Adaptive estimation of HMM transition probabilities

IEEE Transactions on Signal Processing

Volumn 46, Issue 5, 1998, Pages 1374-1385

  Ford, Jason J ^a,b   Moore, John B ^a,b  

^a IEEE   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Hidden Markov models; Parameter estimation; Recursive estimation

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PROBABILITY;

EXTENDED LEAST SQUARES (ELS) METHOD; HIDDEN MARKOV MODELS (HMM); RECURSIVE STATE PREDICTION ERROR (RSPE) METHOD;

SIGNAL PROCESSING;

EID: 0032075655     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.668799     Document Type: Article

References (23)

1. J. G. Kemeny and J. L. Snell, Finite Markov Chains. Princeton, NJ: Van Nostrand, 1960.
2. R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models, Estimation and Control. New York: Springer-Verlag, 1995.
3. D. Clements and B. D. O. Anderson, A nonlinear fixed-lag smoother for finite-state Markov processes, IEEE Trans. Inform. Theory, vol. IT-21, pp. 44652, July 1975.
4. I. B. Collings and J. B. Moore, Adaptive HMM filters for signals in noisy fading channels, in Proc. Int. Conf. Acoust., Speech, Signal Process. ICASSP, Adelaide, Australia, 1994, vol. 3, pp. 305-308.
5. V. Krishnamurthy and J. B. Moore, On-line estimation of hidden Markov model parameters based on the Kullback-Leibler information measure, IEEE Trans. Signal Processing, vol. 41, Aug. 1993.
6. L. R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, Proc. IEEE, vol. 77, pp. 257-285, 1989.
7. P. Meyer, Martingales and Stochastic Integrals-I, Lecture Notes in Mathematics Series no. 284. New York: Springer-Verlag, 1972.
8. J. Neveu, Discrete Parameter Martingales. Amsterdam, The Netherlands: North Holland, 1975.
9. M. Loeve, Probability Theory, 2nd éd. Princeton, NJ: Van Nostrand, 1960.
10. A. E. Bryson and Y. Ho, Applied Optimal Control. London, U.K.: Ginn, 1969.
11. J. J. Ford and J. B. Moore, On adaptive HMM state estimation, IEEE Trans. Signal Processing, to be published.
12. S. H. Chung, V. Krishnamurthy, and J. B. Moore, Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences, Philos. Trans. R. Soc. Land. B, vol. 334, pp. 357-384, 1991.
13. I. B. Collings, V. Krishnamurthy, and J. B. Moore, Online identification of hidden Markov models via recursive prediction error techniques, IEEE Trans. Signal Processing, vol. 42, pp. 3535-3539, Dec. 1994.
14. L. Ljung and T. Söderström, Theory and Practice of Recursive Identification. Cambridge, MA: MIT Press, 1983.
15. L. Ljung, Analysis of recursive stochastic algorithms, IEEE Trans. Automat. Contr., vol. AC-22, pp. 551-575, Aug. 1977.
16. B. T. Polyak and A. B. Juditsky, Acceleration of stochastic approximation by averaging, SIAM J. Contr. Optim., vol. 30, pp. 838-855, July 1992.
17. J. Sternby, On consistency for the method of least squares using Martingale theory, IEEE Trans. Automat. Contr., vol. AC-22, June 1977.
18. R. K. Boel, J. B. Moore, and S. Dey, Geometric convergence of filters for hidden Markov models, in Proc. CDC, New Orleans, LA, pp. 69-74 1995.
19. L. Shue, B. D. O. Anderson, and S. Dey, Exponential stability of filters and smoothers for hidden Markov models, in Proc. ECC, Brussels, Belgium, July 1-4, 1997.
20. F. Le Gland and L. Mevel, Geometric ergodicity in hidden Markov models, IRISA, Int. Pub. 1028, July 1996.
21. I. B. Collings and J. B. Moore, Multiple-prediction-horizon recursive identification of hidden Markov models, in Proc. ICASSP, Atlanta, GA, 1996.
22. P. R. Kumar and P. Varaiya, Stochastic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1986.
23. T. Söderström and P. Stoica, System Identification. Englewood Cliffs, NJ: Prentice-Hall, 1988.