Recursive maximum likelihood identification of jump markov nonlinear systems

IEEE Transactions on Signal Processing

Volumn 63, Issue 3, 2015, Pages 754-765

  Ozkan, Emre ^a   Lindsten, Fredrik ^b   Fritsche, Carsten ^a   Gustafsson, Fredrik ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Adaptive filtering; expectation maximization; identification; jump Markov systems; parameter estimation; particle filter; Rao Blackwellization; transition probability estimation

Indexed keywords

ADAPTIVE FILTERING; ALGORITHMS; DISTRIBUTED COMPUTER SYSTEMS; IDENTIFICATION (CONTROL SYSTEMS); IMAGE SEGMENTATION; LINEAR SYSTEMS; MAXIMUM LIKELIHOOD; MAXIMUM LIKELIHOOD ESTIMATION; MAXIMUM PRINCIPLE; MONTE CARLO METHODS; NONLINEAR SYSTEMS; ONLINE SYSTEMS; SIGNAL FILTERING AND PREDICTION; SOCIAL NETWORKING (ONLINE); TARGET TRACKING;

EXPECTATION - MAXIMIZATIONS; JUMP MARKOV SYSTEM; PARTICLE FILTER; RAO-BLACKWELLIZATION; TRANSITION PROBABILITIES;

PARAMETER ESTIMATION;

EID: 84920999773     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2014.2385039     Document Type: Article

References (51)

