Particle filters with independent resampling

In many signal processing applications we aim to track a state of interest given available observations. Among existing techniques, sequential Monte Carlo filters are importance sampling-based algorithms meant to propagate in time a set of weighted particles which represent the a posteriori density of interest. As is well known weights tend to degenerate over time, and resampling is a commonly used rescue for discarding particles with low weight. Unfortunately conditionally independent resampling produces a set of dependent samples and the technique suffers from sample impoverishment. In this paper we modify the resampling step of particle filtering techniques in order to produce independent samples per iteration. We validate our technique via simulations.

[1]  Haikady N. Nagaraja,et al.  Inference in Hidden Markov Models , 2006, Technometrics.

[2]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

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

[4]  Yohan Petetin,et al.  Optimal SIR algorithm vs. fully adapted auxiliary particle filter: a non asymptotic analysis , 2012, Statistics and Computing.

[5]  Petar M. Djuric,et al.  Resampling Methods for Particle Filtering: Classification, implementation, and strategies , 2015, IEEE Signal Processing Magazine.

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

[7]  Jun S. Liu,et al.  Blind Deconvolution via Sequential Imputations , 1995 .

[8]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[9]  Eric Moulines,et al.  On parallel implementation of sequential Monte Carlo methods: the island particle model , 2013, Stat. Comput..

[10]  François Septier,et al.  Bayesian nonparametric state and impulsive measurement noise density estimation in nonlinear dynamic systems , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  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..

[12]  Fredrik Lindsten,et al.  Nested Sequential Monte Carlo Methods , 2015, ICML.

[13]  Fredrik Gustafsson,et al.  On Resampling Algorithms for Particle Filters , 2006, 2006 IEEE Nonlinear Statistical Signal Processing Workshop.

[14]  Y. Ho,et al.  A Bayesian approach to problems in stochastic estimation and control , 1964 .