EXPONENTIAL STABILITY OF FILTERS AND SMOOTHERS FOR HIDDEN MARKOV-MODELS

In this paper, we address the problem of filtering and fixed-lag smoot hing for discrete-time and discrete-state hidden Markov models (HMM's) , with the intention of extending some important results in Kalman fil tering, notably the property of exponential stability, By appealing to a generalized Perron-Frobenius result for non-negative matrices, we a re able to demonstrate exponential forgetting for both the recursive f ilters and smoothers; furthermore, methods for deriving overbounds on the convergence rate are indicated. Simulation studies for a two-state and two output HMM verify qualitatively some of the theoretical predi ctions, and the observed convergence rate is shown to be bounded in ac cordance with the theoretical predictions.