Exponential stability of filters and smoothers for hidden markov models

In this paper, we address the problem of exponential stability of filters and fixed-lag smoothers for discrete-time and discrete-state Hidden Markov Models (HMMs). By appealing to a generalised Perron-Frobenius result for nonnegative matrices, we demonstrate exponential forgetting for both the recursive filters and smoothers, and obtain overbounds on the rate of forgetting. Simulation studies are carried out to substantiate the results