Optimal networked state estimation in the presence of multi-channel correlated packet losses

Abstract

This paper studies the optimal estimation problem for linear time-invariant systems over lossy communication networks subject to multi-channel packet losses. In its full generality, we assume that the random packet losses are spatially correlated across different channels. The problem is addressed by employing a modified Kalman filter to estimate the system’s states, and the primary issue under study is the convergence of the state estimate under a mean-square criterion. This convergence is shown to be equivalent to the existence of a stabilizing solution to a modified algebraic Riccati equation. We provide a necessary and sufficient condition to characterize the existence of the stabilizing solution, and show that the solution can be computed by solving a set of linear matrix inequalities. Additionally, from a robust convergence perspective, we consider further packet losses whose probabilities are unknown and uncertain. We develop a matrix measure referred to as the critical matrix to characterize the maximal tolerance for the modified Kalman filter to converge. Specifically, we show that the mean-square estimation error is bounded if and only if the critical matrix satisfies a positive semi-definiteness condition.