Relative entropy rate based multiple hidden Markov model approximation

IEEE Transactions on Signal Processing

Volumn 58, Issue 1, 2010, Pages 165-174

  Lai, John ^a   Ford, Jason J ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Detection; Hidden markov models; Markov processes; Relative entropy rate

Indexed keywords

ENTROPY; ERROR DETECTION; IMAGE PROCESSING; MARKOV PROCESSES; SIGNAL THEORY; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TRELLIS CODES;

APPROXIMATION PERFORMANCE; CONDITIONAL MEAN ESTIMATION; DIM TARGET DETECTION; ESTIMATION PERFORMANCE; MIN-MAX OPTIMISATION; MINIMIZATION PROBLEMS; MODEL SELECTION CRITERIA; RELATIVE ENTROPY RATES;

HIDDEN MARKOV MODELS;

EID: 72949086700     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2028115     Document Type: Article

References (41)

1. H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, 2nd ed. New York: Springer- Verlag, 2001.
2. J. J. Ford and V. A. Ugrinovskii, "Robust control of nonlinear jump parameter systems governed by uncertain chains," IEEE Trans. Autom. Control, vol.53, pp. 1520-1526, Jul. 2008.
3. S. M. Tonissen and R. J. Evans, "Performance of dynamic programming techniques for track-before-detect," IEEE Trans. Aerosp. Electron. Syst., vol.32, pp. 1440-1451, Oct. 1996.
4. Y. Barniv and O. Kella, "Dynamic programming solution for detecting dim moving targets-Part II: Analysis," IEEE Trans. Aerosp. Electron. Syst., vol.AES-23, pp. 776-788, Nov. 1987.
5. M. G. S. Bruno and J. M. F. Moura, "Multiframe detector/tracker: Optimal performance," IEEE Trans. Aerosp. Electron. Syst., vol.37, pp. 925-945, Jul. 2001.
6. H. S. Parka and S. W. Lee, "Off-line recognition of large-set handwritten characters with multiple hidden Markov models," Pattern Recognit., vol.29, pp. 231-244, Feb. 1996.
7. R. L. Streit and R. F. Barrett, "Frequency line tracking using hidden Markov models," IEEE Trans. Acoust., Speech, Signal Process., vol.38, no.4, pp. 586-598, Apr. 1990.
8. L. R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition," Proc. IEEE, vol.77, pp. 257-286, 1989.
9. C. Carlemalm, H. V. Poor, and A. Logothetis, "Suppression of multiple narrowband interferers in a spread-spectrum communication system," IEEE J. Sel. Areas Commun., vol.18, pp. 1365-1374, Aug. 2000.
10. 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. Roy. Soc. London B, vol.334, pp. 357-384, 1991.
11. Y. Barniv, "Dynamic programming solution for detecting dim moving targets," IEEE Trans. Aerosp. Electron. Syst., vol.AES-21, pp. 144-156, Jan. 1985.
12. 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.
13. H. Akaike, "Stochastic theory of minimal realization," IEEE Trans. Autom. Control, vol.19, no.6, pp. 667-674, 1974.
14. G. J. McLachlan and T. Krishnan, The EM Algorithm and Extensions. New York: Wiley, 1997.
15. L. Ljung, System Identification: Theory for the User. Englewood Cliffs, NJ: Prentice-Hall, 1987.
16. R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models: Estimation and Control. Berlin, Germany: Springer-Verlag, 1995.
17. Y. Singer and M. K.Warmuth, "Training algorithms for hidden Markov models using entropy based distance functions," in Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 1996, vol.9, pp. 641-647.
18. J. J. Ford and J. B. Moore, "On adaptive HMM state estimation," IEEE Trans. Signal Process., vol.46, no.2, pp. 475-486, Feb. 1998.
19. J. J. Ford and J. B. Moore, "Adaptive estimation of HMM transition probabilities," IEEE Trans. Signal Process., vol.46, no.5, pp. 1374-1385, May 1998.
20. V. Krishnamurthy and J. B. Moore, "On-line estimation of hidden Markov model parameters based on the Kullback-Leibler information measure," IEEE Trans. Signal Process., vol.41, no.8, pp. 2557-2573, Aug. 1993.
