Sensor Selection Based on Generalized Information Gain for Target Tracking in Large Sensor Networks

Abstract

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 lookahead 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.

On the resource allocation problem in wireless networked control systems

“…For minimization of both the final or average estimation error, myopic policies, policies which look ahead only one time-step, are shown to be optimal through the usage of a generalized information gain function under some regularity conditions [13]. By using an importance indicator based on the difference between the mean-square error estimate at local sensors and the prediction at the central processor side, sensor scheduling for a shared channel is investigated in [16].…”

Sensor Selection for Estimation with Correlated Measurement Noise

“…In [18]- [20], the problem of sensor selection with correlated noise was formulated so as to minimize an approximate expression of the estimation error subject to an energy conarXiv:1508.03690v2 [stat.AP] 21 Mar 2016 straint or to minimize the energy consumption subject to an approximate estimation constraint. In [21], a reformulation of the multi-step Kalman filter was introduced to schedule sensors for linear dynamical systems with correlated noise.…”

“…We also propose a greedy algorithm to solve the corresponding sensor selection problem, where we show that when an inactive sensor is made active, the increase in Fisher information yields an information gain in terms of a rank-one matrix. The proposed sensor selection framework yields a more accurate sensor selection scheme than those presented in [18]- [20], because the schemes of [18]- [20] consider an approximate formulation where the noise covariance matrix is assumed to be independent of the sensor selection variables. We further demonstrate that the prior formulations for sensor selection are valid only when measurement noises are weakly correlated.…”

“…We further demonstrate that the prior formulations for sensor selection are valid only when measurement noises are weakly correlated. In this scenario, maximization of the trace of the Fisher information matrix used in [20] is equivalent to the problem of maximizing a convex quadratic function over a bounded polyhedron. The resutling problem structure enables the use of optimization methods with reduced computational complexity.…”

“…In a preliminary version of this paper [22], we studied the problem of sensor selection using the same framework as in [18]- [20]. Compared to [22], we have the following new contributions in this paper.…”