Title :
Exponential stability of filters and smoothers for Hidden Markov Models
Author :
Shue, L. ; Anderson, B.D.O. ; Dey, S.
Author_Institution :
Dept. of Syst. Eng., Australian Nat. Univ., Canberra, ACT, Australia
Abstract :
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.
Keywords :
Kalman filters; asymptotic stability; continuous time systems; discrete time systems; hidden Markov models; matrix algebra; recursive filters; smoothing methods; HMM; Kalman filter; continuous-time model; discrete-state model; discrete-time model; exponential stability; fixed-lag smoother; hidden Markov model; nonnegative matrix; recursive filter; Convergence; Hidden Markov models; Kalman filters; Markov processes; Smoothing methods; Steady-state; Time measurement; Estimation; Stability; Stochastic;
Conference_Titel :
Control Conference (ECC), 1997 European
Conference_Location :
Brussels
Print_ISBN :
978-3-9524269-0-6