21. I. E. Baum and T. Petrie, "Statistical inference for probabilistic functions of finite state Markov chains," Ann. Inst. Statist. Math., vol.37, pp. 1554-1563, 1966.
22. B. Vanluyten, J. C. Willems, and B. D. Moor, "Equivalence of state representations for hidden Markov models," Syst. Control Lett., vol.57, no.5, pp. 410-419, May 2008.
23. M. Vidyasagar, "The realization problem for hidden Markov models: The complete realization problem," in Proc. 44th IEEE Conf. Decision Control Eur. Control, 2005, pp. 6632-6637.
24. B. D. Anderson, "The realization problem for hidden Markov models," Math. Control, Signals, Syst. (MCSS), vol.12, no.1, pp. 80-120, 1999.
25. L. Finesso, A. Grassi, and P. Spreij, Approximation of Stationary Processes by Hidden Markov Models, Mathematics arXiv OC/0606591v2, 2008.
26. L. Finesso and P. Spreij, "Approximate realization of hidden Markov chains," in Proc. IEEE Information Theory Workshop, 2002, pp. 90-93.
27. L. Xie, V. A. Ugrinovskii, and I. R. Petersen, "Probabilistic distances between finite-state finite-alphabet hidden Markov models," IEEE Trans. Autom. Control, vol.50, no.4, pp. 505-511, Apr. 2005.
28. M. Vidyasagar, "Bounds on the Kullback-Leibler divergence rate between hidden Markov models," in Proc. 46th IEEE Conf. Decision Control, 2007, pp. 6160-6165.
29. J. Lai, J. J. Ford, P. O'Shea, and R. Walker, "Hidden Markov model filter banks for dim target detection from image sequences," presented at the Digital Image Computing: Techniques and Applications (DICTA) Conf., Canberra, Australia, Dec. 1-3, 2008, Paper 132.
30. Y. Bar-Shalom, X.-R Li, and T. Kirubarajan, Estimation With Applications to Tracking and Navigation: Theory, Algorithms and Software. New York: Wiley, 2001.
31. X. R. Li and V. P. Jilkov, "Survey of maneuvering target tracking. Part V: multiple-model methods," IEEE Trans. Aerosp. Electron. Syst., vol.41, pp. 1255-1321, Oct. 2005.
32. J. Arnold, S. W. Shaw, and H. Pasternack, "Efficient target tracking using dynamic programming," IEEE Trans. Aerosp. Electron. Syst., vol.29, pp. 44-56, Jan. 1993.
33. S. J. Davey, M. G. Rutten, and B. Cheung, "A comparison of detection performance for several track-before-detect algorithms," EURASIP J. Adv. Signal Process., pp. 1-10, Oct. 2008.
34. M. G. S. Bruno, "Bayesian methods for multiaspect target tracking in image sequences," IEEE Trans. Signal Process., vol.52, no.7, pp. 1848-1861, Jul. 2004.
35. P. Billingsley, Probability and Measure, 3rd ed. New York: Wiley, 1995.
36. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York: Wiley, 2006.
37. G. Iuculano, M. Cox, G. Pellegrinil, and A. Zanobini, "Evaluation of measurement uncertainty by Bayesian-entropic approach," in Proc. 21st IEEE Instrumentation Measurement Technology Conf., 2004, vol.2, pp. 1240-1245.
38. Y. Baram and N. Sandell, Jr., "Consistent estimation on finite parameter sets with application to linear systems identification," IEEE Trans. Autom. Control, vol.23, pp. 451-454, Jun. 1978.
39. Z. Zhao and X. R. Li, "The behaviour of model probability in multiple model algorithms," in Proc. 8th Int. Conf. Information Fusion, Jul. 2005, vol.1, pp. 331-336.
40. E. Behrends, Introduction to Markov Chains-With Special Emphasis on Rapid Mixing. Braunschweig, Germany: Vieweg, 2000.
41. J. Lai, J. J. Ford, P. O'Shea, R. Walker, and M. Bosse, "A study of morphological pre-processing approaches for track-before-detect dim target detection," presented at the Australasian Conf. Robotics Automation (ACRA), Canberra, Australia, Dec. 3-5, 2008.