On Resampling Algorithms for Particle Filters

In this paper a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms with respect to their resampling quality and computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in terms of resampling quality and computational complexity.

[1]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[2]  A. Winsor Sampling techniques. , 2000, Nursing times.

[3]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[4]  A. Narayanan Probability and statistics in engineering and management science , 1972 .

[5]  Arnaud Doucet,et al.  A survey of convergence results on particle filtering methods for practitioners , 2002, IEEE Trans. Signal Process..

[6]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[7]  C. Chatfield Probability and statistics in engineering and management science , 1973 .

[8]  A. Owen Monte Carlo Variance of Scrambled Net Quadrature , 1997 .

[9]  G. Kitagawa Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[10]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[11]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[12]  Jeroen D. Hol,et al.  Resampling in particle filters , 2004 .

[13]  P. Gruber,et al.  Funktionen von beschränkter Variation in der Theorie der Gleichverteilung , 1990 .

[14]  Eric Moulines,et al.  Comparison of resampling schemes for particle filtering , 2005, ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005..

[15]  E. Hlawka Funktionen von beschränkter Variatiou in der Theorie der Gleichverteilung , 1961 .

[16]  Kristine L. Bell,et al.  A Tutorial on Particle Filters for Online Nonlinear/NonGaussian Bayesian Tracking , 2007 .

[17]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.