In Search for Improved Auxiliary Particle Filters

In designing a particle filter, the most important task is choosing the importance function that can generate good particles. If the importance function, also calledproposal, does a satisfactory job, the particles of the filter are placed in parts where the explored state space has high probability mass. Further, the weights of these particles are not too disparate in values. An important class of particle filtering that uses a clever approach to create good importance functions is known as auxiliary particle filtering. In this paper, we first analyze the approximations used for computing the particle weights of the standard auxiliary particle filter. We show that these approximations can be detrimental to the performance of the auxiliary particle filter. Further, we propose a more comprehensive evaluation of the weights, which leads to a much enhanced performance of the auxiliary particle filter. We also demonstrate the improvements with computer simulations.

[1]  Jukka Corander,et al.  Layered adaptive importance sampling , 2015, Statistics and Computing.

[2]  Walter R. Gilks,et al.  RESAMPLE-MOVE Filtering with Cross-Model Jumps , 2001, Sequential Monte Carlo Methods in Practice.

[3]  A. M. Johansen,et al.  The Iterated Auxiliary Particle Filter , 2015, 1511.06286.

[4]  Nicholas G. Polson,et al.  Particle Filtering , 2006 .

[5]  Fredrik Gustafsson,et al.  Particle filters for positioning, navigation, and tracking , 2002, IEEE Trans. Signal Process..

[6]  Luca Martino,et al.  Weighting a resampled particle in Sequential Monte Carlo , 2016, 2016 IEEE Statistical Signal Processing Workshop (SSP).

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

[8]  Mónica F. Bugallo,et al.  Population Monte Carlo schemes with reduced path degeneracy , 2017, 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[9]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[10]  Joaquín Míguez,et al.  A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models , 2012, Stat. Comput..

[11]  Petar M. Djuric,et al.  New resampling algorithms for particle filters , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

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

[13]  Luca Martino,et al.  Improving population Monte Carlo: Alternative weighting and resampling schemes , 2016, Signal Process..

[14]  James V. Candy,et al.  Bayesian Signal Processing: Classical, Modern and Particle Filtering Methods , 2009 .

[15]  Ángel F. García-Fernández,et al.  Adaptive Auxiliary Particle Filter for Track-Before-Detect With Multiple Targets , 2017, IEEE Transactions on Aerospace and Electronic Systems.

[16]  Luca Martino,et al.  Effective sample size for importance sampling based on discrepancy measures , 2016, Signal Process..

[17]  Michael K. Pitt,et al.  Auxiliary Variable Based Particle Filters , 2001, Sequential Monte Carlo Methods in Practice.

[18]  David Luengo,et al.  Generalized Multiple Importance Sampling , 2015, Statistical Science.

[19]  Xiao-Li Meng,et al.  Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling , 1998 .

[20]  Petar M. Djuric,et al.  Assessment of Nonlinear Dynamic Models by Kolmogorov–Smirnov Statistics , 2010, IEEE Transactions on Signal Processing.

[21]  Ömer Deniz Akyildiz,et al.  Nudging the particle filter , 2017, Statistics and Computing.

[22]  Petar M. Djuric,et al.  Adaptive Importance Sampling: The past, the present, and the future , 2017, IEEE Signal Processing Magazine.

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

[24]  T. Bertozzi,et al.  On particle filtering for digital communications , 2003, 2003 4th IEEE Workshop on Signal Processing Advances in Wireless Communications - SPAWC 2003 (IEEE Cat. No.03EX689).

[25]  Petar M. Djuric,et al.  Resampling Methods for Particle Filtering , 2015 .

[26]  Wen-Hua Chen,et al.  An Auxiliary Particle Filtering Algorithm With Inequality Constraints , 2017, IEEE Transactions on Automatic Control.