An Improved Stability Condition for Kalman Filtering with Bounded Markovian Packet Losses

TL;DR

This paper presents a less conservative, invariant stability condition for Kalman filtering under Markovian packet losses, formulated as an LMI feasibility problem, with demonstrated effectiveness through numerical examples.

Contribution

It introduces an improved, invariant stability criterion for Kalman filtering with Markovian packet losses, formulated as an LMI, reducing conservativeness compared to prior results.

Findings

The stability condition is invariant under similarity transformations.

The new condition is less conservative than existing criteria.

Numerical examples confirm the effectiveness of the proposed stability check.

Abstract

In this paper, we consider the peak-covariance stability of Kalman filtering subject to packet losses. The length of consecutive packet losses is governed by a time-homogeneous finite-state Markov chain. We establish a sufficient condition for peak-covariance stability and show that this stability check can be recast as a linear matrix inequality (LMI) feasibility problem. Comparing with the literature, the stability condition given in this paper is invariant with respect to similarity state transformations; moreover, our condition is proved to be less conservative than the existing results. Numerical examples are provided to demonstrate the effectiveness of our result.