Stability of Kalman filtering with a random measurement equation: Application to sensor scheduling with intermittent observations

Abstract

Studying the stability of the Kalman filter whose measurements are randomly lost has been an active research topic for over a decade. In this paper we extend the existing results to a far more general setting in which the measurement equation, i.e., the measurement matrix and the measurement error covariance, are random. Our result also generalizes existing ones in the sense that it does not require the system matrix to be diagonalizable. For this general setting, we state a necessary and a sufficient condition for stability, and address their numerical computation. An important application of our generalization is a networking setting with multiple sensors which transmit their measurements to the estimator using a sensor scheduling protocol over a lossy network. We demonstrate how our result is used for assessing the stability of a Kalman filter in this multi-sensor setting.

Multi-sensor state estimation over lossy channels using coded measurements

“…We have that {D t : t ∈ N} is a sequence of random matrices, with discrete distribution, such that {D t : t ∈ N} is a statistically independent set, and whose statistics are cyclostationary with period M . Hence, it follows from [15,Proposition 18] that the conditions for [15,Theorem 14] are guaranteed. Also, these conditions consider all FMO blocks of (6)- (7).…”

“…Theorem 6 (Combination of [15,Proposition 18] and [15,Theorem 14]) Suppose that the sequence of coding matrices {H t : t ∈ N} is P -periodic, i.e., H t+P = H t , for all t ∈ N. Then, the MMSE estimator using coded measurements is stable if…”

“…In [15], the authors derived a necessary and sufficient condition, having a trivial gap, for the stability of a MMSE estimator. These condition is stated in very general terms, so it can be applied in a wide range of settings.…”

Estimation-Based and Dropout-Dependent Control Design for Aeroengine Distributed Control System with Packet Dropout

“…Furthermore, the peakcovariance stability of Kalman filters is proven to be the mean-square stability for a random packet dropout [10,11]. These theories extend to the analysis of Kalman filters with complicated systems [12][13][14][15][16]. The design of Kalman filters with state-dependent packet dropout for the hybrid measurement system is investigated in reference [12].…”

“…Marelli analyzed the stability for Kalman filters with random measurement matrices, the necessary and sufficient conditions are given in reference [14]. An extension of the fruits of [14] is made in reference [15] to demonstrate the stability of multisensor Kalman filter over a lossy network. Similarly, the stability analysis of multisensor Kalman filter over lossy networks is also discussed in reference [16].…”