1. A. Doucet, N. J. 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.
2. 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.
3. J. Tugnait, "Adaptive estimation and identification for discrete systems with Markov jump parameters," IEEE Trans. Autom. Control, vol. 27, no. 5, pp. 1054-1065, May 1982.
4. H. Blom and Y. Bar-Shalom, "The interacting multiple model algorithmfor systems withMarkovian switching coefficients," IEEE Trans. Autom. Control, vol. 33, no. 8, pp. 780-783, Aug. 1988.
5. 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, no. 1, pp. 103-123, Jan. 1998.
6. R. Chen and J. S. Liu, "Mixture Kalman filters," J. Roy. Statist. Soc.: Series B, vol. 62, no. 3, pp. 493-508, 2000.
7. A. Doucet, S. J. Godsill, and C. Andrieu, "On sequential Monte Carlo sampling methods for Bayesian filtering," Statist. Comput., vol. 10, no. 3, pp. 197-208, 2000.
8. W. Pieczynski, "Exact filtering in conditionally Markov switching hidden linear models," Comptes Rendus Mathematique, vol. 349, no. 9, pp. 587-590, 2011.
9. N. Abbassi, D. Benboudjema, and W. Pieczynski, "Kalman filtering approximations in tripletMarkov Gaussian switchingmodels," in IEEE Statist. Signal Process. Workshop (SSP), Nice, France, Jun. 2011, pp. 77-80.
10. S. Derrode and W. Pieczynski, "Exact fast computation of optimal filter in Gaussian switching linear systems," IEEE Signal Process. Lett., vol. 20, no. 7, pp. 701-704, Jul. 2013.
11. R. Shumway and D. Stoffer, "Dynamic linear models with switching," J. Amer. Statist. Assoc., vol. 86, no. 415, pp. 763-769, 1991.
12. E. Cinquemani, R. Porreca, G. Ferrari-Trecate, and J. Lygeros, "A general framework for the identification of jump Markov linear systems," in Proc. 46th IEEE Conf. Decision Contr., New Orleans, LA, USA, Dec. 2007, pp. 5737-5742.
13. A. Munir and D. Atherton, "Adaptive interacting multiple model algorithm for tracking a manoeuvring target," IEE Proc. Radar, Sonar, Navig., vol. 142, no. 1, pp. 11-17, 1995.
14. B.-N.Vo, A. Pasha, andH.D. Tuan, "AGaussian mixture PHDfilter for nonlinear jump Markov models," in Proc. 45th IEEE Conf. Decision Contr., San Diego, CA, USA, Dec. 2006, pp. 3162-3167.
15. X.-R. Li and V. P. Jilkov, "Survey of maneuvering target tracking. Part V:Multiple-model methods," IEEE Trans. Aerosp. Electron. Syst., vol. 41, no. 4, pp. 1255-1321, Oct. 2005.
16. M. Nicoli, C.Morelli, andV. Rampa, "AjumpMarkov particle filter for localization of moving terminals in multipath indoor scenarios," IEEE Trans. Signal Process., vol. 56, no. 8, pp. 3801-3809, Aug. 2008.
17. L. Mihaylova, D. Angelova, S. Honary, D. Bull, C. N. Canagarajah, and B. Ristic, "Mobility tracking in cellular networks using particle filtering," IEEE Trans. Wireless Commun., vol. 6, pp. 3589-3599, Oct. 2007.
18. C.M. Carvalho and H. F. Lopes, "Simulation-based sequential analysis of Markov switching stochastic volatility models," Comput. Statist. Data Anal., vol. 51, pp. 4526-4542, 2007.
19. 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, Jun. 2003.
20. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Roy. Statist. Soc.: Series B, vol. 39, no. 1, pp. 1-38, 1977.
21. G. J. McLachlan and T. Krishnan, The EM Algorithm and Extensions, ser. Wiley Series in Probability and Statistics. New York, NY, USA: Wiley, 1997.
22. J. Delmas, "An equivalence of the EM and ICE algorithm for exponential family," IEEE Trans. Signal Process., vol. 45, no. 10, pp. 2613-2615, Oct. 1997.
23. G. Mongillo and S. Denève, "Online learning with hidden Markov models," Neural Comput., vol. 20, no. 7, pp. 1706-1716, 2008.
24. O. Cappé, "Online EM algorithm for hidden Markov models," J. Comput. Graphical Statist., vol. 20, no. 3, pp. 728-749, 2011.
25. O. Cappé, "Online sequential Monte Carlo EM algorithm," in Proc. IEEE/SP 15th Workshop Statist. Signal Process. (SSP), Cardiff, U.K., Sept. 2009, pp. 37-40.
26. P. Del Moral, A. Doucet, and S. S. Singh, Forward Smoothing Using Sequential Monte Carlo Engineering Dept., Cambridge Univ., Cambridge, U.K., Tech. Rep. CUED/F-INFENG/TR 638, 2009.
27. S. Le Corff, G. Fort, and E.Moulines, "Online Expectation Maximization algorithm to solve the SLAM problem," in Proc. IEEE Statist. Signal Process.Workshop (SSP),Nice, France, June 2011, pp. 225-228.
28. S. Yldrm, S. S. Singh, and A. Doucet, "An online Expectation-Maximization algorithm for changepoint models," J. Comput. Graphical Statist., vol. 22, no. 4, pp. 906-926, 2013.
