Moving-horizon estimation for linear systems with random packet losses: suboptimal arrival cost improves robustness

This paper addresses the problem of estimating the state of a linear system whose output measurements are transmitted over a communication channel subject to random packet losses. For such systems, it is well established that mean-square stability of an optimal linear estimator requires the packet arrival probability to exceed a critical threshold. Although this fundamental limit cannot be circumvented, we show, both theoretically and through examples, that a movinghorizon estimator (MHE) with a carefully designed suboptimal arrival cost can achieve mean stability for arbitrarily low arrival probability. The result decouples mean stability from the more stringent mean-square condition, offering a robust estimation strategy for channels with low data rates.