332 research outputs found
Sensor Selection Based on Generalized Information Gain for Target Tracking in Large Sensor Networks
In this paper, sensor selection problems for target tracking in large sensor
networks with linear equality or inequality constraints are considered. First,
we derive an equivalent Kalman filter for sensor selection, i.e., generalized
information filter. Then, under a regularity condition, we prove that the
multistage look-ahead policy that minimizes either the final or the average
estimation error covariances of next multiple time steps is equivalent to a
myopic sensor selection policy that maximizes the trace of the generalized
information gain at each time step. Moreover, when the measurement noises are
uncorrelated between sensors, the optimal solution can be obtained analytically
for sensor selection when constraints are temporally separable. When
constraints are temporally inseparable, sensor selections can be obtained by
approximately solving a linear programming problem so that the sensor selection
problem for a large sensor network can be dealt with quickly. Although there is
no guarantee that the gap between the performance of the chosen subset and the
performance bound is always small, numerical examples suggest that the
algorithm is near-optimal in many cases. Finally, when the measurement noises
are correlated between sensors, the sensor selection problem with temporally
inseparable constraints can be relaxed to a Boolean quadratic programming
problem which can be efficiently solved by a Gaussian randomization procedure
along with solving a semi-definite programming problem. Numerical examples show
that the proposed method is much better than the method that ignores dependence
of noises.Comment: 38 pages, 14 figures, submitted to Journa
Adaptive Non-myopic Quantizer Design for Target Tracking in Wireless Sensor Networks
In this paper, we investigate the problem of nonmyopic (multi-step ahead)
quantizer design for target tracking using a wireless sensor network. Adopting
the alternative conditional posterior Cramer-Rao lower bound (A-CPCRLB) as the
optimization metric, we theoretically show that this problem can be temporally
decomposed over a certain time window. Based on sequential Monte-Carlo methods
for tracking, i.e., particle filters, we design the local quantizer adaptively
by solving a particlebased non-linear optimization problem which is well suited
for the use of interior-point algorithm and easily embedded in the filtering
process. Simulation results are provided to illustrate the effectiveness of our
proposed approach.Comment: Submitted to 2013 Asilomar Conference on Signals, Systems, and
Computer
Monte Carlo Set-Membership Filtering for Nonlinear Dynamic Systems
This chapter considers the nonlinear filtering problem involving noises that are unknown and bounded. We propose a new filtering method via set-membership theory and boundary sampling technique to determine a state estimation ellipsoid. In order to guarantee the online usage, the nonlinear dynamics are linearized about the current estimate, and the remainder term is then bounded by an optimization ellipsoid, which can be described as the solution of a semi-infinite optimization problem. It is an analytically intractable problem for general nonlinear dynamic systems. Nevertheless, for a typical nonlinear dynamic system in target tracking, some certain regular properties for the remainder are analytically derived; then, we use a randomized method to approximate the semi-infinite optimization problem efficiently. Moreover, for some quadratic nonlinear dynamic systems, the semi-infinite optimization problem is equivalent to solving a semi-definite program problem. Finally, the set-membership prediction and measurement update are derived based on the recent optimization method and the online bounding ellipsoid of the remainder other than a priori bound. Numerical example shows that the proposed method performs better than the extended set-membership filter, especially in the situation of the larger noise
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