Optimal Periodic Sensor Scheduling in Networks of Dynamical Systems

Abstract

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.

Energy-Aware Sensor Selection in Field Reconstruction

“…Therefore, we also write as , where is the row-wise vector of . To address the problem of sensor selection in the context of field estimation, it was shown in [3] that the non-zero columns of coefficient matrix characterize the selected sensor measurements. Suppose, for example, that only the th sensor reports its th measurement to the FC.…”

Sparsity-aware field estimation via ordinary Kriging

“…For a nonconvex problem, such as the one considered here, the convergence of ADMM is not guaranteed [9]. However, our simulations and those in other works such as [9], [12], [13], [16] demonstrate that ADMM converges well when the value of ρ is chosen to be appropriately large. We refer interested readers to [9,Sec.3] for the discussion on the choice of ρ.…”

Sensor Selection for Estimation with Correlated Measurement Noise

“…We remark that the decomposition given in (8) is readily obtained through an eigenvalue decomposition of the positive definite matrix R, and it helps us in deriving the closed form of the Fisher information matrix with respect to w. Substituting (8) into (6), we obtain…”

“…Therefore, the problem of sensor selection/scheduling arises, which aims to strike a balance between estimation accuracy and sensor activations over space and/or time. The importance of sensor selection has been discussed extensively in the context of various applications, such as target tracking [4], bit allocation [5], field monitoring [6], [7], optimal control [8], power allocation [9], [10], optimal experiment design [11], and leader selection in consensus networks [12].…”