Exponential stability of filters and smoothers for hidden markov models

IEEE Transactions on Signal Processing

Volumn 46, Issue 8, 1998, Pages 2180-2194

  Shue, Louis ^a   Anderson, Brian D O ^a   Dey, Subhrakanti ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Exponential forgetting; Fixed lag smoothing; Hidden markov model

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; MATHEMATICAL MODELS; MATRIX ALGEBRA;

EXPONENTIAL STABILITY; FIXED LAG SMOOTHING; HIDDEN MARKOV MODELS;

KALMAN FILTERING;

EID: 0032141046     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.705429     Document Type: Article

References (12)

1. A. Arapostathis and S. I. Marcus, "Analysis of an identification algorithm arising in the adaptive estimation of Markov chains," Math. Contr. Signals, Syst., vol. 3, pp. 1-29, Jan 1990.
2. B. D. O. Anderson, "Properties of optimal linear smoothing," IEE Trans. Automat. Contr., vol. AC-14, pp. 114-115, Feb 1969.
3. B. D. O. Anderson and T. Kailath, "Forward and backward models fo finite-state Markov processes," Adv. Applied Prob., vol. 11, pp. 118-133 1979.
4. B. D. O. Anderson and J. B. Moore, Optimal Filtering. Englewoo Cliffs, NJ: Prentice-Hall, 1979.
5. B. D. O. Anderson and I. Rhodes, "Smoothing algorithms for nonlinea finite-dimensional systems," Stochastics, vol. 9, pp. 139-165, 1983.
6. R. K. Boel, J. B. Moore, and S. Dey, "Geometric convergence of filter for Hidden Markov Models," in Proc. 34th Conf. Decision Contr., 1995 pp. 69-74.
7. D. Clements and B. D. O. Anderson, "A nonlinear fixed-lag smoother fo finite-state Markov processes," IEEE Trans. Inform. Theory, vol. IT-21 pp. 446-452, 1975.
8. R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models Estimation and Control. New York: Springer-Verlag, 1994.
9. V. Krishnamurthy and J. B. Moore, "On-line estimation of Hidde Markov Model parameters based on th Kullback-Leibler informatio measure," IEEE Trans. Signal Processing, vol. 41, pp. 2557-2573, Aug 1993.
10. L. R. Rabiner, "A tutorial on Hidden Markov Models and selecte applications in speech recognition," Proc. IEEE, vol. 77, pp. 257-285 Feb. 1989.
11. A. Segall, "Recursive estimation from discrete-time point processes, IEEE Trans. Inform. Theory, vol. IT-22, pp. 42231, 1976.
12. E. Seneta, Non-Negative Matrices and Markov Chains, 2nd ed. Ne York: Springer-Verlag, 1981, ch. 31