Stability and Uniform Particle Approximation of Nonlinear Filters in Case of Non Ergodic Signals

REFERENCES

• Atar , R. , and O. Zeitouni . 1997 . Exponential stability for nonlinear filtering . Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 33 ( 6 ): 697 – 725 .
   Web of Science ®Google Scholar
• Atar , R. , and O. Zeitouni . 1997 . Lyapunov exponents for finite state nonlinear filtering . SIAM Journal on Control and Optimization 35 ( 1 ): 36 – 55 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Atar , R. 1998 . Exponential stability for nonlinear filtering of diffusion processes in a noncompact domain . The Annals of Probability 26 ( 4 ): 1552 – 1574 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Atar , R. , Viens , and O. Zeitouni . 1999 . Robustness of Zakai's equation via Feynman–Kac representations . In Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, Systems & Control: Foundations & Applications , eds. W. M. McEneaney , G. G. Yin , and Q. Zhang , Boston , MA : Birkäuser , 339 – 352 .
   Google Scholar
• Azencott , R. 1984 . Densité des diffusions en temps petit: Développements asymptotiques (Partie I) . Séminaire de Probablités XVIII , Lectures Notes in Mathematics, Springer , Berlin , 402 – 498 .
   Google Scholar
• Budhiraja , A. S. , and D. L. Ocone . 1997 . Exponential stability of discrete–time filters for bounded observation noise . Systems & Control Letters 30 ( 4 ): 185 – 193 . [INFOTRIEVE] [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Budhiraja , A. S. , and D. L. Ocone . 1999 . Exponential stability in discrete–time filtering for non–ergodic signals . Stochastic Processes and Their Applications 82 ( 2 ): 245 – 257 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Da Prato , G. , M. Fuhrman , and P. Malliavin . 1999 . Asymptotic ergodicity of the process of conditional law in some problem of nonlinear filtering . Journal of Functional Analysis 164 ( 2 ): 356 – 377 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Del Moral , P. , and A. Guionnet . 2001. On the stability of interacting processes with applications to filtering and genetic algorithms. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 37(2):155–194. [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Del Moral , P. , J. Jacod , and P. Protter . 2001 . The Monte-Carlo method for filtering with discrete-time observations . Probab. Theory Related Fields 120 ( 3 ): 346 – 368 . [CSA]
   Web of Science ®Google Scholar
• Kunita , H. 1991 . Ergodic properties of nonlinear filtering processes . In Progress in Probability, Spatial Stochastic Processes: Festschrift in Honor of T.E. Harris , eds. K. S. Alexander and J. C. Watkins , Boston : Birkhäuser , volume 19 , 233 – 256 .
   Google Scholar
• Le Gland , F. , C. Musso , and N. Oudjane . 1998 . An analysis of regularized interacting particle methods for nonlinear filtering . In Preprints of the 3rd IEEE European Workshop on Computer–Intensive Methods in Control and Data Processing , eds. J. Rojícek , M. Valećkova , M. Kárný , and K. Warwick , 167 – 174 .
   Google Scholar
• Le Gland , F. and L. Mevel . 2000 . Basic properties of the projective product, with application to products of column–allowable nonnegative matrices . Mathematics of Control, Signals, and Systems 13 ( 1 ): 41 – 62 . [CSA]
   Web of Science ®Google Scholar
• Le Gland , F. , and L. Mevel . 2000 . Exponential forgetting and geometric ergodicity in hidden Markov models . Mathematics of Control, Signals, and Systems 13 ( 1 ): 63 – 93 . [CSA]
   Web of Science ®Google Scholar
• Le Gland , F. , and N. Oudjane . 2001 . Stability and Uniform Approximation of Nonlinear Filters using the Hilbert Metric, and Application to Particle Filters . Rapport de recherche INRIA Rennes n. 4215 . ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4215.ps.gz .
   Google Scholar
• Le Gland , F. , and N. A. Oudjane . 2003 . A robustification approach to stability and to uniform particle approximation of nonlinear filters: The example of pseudo-mixing signals . Stochastic Processes and their Applications 106 ( 2 ): 279 – 316 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Musso , C. , and N. Oudjane . 1998 . Regularization schemes for branching particle systems as a numerical solving method of the nonlinear filtering problem . In Proceedings of the Irish Signals and Systems Conference , Dublin , Ireland .
   Google Scholar
• Ocone , D. L. , and E. Pardoux . Asymptotic stability of the optimal filter with respect to its initial condition . SIAM Journal on Control and Optimization 34 ( 1 ): 226 – 243 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Oudjane , N. 2000 . Stabilité et approximation particulaires en filtrage non linéaire. Application au pistage. Thése présentée devant l'Université de Rennes 1. , ftp://ftp.irisa.fr/techreports/theses/2000/oudjane.ps.gz .
   Google Scholar
• Stettner , L. 1991 . Invariant measures for the pair: State, approximate filtering process . Colloquium Mathematicum LXII ( 2 ): 347 – 351 . [CSA]
   Google Scholar