Abstract
In this paper we present several new sequential Monte Carlo (SMC) algorithms for online estimation (filtering) of nonlinear dynamic systems. SMC has been shown to be a powerful tool for dealing with complex dynamic systems. It sequentially generates Monte Carlo samples from a proposal distribution, adjusted by a set of importance weight with respect to a target distribution, to facilitate statistical inferences on the characteristic (state) of the system. The key to a successful implementation of SMC in complex problems is the design of an efficient proposal distribution from which the Monte Carlo samples are generated. We propose several such proposal distributions that are efficient yet easy to generate samples from. They are efficient because they tend to utilize both the information in the state process and the observations. They are all Gaussian distributions hence are easy to sample from. The central ideas of the conventional nonlinear filters, such as extended Kalman filter, unscented Kalman filter and the Gaussian quadrature filter, are used to construct these proposal distributions. The effectiveness of the proposed algorithms are demonstrated through two applications—real time target tracking and the multiuser parameter tracking in CDMA communication systems.
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Agate C.S. and Iltis R. 1999. Statistics of the RSS estiamtion algorithm for gaussian measurement noise. IEEE Trans. on Sign. Proc. 47(1): 22–32.
Alspace D.L. and Sorenson H.W. 1972. Nonlinear bayesian estimation using the gaussian sum approximation. IEEE Transaction on Automatic Control 17: 439–448.
Arulampalam S., Maskell S., Gordan N., and Clapp T. 2002. A tutorial on particle filter for on-line non-linear/non-gaussian bayesian tracking. IEEE Trans. Sig. Proc. 50(2): 174–188.
Avitzour D. 1995. A stochastic simulation Bayesian approach to multitarget tracking. lEE Proceedings on Radar, Sonar and Navigation 142: 41–44.
Caffery J. and Stuber G.L. 2000. Nonlinear multiuser parameter estimation and tracking CDMA system. IEEE Trans. on Commun. 48(12): 2053–2063.
Chen R. and Liu J.S. 2000. Mixture Kalman filters. Journal of the Royal Statistical Society, Series B 62: 493–509.
Chen R., Wang X., and Liu J.S. 2000. Adaptive joint detection and decoding in flat-fading channels via mixture Kalman filtering. IEEE Trans. Inform. Theory 46(6): 2079–2094.
Dellaert F., Fox D., Burgard W., and Thrun S. 1999. Monte Carlo localization for mobile robots. In ICRA.
Dellaert F., Fox D., Burgard W., and Thrun S. 1999. Using the condensation algorithm for robust, vision-based mobile robot localization. In CVPR.
Doucet A., Dreitas N.D., Murphy K., and Russell S. 2000. Rao-blackwellised particle filtering for dynamic bayesian networks. In Sixteenth Conference on Uncertainty in Artificial intelligence, Stanford, pp. 176–183.
Doucet A., de Freitas J.F.G., and Gordon N. 2001. Sequential Monte Carlo in Practice. Cambridge University Press.
Doucet A., Godsill S.J., and Andrieu C. 2000. On sequential simulation-based methods for Bayesian filtering. Statisti. Comput. 10(3): 197–208.
Gordon N.J., Salmon D.J., and Ewing C.M. 1995. Bayesian state estimation for tracking and guidance using the bootstrap filter. AIAA Journal of Guidance, Control and Dynamics 18: 1434–1443.
Gerstner T. and Griebel M. 1998. Numerical integration using sparse grids. Numerical Algorithms 18(4): 209–232.
Handschin J.E. 2003. Monte Carlo techniques for prediction and filtering of non-linear stochastic processes. Atomatica, 1970(6): 555–563.
Isard M. and Blake A. 1997. A mixed-state Condensation tracker with automatic model switching. In ECCV.
Isard M. and Blake A. 1998. Condensation—conditional density propogation for visual tracking. In IJCV, vol. 29, pp. 5–28.
Ito K. and Xiong K. 2000. Gaussian filters for nonlinear filtering problems. IEEE Transaction on Automatic Control 45(5): 910–827.
Kong A., Liu J.S., and Wong W.H. 1994. Sequential imputations and Bayesian missing data problems. J. Amer. Statist. Assoc 89: 278–288.
Liu J.S. 2001. Monte Carlo Strategies for Scientific Computing. Springer-Verlag, New York.
Liu J.S. and Chen R. 1995. Blind deconvolution via sequential imputations. Journal of the American Statistical Association 90: 567–576.
Liu J.S. and Chen R. 1998. Sequential Monte Carlo methods for dynamic systems. Journal of the American Statistical Association 93: 1032–1044.
Minka T.P. 2001. Expectation propagation for approximate bayesian inference. In Uncertainty in AP01.
Petras K. 2001. Fast calculation of coefficients in the Smolyak algorithm. Numerical Algorithms 26(2): 93–109.
Pitt M.K. and Shephard N. 1999. Filtering via simulation: auxiliary particle filters. J. Amer. Statist. Assoc. 94(446): 590–601.
Press W., Teukolsky S., Vetterling W., and Flannery B.P. 1992. Numerical Recipes in C: The Art of Scientific Computing, 2nd edition. Cambridge Press, London.
Shephard N. and Pitt M.K. 1997. Likelihood analysis of non-gaussian measurement time series. Biometrika 84: 653–667.
Silverman B.W. 1986. Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York.
Thrun S., Dellaert F., Fox D., and Burgard W. 2001. Robust Monte Carlo localization for mobile robots. In Artifical Intelligence Journel.
Vlasis N., Terwijn B., and Krose B. 2002. Auxiliary partifcle filter robot localization from high-dimensional sensor observations. In IEEE Int. Conf. on Robots and Automation, Wahsington D.C., pp. 7–12.
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This work was supported in part by the U.S. National Science Foundation (NSF) under grants CCR-9875314, CCR-9980599, DMS-9982846, DMS-0073651 and DMS-0073601.
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Guo, D., Wang, X. & Chen, R. New sequential Monte Carlo methods for nonlinear dynamic systems. Stat Comput 15, 135–147 (2005). https://doi.org/10.1007/s11222-005-6846-5
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DOI: https://doi.org/10.1007/s11222-005-6846-5