Closed-form solutions to forward-backward smoothing

IEEE Transactions on Signal Processing

Volumn 60, Issue 1, 2012, Pages 2-17

  Vo, Ba Ngu ^a   Vo, Ba Tuong ^a   Mahler, Ronald P S ^b  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b LOCKHEED MARTIN   (United States)

Author keywords

Bernoulli model; filtering; Gaussian sum smoother; PHD; smoothing; target tracking

Indexed keywords

BACKWARD PROPAGATION; BERNOULLI MODEL; CLOSED FORM; CLOSED FORM SOLUTIONS; COMPLEX PROBLEMS; EXACT SOLUTION; FORWARD PROPAGATION; GAUSSIAN SUM; GAUSSIANS; JOINT DETECTION; MULTIPLE TARGET TRACKING; PHD; PROBABILITY HYPOTHESIS DENSITY; RECURSIONS; SMOOTHING;

CLUTTER (INFORMATION THEORY); CRACK PROPAGATION; FILTRATION; GAUSSIAN DISTRIBUTION;

TARGET TRACKING;

EID: 84555218315     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2168519     Document Type: Article

References (36)

1. D. L. Alspach and H. W. Sorenson, "Nonlinear Bayesian estimation using Gaussian sum approximations," IEEE Trans. Autom. Control, vol. AC-17, no. 4, pp. 439-448, 1972.
2. B. O. Anderson and J. B. Moore, Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
3. Y. Bar-Shalom, X. Li, and T. Kirubarajan, Estimation With Applications to Tracking and Navigation. New York: Wiley, 2001.
4. Y. Bresler, "Two-filter formula for discrete-time non-linear Bayesian smoothing," Int. J. Control, vol. 43, no. 2, pp. 629-641, 1986.
5. M. Briers, A. Doucet, and S. Maskell, "Smoothing algorithms for statespace models," Ann. Inst. Statist. Math., vol. 62, no. 1, pp. 61-89, 2010.
6. A. Doucet, S. Godsill, and C. Andrieu, "On sequential Monte Carlo sampling methods for Bayesian filtering," Statist. Comput., vol. 10, no. 3, pp. 197-208, 2000.
7. A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag, 2001.
8. P. Fearnhead, D.Wyncoll, and J. Tawn, "A sequential smoothing algorithm with linear computational cost," Biometrika, vol. 97, no. 2, pp. 447-464, 2010.
9. W. Fong, S. J. Godsill, A. Doucet, and M. West, "Monte Carlo smoothing with application to audio signal enhancement," IEEE Trans. Signal Process., vol. 50, no. 2, pp. 438-449, Feb. 2002.
10. S. J. Godsill, A. Doucet, and M. West, "Monte Carlo smoothing for nonlinear time series," J. Amer. Statist. Assoc., vol. 99, pp. 156-168, Mar. 2004.
11. N. Gordon, D. Salmond, and Smith, "Novel approach to nonlinear/non- Gaussian Bayesian state estimation," Proc. IEE, vol. 140, no. 2, pp. 107-113, 1993.
12. A. C. Harvey, Forecasting, Structural Time Series Models and the Kalman Filter. New York: Cambridge Univ. Press, 1989.
13. M. Hürzeler and H. R. Künsch, "Monte Carlo approximations for general state space models," J. Comput. Graph. Statist., vol. 7, no. 2, pp. 175-193, Jun. 1998.
14. R. Kalman, "A new approach to linear filtering and prediction problems," Trans. ASME-J. Basic Eng., vol. 82, no. Series D, pp. 35-45, 1960.
15. G. Kitagawa, "Non-Gaussian state space modelling of nonstationary time series," J. Amer. Statist. Assoc., vol. 82, pp. 1032-1063, 1987.
16. G. Kitagawa, "The two-filter formula for smoothing and an implementation of the Gaussian sum smoother," Ann. Inst. Statist. Math., vol. 46, no. 4, pp. 605-623, 1994.
