Abstract-In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the trace of the inverse of the Bayesian Fisher information matrix, is minimized subject to energy constraints. Fisher information has been widely used as an effective sensor selection criterion. However, existing information-based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics. By contrast, here we derive the closed form of the Fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime, and develop both a convex relaxation approach and a greedy algorithm to find near-optimal solutions. We further extend our framework of sensor selection to solve the problem of sensor scheduling, where a greedy algorithm is proposed to determine non-myopic (multi-time step ahead) sensor schedules. Lastly, numerical results are provided to illustrate the effectiveness of our approach, and to reveal the effect of noise correlation on estimation performance.

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In this paper, we study the target tracking problem in wireless sensor networks (WSNs) using quantized sensor measurements under limited bandwidth availability. At each time step of tracking, the available bandwidth R needs to be distributed among the N sensors in the WSN for the next time step.The optimal solution for the bandwidth allocation problem can be obtained by using a combinatorial search which may become computationally prohibitive for large N and R. Therefore, we develop two new computationally efficient suboptimal bandwidth distribution algorithms which are based on convex relaxation and approximate dynamic programming (A-DP). We compare the mean squared error (MSE) and computational complexity performances of convex relaxation and A-DP with other existing suboptimal bandwidth distribution schemes based on generalized Breiman, Friedman, Olshen, and Stone (GBFOS) algorithm and greedy search. Simulation results show that, A-DP, convex optimization and GBFOS yield similar MSE performance, which is very close to that based on the optimal exhaustive search approach and they outperform greedy search and nearest neighbor based bandwidth allocation approaches significantly. Computationally, A-DP is more efficient than the bandwidth allocation schemes based on convex relaxation and GBFOS, especially for a large sensor network.

We consider the problem of finding optimal time-periodic sensor schedules for estimating the state of discrete-time dynamical systems. We assume that multiple sensors have been deployed and that the sensors are subject to resource constraints, which limits the number of times each can be activated over one period of the periodic schedule. We seek an algorithm that strikes a balance between estimation accuracy and total sensor activations over one period. We make a correspondence between active sensors and the nonzero columns of estimator gain. We formulate an optimization problem in which we minimize the trace of the error covariance with respect to the estimator gain while simultaneously penalizing the number of nonzero columns of the estimator gain. This optimization problem is combinatorial in nature, and we employ the alternating direction method of multipliers (ADMM) to find its locally optimal solutions. Numerical results and comparisons with other sensor scheduling algorithms in the literature are provided to illustrate the effectiveness of our proposed method. Index TermsDynamical systems, alternating direction method of multipliers, state estimation, sensor networks, sensor scheduling, sparsity.

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