Exponential stability of filters and smoothers for hidden Markov models

Author

Shue, Louis ; Anderson, Brian D O ; Dey, Subhrakanti

Author_Institution

Dept. of Syst. Eng., Australian Nat. Univ., Canberra, ACT, Australia

Volume

46

Issue

8

fYear

1998

fDate

8/1/1998 12:00:00 AM

Firstpage

2180

Lastpage

2194

Abstract

We address the problem of filtering and fixed-lag smoothing for discrete-time and discrete-state hidden Markov models (HMMs), with the intention of extending some important results in Kalman filtering, notably the property of exponential stability. By appealing to a generalized Perron-Frobenius result for non-negative matrices, we are able to demonstrate exponential forgetting for both the recursive filters 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 predictions, and the observed convergence rate is shown to be bounded in accordance with the theoretical predictions

Keywords

Kalman filters; circuit stability; convergence of numerical methods; discrete time systems; hidden Markov models; matrix algebra; recursive filters; signal processing; smoothing methods; Kalman filtering; convergence rate; discrete-state HMM; discrete-time HMM; exponential forgetting; exponential stability; fixed-lag smoothing; generalized Perron-Frobenius theorem; hidden Markov models; nonnegative matrices; overbounds; recursive filters; signal model; simulation studies; smoothers; two-output HMM; two-state HMM; Adaptive systems; Convergence; Hidden Markov models; Information filtering; Information filters; Kalman filters; Robustness; Smoothing methods; Stability; Systems engineering and theory;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.705429

Filename

705429