An online sequential algorithm for the estimation of transition probabilities for jump Markov linear systems

Automatica

Volumn 42, Issue 10, 2006, Pages 1735-1744

  Orguner, Umut ^a   Demirekler, Mübeccel ^a  

^a MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Jump Markov linear systems; Kullback Leibler distance measure; Stochastic approximation; Transition probability

Indexed keywords

ALGORITHMS; MARKOV PROCESSES; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PROBABILITY; PROBLEM SOLVING; STOCHASTIC CONTROL SYSTEMS;

JUMP MARKOV LINEAR SYSTEMS; KULLBACK-LEIBLER DISTANCE MEASURE; STOCHASTIC APPROXIMATION; TRANSITION PROBABILITY;

LINEAR SYSTEMS;

EID: 33747774840     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.05.002     Document Type: Article

References (26)

1. Ackerson G.A., and Fu K.S. On state estimation in switching environments. IEEE Transactions on Automatic Control 15 1 (1970) 10-17
2. Bar-Shalom Y., and Li X.R. Estimation and tracking: Principles, techniques, and software (1993), Artech House, Norwell, MA
3. Benveniste A., Métivier M., and Priouret P. Adaptive algorithms and stochastic approximations (1990), Springer, Berlin, Germany
4. Blom H.A.P., and Bar-Shalom Y. The interacting multiple model algorithm for systems with Markov switching coefficients. IEEE Transactions on Automatic Control 33 8 (1988) 780-783
5. Boers Y., and Driessen J.N. Interacting multiple model particle filter. IEE Proceedings-Radar Sonar and Navigation 150 5 (2003) 344-349
6. Collings I.B., Krishnamurthy V., and Moore J.B. Online identification of hidden Markov models via recursive prediction error techniques. IEEE Transactions on Signal Processing 42 12 (1994) 3535-3539
7. Costa O.L.V. Linear minimum mean square error estimation for discrete-time Markovian jump linear systems. IEEE Transactions on Automatic Control 39 8 (1994) 1685-1689
8. Cover T.M., and Thomas J.A. Elements of information theory (1991), Wiley, New York
9. Doucet A., Gordon N.J., and Krishnamurthy V. Particle filters for state estimation of jump Markov linear systems. IEEE Transactions on Signal Processing 49 3 (2001) 613-624
10. Doucet A., Logothetis A., and Krishnamurthy V. Stochastic sampling algorithms for state estimation of jump Markov linear systems. IEEE Transactions on Signal Processing 45 1 (2000) 188-202
11. Ford J.J., and Moore J.B. Adaptive estimation of HMM transition probabilities. IEEE Transactions on Signal Processing 46 5 (1998) 1374-1385
12. Jilkov V.P., and Li X.R. Online Bayesian estimation of transition probabilities for Markovian jump systems. IEEE Transactions on Signal Processing 52 6 (2004) 1620-1630
13. Jilkov, V. P., Li, X. R., & Angelova, D. S., (2003). Estimation of Markovian jump systems with unknown transition probabilities through Bayesian sampling. In NMA '02: Revised papers from the fifth international conference on numerical methods and applications, London, UK, Berlin: Springer, pp. 307-315.
14. Johnston L.A., and Krishnamurthy V. An improvement to the interacting multiple model (IMM) algorithm. IEEE Transactions on Signal Processing 49 12 (2001) 2909-2923
15. Krishnamurthy V., and Moore J.B. Online estimation of hidden Markov model parameters based on the Kullback-Leibler information measure. IEEE Transactions on Signal Processing 41 8 (1993) 2557-2573
16. Krishnamurthy V., and Yin G.G. Recursive algorithms for estimation of hidden Markov models and autoregressive models with Markov regime. IEEE Transactions on Information Theory 48 2 (2002) 458-476
17. Kushner H.J., and Yin G.G. Stochastic approximation algorithms and applications (1997), Springer, New York
18. Ljung L. System identification: Theory for the user (1987), Prentice-Hall, Englewood Cliffs, NJ
19. Logothetis A., and Krishnamurthy V. Expectation maximization algorithms for MAP estimation of jump Markov linear systems. IEEE Transactions on Signal Processing 47 8 (1999) 2139-2156
20. Mazor E., Averbuch A., Bar-Shalom Y., and Dayan J. Interacting multiple model methods in target tracking: A survey. IEEE Transactions on Aerospace and Electronic Systems 34 1 (1998) 103-123
21. Poznyak A.S., and Najim K. Learning automata and stochastic optimization (1997), Springer, New York, Secaucus, NJ, USA
22. Robbins H., and Monro S. A stochastic approximation method. Annals of Mathematical Statistics 22 (1951) 400-407
23. Stiller J.C., and Radons G. Online estimation of hidden Markov models. IEEE Signal Processing Letters 6 8 (1999) 213-215
24. Tugnait J.K. Adaptive estimation and identification for discrete systems with Markov jump parameters. IEEE Transactions on Automatic Control 27 5 (1982) 1054-1065
25. Weinstein E., Feder M., and Oppenheim A.V. Sequential algorithms for parameter estimation based on the Kullback-Leibler information measure. IEEE Transactions on Acoustics, Speech and Signal Processing 38 9 (1990) 1652-1654
26. Zhang Q. Optimal filtering of discrete-time hybrid systems. Journal of Optimization Theory and Applications 100 1 (1999) 123-144