Analysis of error propagation in particle filters with approximation

Annals of Applied Probability

Volumn 21, Issue 6, 2011, Pages 2343-2378

  Oreshkin, Boris N ^a   Coates, Mark J ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Collaborative tracking; Error analysis; Particle filtering

Indexed keywords

EID: 82655173714     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AAP760     Document Type: Article

References (25)

1. COATES, M. J. and ING, G. (2005). Sensor network particle filters:Motes as particles. In Proc. IEEE Workshop on Statistical Signal Processing (SSP). Bordeaux, France.
2. CRISAN, D., DEL MORAL, P. and LYONS, T. (1999). Discrete filtering using branching and interacting particle systems. Markov Process. Related Fields 5 293-318. MR1710982
3. DEL MORAL, P. (2004). Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Springer, New York. MR2044973
4. DEL MORAL, P. and GUIONNET, A. (2001). On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. H. Poincaré Probab. Statist. 37 155-194. MR1819122
5. DEL MORAL, P. and MICLO, L. (2002). On the stability of nonlinear Feynman-Kac semigroups. Ann. Fac. Sci. Toulouse Math. (6) 11 135-175. MR1988460
6. DEVROYE, L. and LUGOSI, G. (2001). Combinatorial Methods in Density Estimation. Springer, New York. MR1843146
7. DOUC, R. and CAPPE, O. (2005). Comparison of resampling schemes for particle filtering. In Proc. 4th International Symp. Image and Sig. Process. and Analysis. Zagreb, Croatia 64-69. IEEE, New York. (Pubitemid 44459664)
8. DOUCET, A., DE FREITAS, N. and GORDON, N. (eds.) (2001). Sequential Monte Carlo Methods in Practice. Springer, New York. MR1847783
9. IHLER, A., FISHER, J. andWILLSKY, A. (2005). Particle filtering under communication constraints. In Proc. IEEE Workshop on Statistical Signal Processing. Bordeaux, France.
10. KOTECHA, J. H. and DJURÍC, P. M. (2003). Gaussian sum particle filtering. IEEE Trans. Signal Process. 51 2602-2612. MR2003067
11. KUNITA, H. (1971). Asymptotic behavior of the nonlinear filtering errors of Markov processes. J. Multivariate Anal. 1 365-393. MR0301812
12. LE GLAND, F., MUSSO, C. and OUDJANE, N. (1998). An analysis of regularized interacting particle methods for nonlinear filtering. In Proc. IEEE European Workshop Comp.- Intensive Methods in Control and Data Process. Prague, Czech Republic 167-174. IEEE, New York.
13. LE GLAND, F. and OUDJANE, N. (2004). Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters. Ann. Appl. Probab. 14 144-187. MR2023019 (Pubitemid 41449255)
14. LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces: Isoperimetry and Processes. Ergebnisse der Mathematik und Ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] 23. Springer, Berlin. MR1102015
15. LEGLAND, F. and OUDJANE, N. (2003). A robustification approach to stability and to uniform particle approximation of nonlinear filters: The example of pseudo-mixing signals. Stochastic Process. Appl. 106 279-316. MR1989630 (Pubitemid 36742401)
16. LI, J. Q. and BARRON, A. R. (1999). Mixture density estimation. In Advances in Neural Information Processing Systems 12 279-285. MIT Press, Cambridge, MA.
17. LIU, J., REICH, J. and ZHAO, F. (2003). Collaborative in-network processing for target tracking. EURASIP J. Appl. Signal Process. 2003 378-391.
18. OCONE, D. and PARDOUX, E. (1996). Asymptotic stability of the optimal filter with respect to its initial condition. SIAM J. Control Optim. 34 226-243. MR1372912 (Pubitemid 126562697)
19. ORESHKIN, B. N. and COATES, M. J. (2009). Error propagation in particle filters with approximation steps. Technical report, McGill Univ. Available at http://www.tsp.ece.mcgill. ca/Networks/publications-techreport.html.
20. RAKHLIN, A. (2006). Applications of Empirical Processes in Learning Theory: Algorithmic Stability and Generalization Bounds. ProQuest LLC, Ann Arbor, MI. MR2717338
21. RAKHLIN, A., PANCHENKO, D. andMUKHERJEE, S. (2005). Risk bounds for mixture density estimation. ESAIM Probab. Stat. 9 220-229 (electronic). MR2148968 (Pubitemid 41643444)
22. VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. Springer, New York. MR1385671
23. WILLIAMS, J. L., FISHER, J. W., III and WILLSKY, A. S. (2007). Approximate dynamic programming for communication-constrained sensor network management. IEEE Trans. Signal Process. 55 4300-4311. MR2464439 (Pubitemid 47261545)
24. ZHANG, T. (2003). Sequential greedy approximation for certain convex optimization problems. IEEE Trans. Inform. Theory 49 682-691. MR1967192
25. ZHAO, F., SHIN, J. and REICH, J. (2002). Information-driven dynamic sensor collaboration. IEEE Signal Processing Magazine 19 61-72. (Pubitemid 34307894)