17. G. Kitagawa, "Monte Carlo filter and smoother for nonlinear non-Gaussian state-space models," J. Comput. Graph. Statist., vol. 5, no. 1, pp. 1-25, Mar. 1996.
18. G. Kitagawa and G. Gersch, "Smoothness priors analysis of time series," in Lecture Notes in Statistics. New York: Springer, 1996, vol. 116.
19. J. T.-H. Lo, "Finite-dimensional sensor orbits and optimal non-linear filtering," IEEE Trans. Inf. Theory, vol. IT-18, no. 5, pp. 583-588, 1972.
20. R. Mahler, "Multi-target Bayes filtering via first-order multi-target moments," IEEE Trans. Aerosp. Electron. Syst., vol. 39, no. 4, pp. 1152-1178, 2003.
21. R. Mahler, Statistical Multisource Multitarget Information Fusion. Norwood, MA: Artech House, 2007.
22. R. Mahler, "PHD filters of higher order in target number," IEEE Trans. Aerosp. Electron. Syst., vol. 43, no. 3, pp. 1523-1543, Jul. 2007.
23. R. Mahler, B.-N. Vo, and B.-T. Vo, "Multi-target forward-backward smoothing with the probability hypothesis density," IEEE Trans. Aerosp. Electron. Syst., to be published.
24. J. Meditch, "A survey of data smoothing for linear and nonlinear dynamic systems," Automatica, vol. 9, pp. 151-162, 1973.
25. N. Nandakumaran, T. Kirubarajan, T. Lang, M. McDonald, and K. Punithakumar, "Multitarget tracking using probability hypothesis density smoothing," IEEE Trans. Aerosp. Electron. Syst., vol. 47, no. 4, pp. 2344-2360, 2011.
26. D. Schuhmacher, B.-T. Vo, and B.-N. Vo, "A consistent metric for performance evaluation of multi-object filters," IEEE Trans. Signal Process., vol. 56, no. 8, pp. 3447-3457, Aug. 2008.
27. H. W. Sorenson and D. L. Alspach, "Recursive Bayesian estimation using Gaussian sum," Automatica, vol. 7, pp. 465-479, 1971.
28. B.-N. Vo, S. Singh, and A. Doucet, "Sequential Monte Carlo methods for multi-target filtering with random finite sets," IEEE Trans. Aerosp. Electron. Syst., vol. 41, no. 4, pp. 1224-1245, 2005.
29. B.-N. Vo and W.-K. Ma, "The Gaussian mixture probability hypothesis density filter," IEEE Trans. Signal Process., vol. 54, no. 11, pp. 4091-4104, 2006.
30. B.-T. Vo, B.-N. Vo, and A. Cantoni, "Analytic implementations of the cardinalized probability hypothesis density filter," IEEE Trans. Signal Process., vol. 55, no. 7, pp. 3553-3567, Jul. 2007.
31. B.-T. Vo, B.-N. Vo, and A. Cantoni, "Bayesian filtering with random finite set observations," IEEE Trans. Signal Process., vol. 56, no. 4, pp. 1313-1326, 2008.
32. B.-T. Vo, "Random finite sets in multi-object filtering," Ph.D. dissertation, Univ. of Western Australia, Crawley, 2008.
33. B.-N. Vo, B.-T. Vo, and R. Mahler, "A closed form solution to the probability hypothesis density smoother," presented at the 13th Annu. Conf. Inf. Fusion, Edinburgh, U.K., 2010.
34. B.-T. Vo, C.-M. See, N. Ma, and W.-T. Ng, "Multi-sensor joint detection and tracking with the Bernoulli filter," IEEE Trans. Aerosp. Electron. Syst., to be published.
35. B.-T. Vo, D. Clark, B.-N. Vo, and B. Ristic, "Bernoulli forward-backward smoothing for joint target detection and tracking," IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4473-4477, 2011.
36. M. West and J. Harrison, Bayesian Forecasting and Dynamic Models, ser. Springer Series in Statistics. New York: Springer, 1989.