor operations. In this paper, it
is employed for another purpose: selecting a subset
Λ
of all
N
sensors with as much unbiased sensor reports as
possible.
Two key points need to be elaborated here. One is to
construct the objective function to optimize. The other one is
to develop an efficient method to solve the optimization
model. In view of the fact that unbiased local estimates is
affected only by random errors, we assumed that unbiased
local estimates gather together into a cluster, compared with
biased ones. This inspires us to construct the criterion to
optimize based on the similarity measure among local
estimates. In addition, sensor selection is a complex
combinatorial optimization problem in essence. One of its
biggest difficulties is the combinatorial nature. Along with the
increasing of the sensor number, the complexity of the
problem is challenging. Here, we invoke the cross entropy
(CE) method [18-21] to solve the above optimization model.
The CE (cross-entropy) method is a generalized Monte-Carlo
technique for combinatorial and continuous optimization, and
(originally) for estimation of rare-event probabilities. The
main idea behind the CEO is representing the solution space
with a set of parameters and defining a probability distribution
on these parameters. Then, two successive steps are iterated:
sampling from the existing distribution, and updating this
distribution using a set of elite (better value) samples[18].
They are inherently global search methods and, therefore,
may reduce the risk of getting stuck in shallow local maxima.
The rest of the paper is organized as follows. Section Ⅱ
formulates the problem of sensor selection-based fusion.
Section Ⅲ illustrates the procedure of implementing the
proposed sensor selection-based fusion model by CE method.
Simulation results compared with competitive algorithms are
given in Section Ⅳto demonstrate the power of the proposed
approach. Finally, concluding remarks are in Section Ⅴ.
Ⅱ. PROBLEM FORMULATION
Consider an estimation fusion problem with
N
sensors and
one target in the surveillance region. It is assumed that one
part of sensor reports is believable (unbiased), and the other
part is faulty (biased). Each local track at time k is represented
by a two-tuples
ˆ
{, }
mm
kk
xP ( 1,2,..., ;)
s
mN= .
where
ˆ
m
k
x and
m
k
mean the state estimate and error
covariance, respectively. To simplify, the time index k will be
omitted later.
Obviously, local tracks produced by biased measurements
are also biased. In this case, local estimates from different
sensors may differ from each other significantly. For example,
one position estimate is far from another by more than a
kilometer, but their respective covariance matrixes are in a
small level indicating that the estimate is accurate to within a
few meters [13]. This is due to that, the measurement model
adopted by some local tracker mismatch with the real one
(where the covariance information is convincing no longer,
which cannot reflect the accuracy of the local estimate well).
The objective of the paper is to select a subset
Λ
of all
N
sensors with as much unbiased sensor reports as possible.