Maximum likelihood estimation of transition probabilities of jump Markov linear systems

IEEE Transactions on Signal Processing

Volumn 56, Issue 10 II, 2008, Pages 5093-5108

  Orguner, Umut ^a,b   Demirekler, Mübeccel ^a  

^a MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

^b LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Interacting multiple model (IMM); Jump Markov linear system (JMLS); Maximum likelihood (ML); Transition probability matrix (TPM)

Indexed keywords

EID: 54749144272     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.928936     Document Type: Article

References (34)

1. A. Logothetis and V. Krishnamurthy, "Expectation maximization algorithms for MAP estimation of jump Markov linear systems," IEEE Trans. Signal Process., vol. 47, no. 8, pp. 2139-2156, Aug. 1999.
2. Y. Bar-Shalom and X. R. Li, Estimation and Tracking: Principles, Techniques, and Software. Norwell, MA: Artech House, 1993.
3. E. Mazor, A. Averbuch, Y. Bar-Shalom, and J. Dayan, "Interacting multiple model methods in target tracking: A survey," IEEE Trans. Aerosp. Electron Syst., vol. 34, pp. 103-123, Jan. 1998.
4. O. Costa, "Linear minimum mean square error estimation for discretetime Markovian jump linear systems," IEEE Trans. Autom. Control, vol. 39, pp. 1685-1689, Aug. 1994.
5. L. Johnston and V. Krishnamurthy, "An improvement to the interacting multiple model (IMM) algorithm," IEEE Trans. Signal Process., vol. 49, no. 12, pp. 2909-2923, Dec. 2001.
6. Q. Zhang, "Optimal filtering of discrete-time hybrid systems," J. Optim. Theory Applications, vol. 100, no. 1, pp. 123-144, Jan. 1999.
7. T. Ho and B. Chen, "Novel extended Viterbi-based multiple-model algorithms for state estimation of discrete-time systems with Markov jump parameters," IEEE Trans. Signal Process., vol. 54, no. 2, pp. 393-404, Feb. 2006.
8. R. J. Elliott, F. Dufour, and W. P. Malcolm, "State and mode estimation for discrete-time jump Markov systems," SIAM J. Contr. Optim., vol. 44, no. 3, pp. 1081-1104, 2005.
9. G. Ackerson and K. Fu, "On state estimation in switching environments," IEEE Trans. Autom. Control, vol. AC-15, pp. 10-17, Aug. 1970.
10. J. K. Tugnait, "Adaptive estimation and identification for discrete systems with Markov jump parameters," IEEE Trans. Autom. Control, vol. AC-27, pp. 1054-1065, Oct. 1982.
11. H. A. P. Blom and Y. Bar-Shalom, "The interacting multiple model algorithm for systems with Markov switching coefficients," IEEE Trans. Autom. Control, vol. 33, pp. 780-783, Aug. 1988.
12. A. Doucet, N. Gordon, and V. Krishnamurthy, "Particle filters for state estimation of jump Markov linear systems," IEEE Trans. Signal Process., vol. 49, no. 3, pp. 613-624, Mar. 2001.
13. A. Doucet, A. Logothetis, and V. Krishnamurthy, "Stochastic sampling algorithms for state estimation of jump Markov linear systems," IEEE Trans. Autom. Control, vol. 45, no. 2, pp. 188-202, Feb. 2000.
14. Y. Boers and J. Driessen, "Interacting multiple model particle filter," Proc. Inst. Electr. Eng. Radar Sonar Navig., vol. 150, no. 5, pp. 344-349, Oct. 2003.
15. H. Driessen and Y. Boers, "Efficient particle filter for jump Markov nonlinear systems," Proc. Inst. Elect. Eng. Radar Sonar Navig., vol. 152, no. 5, pp. 323-326, Oct. 2005.
16. C. Andrieu, M. Davy, and A. Doucet, "Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions," IEEE Trans. Signal Process., vol. 51, no. 7, pp. 1762-1770, Jul. 2003.
17. F. Caron, M. Davy, E. Duflos, and P. Vanheeghe, "Particle filtering for multisensor data fusion with switching observation models: Application to land vehicle positioning," IEEE Trans. Signal Process., vol. 55, no. 6, pp. 2703-2719, Jun. 2007.
18. Y. Sawaragi, T. Katayama, and S. Fujishige, "Adaptive estimation for a linear system with interrupted observation," IEEE Trans. Autom. Control, vol. AC-18, pp. 152-154, Apr. 1973.
19. J. K. Tugnait and A. H. Haddad, "State estimation under uncertain observations with unknown statistics," IEEE Trans. Autom. Control vol. 24, pp. 201-210, Apr. 1979.
20. J. K. Tugnait and A. H. Haddad, "Adaptive estimation in linear systems with unknown Markovian noise statistics," IEEE Trans. Inf. Theory vol. IT-26, pp. 66-78, Jan. 1980.
21. Z. Ghahramani and G. E. Hinton, "Variational learning for switching state-space models," Neural Comput., vol. 12, no. 4, pp. 831-864, Apr. 2000.
22. E. K. Boukas, Stochastic Switching Systems: Analysis and Design. Boston, MA: Birkhäuser, 2006.
23. V. P. Jilkov and X. R. Li, "Online Bayesian estimation of transition probabilities for Markovian jump systems," IEEE Trans. Signal Process., vol. 52, no. 6, pp. 1620-1630, Jun. 2004.
24. A. Doucet and B. Ristic, "Recursive state estimation for multiple switching models with unknown transition probabilities," IEEE Trans. Aerosp. Electron. Syst., vol. 38, pp. 1098-1104, Jul. 2002.
25. J. Xiong and J. Lam, "Fixed-order robust H∞ filter design for Markovian jump systems with uncertain switching probabilities," IEEE Trans. Signal Process., vol. 54, no. 4, pp. 1421-1430, Apr. 2006.
26. V. P. Jilkov, X. R. Li, and D. S. Angelova, "Estimation of Markovian jump systems with unknown transition probabilities through Bayesian sampling," in Proc. Revised Papers 5th Int. Conf. Numer. Methods Applicat. (NMA '02), London, U.K., 2003, pp. 307-315.
27. U. Orguner and M. Demirekler, "An online sequential algorithm for the estimation of transition probabilities for jump Markov linear systems," Automatica, vol. 42, no. 10, pp. 1735-1744, Oct. 2006.
28. L. Aggoun and R. J. Elliott, Measure Theory and Filtering: Introduction with Applications. Cambridge, U.K.: Cambridge Univ. Press, 2004.
29. R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models: Estimation and Control. New York: Springer-Verlag, 1994.
30. P. R. Kumar and P. Varaiya, Stochastic Systems: Estimation, Identification and Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1986.
31. R. J. Elliott, F. Dufour, and D. D. Sworder, "Exact hybrid filters in discrete time," IEEE Trans. Autom. Control, vol. 41, pp. 1807-1810, Dec. 1996.
32. L. Ljung, System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall, 1999.
33. U. Orguner and M. Demirekler, "Risk-sensitive filtering for jump Markov linear systems," Automatica, vol. 44, no. 1, pp. 109-118, Jan. 2008.
34. U. Orguner, "Improved state estimation for jump Markov linear systems," Ph.D. dissertation, Middle East Technical Univ., Ankara, Turkey, 2006.