State estimation for systems with unobservable packet losses: Approximate estimation, stability, and performance analysis

Abstract

AbstractFor a system with packet losses, if the estimator can observe the status of packet losses, it is called a system with observable packet losses (an OPL system); otherwise, it is called a system with unobservable packet losses (a UPL system). We obtain the optimal estimator (OE) for UPL systems, which consists of an exponentially increasing number of items, and thus is computationally intractable. To address the computation issue, we design an approximate optimal estimator (AOE), which can be computed recursively. The proposed AOE features a theoretically‐proven stability condition and a theoretically‐guaranteed superiority to the optimal linear estimator (OLE). Specifically, for stability, we prove that for a stable UPL system, both the OE and the proposed AOE are stable; for performance, we show that both the OE and the proposed AOE are superior to the OLE in the mean sense. Then, we obtain a tight upper bound of the performance deviation between the OE and the proposed AOE. Finally, numerical examples are presented to illustrate the obtained results and the effectiveness of the proposed AOE in estimating system states when the packet‐loss status, that is, the private information of packet losses, cannot be observed.