Optimal Stationary State Estimation Over Multiple Markovian Packet Drop Channels

TL;DR

This paper develops an optimal stationary state estimator for systems with multiple Markovian packet drop channels, providing conditions for stability and detectability, and proposing a computationally efficient locally optimal estimator.

Contribution

It introduces a new optimal stationary estimator for multi-channel Markovian drop systems and derives explicit stability and detectability conditions, including a decoupling approach for complexity reduction.

Findings

Derived necessary and sufficient conditions for MS stabilizing solutions.

Proposed a decoupling method for MS detectability analysis.

Numerical simulations validate the estimator performance and theoretical conditions.

Abstract

In this paper, we investigate the state estimation problem over multiple Markovian packet drop channels. In this problem setup, a remote estimator receives measurement data transmitted from multiple sensors over individual channels. By the method of Markovian jump linear systems, an optimal stationary estimator that minimizes the error variance in the steady state is obtained, based on the mean-square (MS) stabilizing solution to the coupled algebraic Riccati equations. An explicit necessary and sufficient condition is derived for the existence of the MS stabilizing solution, which coincides with that of the standard Kalman filter. More importantly, we provide a sufficient condition under which the MS detectability with multiple Markovian packet drop channels can be decoupled, and propose a locally optimal stationary estimator but computationally more tractable. Analytic sufficient and necessary MS detectability conditions are presented for the decoupled subsystems subsequently. Finally, numerical simulations are conducted to illustrate the results on the MS stabilizing solution, the MS detectability, and the performance of the optimal and locally optimal stationary estimators.