Event-based state estimation of discrete-state hidden Markov models

Abstract

The state estimation problem for hidden Markov models subject to event-based sensor measurement updates is considered in this work, using the change of probability approach. We assume the measurement updates are transmitted through wired or wireless communication networks. For the scenarios with reliable and unreliable communication channels, analytical expressions for the probability distributions of the states conditioned on all the past point- and set-valued measurement information are obtained. Also, we show that the scenario with a lossy channel, but without the event-trigger, can be treated as a special case of the reliable channel results. Based on these results, closed-form expressions for the estimated communication rates under the original probability measure are presented, which are shown to be the ratio between a weighted 1-norm and the 1-norm of the unnormalized conditional probability distributions of the states under the new probability measures constructed. Implementation issues are discussed, and the effectiveness of the results is illustrated by numerical examples and comparative simulations.