29. E. Özkan, C. Fritsche, and F. Gustafsson, "Online EM algorithm for joint state and mixture measurement noise estimation," in Proc. 15th Int. Conf. Inf. Fusion (FUSION), Singapore, 2012, pp. 1935-1940.
30. C. Fritsche, E. Özkan, and F. Gustafsson, "Online EM algorithm for jumpMarkov systems," in Proc. 15th Int. Conf. Inf. Fusion (FUSION), Singapore, 2012, pp. 1941-1946.
31. A. Doucet and A. Johansen, "A tutorial on particle filtering and smoothing: Fifteen years later," in The Oxford Handbook of Nonlinear Filtering, D. Crisan and B. Rozovskii, Eds. London, U.K.: Oxford Univ. Press, 2011.
32. F. Gustafsson, "Particle filter theory and practice with positioning applications," IEEE Aerosp. Electron. Syst. Mag., vol. 25, no. 7, pp. 53-82, Jul. 2010.
33. H. Driessen and Y. Boers, "Efficient particle filter for jump Markov nonlinear systems," IEE Proc. Radar, Sonar, Navig., vol. 152, no. 5, pp. 323-326, 2005.
34. N. Whiteley and A. Johansen, "Recent developments in auxiliary particle filtering," in Inference and Learning in Dynamic Models. Cambridge, U.K.: Cambridge Univ. Press, 2013, (to appear).
35. C. Andrieu and A. Doucet, "Particle filtering for partially observed Gaussian state space models," J. Roy. Statist. Soc.: Series B, vol. 64, no. 4, pp. 827-836, 2002.
36. T. Schön, F.Gustafsson, and P.-J. Nordlund, "Marginalized particle filters formixed linear/nonlinear state-space models," IEEE Trans. Signal Process., vol. 53, no. 7, pp. 2279-2289, Jul. 2005.
37. F. Lindsten, T. B. Schön, and J. Olsson, "An explicit variance reduction expression for the Rao-Blackwellised particle filter," in Proc. 18th IFAC World Congress, Milan, Italy, Aug. 2011.
38. N. Chopin, "Central limit theorem for sequentialMonte Carlo methods and its application to Bayesian inference," Ann. Statist., vol. 32, no. 6, pp. 2385-2411, 2004.
39. S. Saha and G. Hendeby, "Rao-Blackwellized particle filter forMarkov modulated nonlinear dynamic systems," in Proc. IEEE Workshop Statist. Signal Process. (SSP), Gold Coast, Australia, Jun. 2014, pp. 272-275.
40. C. F. J. Wu, "On the convergence properties of the EM algorithm," Ann. Statist., vol. 11, no. 1, pp. 95-103, 1983.
41. O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models, ser. Springer Series in Statistics. New York, NY, USA: Springer Science+Business Media, LLC, 2005.
42. F. Lindsten and T. B. Schön, "Backward simulationmethods forMonte Carlo statistical inference," Foundations Trends Mach. Learn., vol. 6, no. 1, pp. 1-143, 2013.
43. A. Kong, J. S. Liu, and W. H. Wong, "Sequential imputations and Bayesian missing data problems," J. Amer. Statist. Assoc., vol. 89, no. 425, pp. 278-288, 1994.
44. M. K. Pitt and N. Shephard, "Filtering via simulation: Auxiliary particle filters," J. Amer. Statist. Assoc., vol. 94, no. 446, pp. 590-599, 1999.
45. W. R. Gilks and C. Berzuini, "Following a moving target-Monte Carlo inference for dynamic Bayesian models," J. Roy. Statist. Soc., Series B (Statist. Methodol.), vol. 63, no. 1, pp. 127-146, 2001.
46. V. Jilkov and X. Li, "Online Bayesian estimation of transition probabilities for Markovian jump systems," IEEE Trans. Signal Process., vol. 52, no. 6, pp. 1620-1630, Jun. 2004.
47. U. Orguner andM.Demirekler, "An online sequential algorithmfor the estimation of transition probabilities for jumpMarkov linear systems," Automatica, vol. 42, no. 10, pp. 1735-1744, 2006.
48. U. Orguner and M. Demirekler, "Maximum Likelihood estimation of transition probabilities of jump Markov linear systems," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 5093-5108, Oct. 2008.
49. J. Medbo, I. Siomina, A. Kangas, and J. Furuskog, "Propagation channel impact on LTE positioning accuracy-A study based on real measurements of observed time difference of arrival," in Proc. IEEE Int. Symp. Personal, Indoor, Mobile Radio Commun., Tokyo, Japan, Sep. 2009, pp. 2213-2217.
50. C. Fritsche, U. Hammes, A. Klein, and A. Zoubir, "Robust mobile terminal tracking in NLOS environments using interacting multiple model algorithm," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process., Taipei, Taiwan, Apr. 2009, pp. 3049-3052.
51. J. Liao and C. B. S. , "Robust mobile location estimator with NLOS mitigation using IMMalgorithm," IEEE Trans.Wireless Commun., vol. 5, no. 11, pp. 3002-3006, Nov. 2006.