Smoothing algorithms for state-space models

Annals of the Institute of Statistical Mathematics

Volumn 62, Issue 1, 2010, Pages 61-89

  Briers, Mark ^a,c   Doucet, Arnaud ^b   Maskell, Simon ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^c QINETIQ   (United Kingdom)

Author keywords

Non linear diffusion; Parameter estimation; Rao blackwellisation; Sequential monte carlo; State space models; Two filter smoothing

Indexed keywords

BAYESIAN FILTERS; CLOSED FORM; CLOSED-FORM EXPRESSION; HIDDEN MARKOV PROCESS; INFORMATION FILTER; NON-LINEAR NON-GAUSSIAN; NONLINEAR DIFFUSION; NUMERICAL TECHNIQUES; PROBABILITY MEASURES; RAOBLACKWELLISATION; RECURSIONS; SEQUENTIAL MONTE CARLO; SMOOTHING ALGORITHMS; SMOOTHING FORMULAS; STATE-SPACE MODELS;

MARKOV PROCESSES; MONTE CARLO METHODS; PARAMETER ESTIMATION;

PROBABILITY DISTRIBUTIONS;

EID: 77950691868     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-009-0236-2     Document Type: Article

References (23)

1. Andrieu, C., Doucet, A. (2002). Particle filtering for partially observed Gaussian state-space models. Journal of the Royal Statistical Society B, 64, 4, 827-836.
2. Bresler, Y. (1986). Two-filter formula for discrete-time non-linear Bayesian smoothing. International Journal of Control, 43, 2, 629-641.
3. Briers, M., Doucet, A., Maskell, S. (2004). Smoothing algorithms for state-space models, Technical report, Cambridge University CUED/F-INFENG.TR. 498.
4. Briers, M., Doucet, A., Singh, S. S. (2005). Sequential auxiliary particle belief propagation. In Eighth international conference of information fusion.
5. Cappé O., Doucet, A., Moulines, E., Lavielle, M. (1999). Simulation-based methods for blind maximumlikelihood filter identification. Signal Processing, 73, 1, 3-25.
6. Chen, R., Liu, J. S. (2000).Mixture Kalman filters. Journal of the Royal Statistical Society B, 62, 493-508
7. de Jong, P. (1997). The scan sampler. Biometrika, 84, 929-937.
8. Del Moral, P. (2004). Feynman-Kac formulae: Genealogical and interacting particle systems with applications, series probability and applications. New York: Springer.
9. Doucet, A., Andrieu, C. (2001). Iterative algorithms for state estimation of jump Markov linear systems. IEEE Transactions on Signal Processing, 49, 6, 1216-1227 (Pubitemid 32512282)
10. Doucet, A., Godsill, S. J., Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10, 197-208.
11. Doucet, A., de Freitas, J. F. G., Gordon, N. J. (Eds.) (2001). Sequential Monte Carlo methods in practice. New York: Springer.
12. Fearnhead, P., Papaspiliopoulos, O., Roberts, G. O. (2008a). Particle filters for partially-observed diffusions. Journal of the Royal Statistical Society B, 70, 4, 755-777.
13. Fearnhead, P.,Wyncoll, D., Tawn, J. (2008b). A sequential smoothing algorithm with linear computational cost. Technical report, Department of Statistics, Lancaster University.
14. Godsill, S. J., Doucet, A., West, M. (2004). Monte Carlo smoothing for non-linear time series. Journal of the American Statistical Association, 99, 156-168.
15. Helmick, R. E., Blair, W. D., Hoffman, S. A. (1995). Fixed-interval smoothing for Markovian switching systems. IEEE Transactions on Information Theory, 41, 6, 1845-1855.
16. Isard, M., Blake, A. (1998).Asmoothing filter for Condensation. In Fifth European conference on computer vision (pp. 767-781).
17. Kitagawa, G. (1987). Non-Gaussian state-space modeling of nonstationary time series. Journal of the American Statistical Association, 82, 1032-1063.
18. Kitagawa, G. (1994). The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother. Annals of the Institute of Statistical Mathematics, 46, 4, 605-623.
19. Kitagawa, G. (1996). Monte Carlo filter and smoother for non-Gaussian non-linear state space models. Journal of Computational and Graphical Statistics, 5, 1-25.
20. Kitagawa, G., Sato, S. (2001).Monte Carlo smoothing and self-organizing state-space model. In A. Doucet, J. F. G. de Freitas, N. J. Gordon (Eds.), Sequential Monte Carlo methods in practice (pp. 177-195). New York: Springer.
21. Klaas, M., Briers, M., De Freitas, N., Doucet, A., Maskell, S., Lang, D. (2006). Fast particle smoothing: If I had a million particles. In International conference on machine learning.
22. Liu, J. S., Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association, 93, 1032-1044.
23. Mayne, D. Q. (1966). A solution of the smoothing problem for linear dynamic systems, Automatica, 4, 73-92.