State estimation with unknown measurement losses: A detector-based approach

Abstract

In this paper, we are devoted to solving the problems of designing an estimator, and determining its estimator stability and estimation performance for a system with unknown measurement losses (UML). The solutions to these problems include three steps: first, we design two measurement-loss detectors to detect the measurement losses; Then, we design a detector-based estimator for UML systems. Finally, by analyzing the upper and lower bounds of the covariances of the proposed estimator, we establish a stability condition and determine the estimation performance. Detailed findings and main contributions of this paper are summarized as follows: (i) from the estimator stability perspective, we obtain a necessary and sufficient stability condition. Specifically, the estimator is stable almost surely if and only if the measurement-loss rate is less than a critical value. (ii) From the estimation performance perspective, we prove that under some conditions, the performance of the proposed estimator is almost surely the same as that of the optimal estimator for the system with known measurement losses.