Performance and stability analysis of interacting multiple model estimator under unobservable packet loss

For a system with packet loss, if the estimator cannot observe the packet-loss status (PLS), the system is called an unobservable-packet-loss (UPL) system. Otherwise, it is called an observable-packet-loss (OPL) system. This paper studies the interacting multiple model (IMM) estimator for UPL systems, and the main contributions are twofold. (i) Estimation accuracy of the unobservable PLS. For an unstable UPL system, we prove that the UPL system will become an OPL one with time, since the PLS can be exactly estimated with time. For a stable UPL system, there exists an accuracy threshold such that the estimation accuracy of the PLS cannot be better than this threshold. (ii) Stability of the IMM estimator. For an unstable UPL system, we establish a necessary and sufficient condition: there exists a threshold such that the IMM estimator is stable almost everywhere if and only if the packet-arrival rate is greater than this threshold. For a stable UPL system, we show that the IMM estimator is stable, no matter what value the packet-arrival rate is.