Feedback particle filter: Application and evaluation

Recent research has provided several new methods for avoiding degeneracy in particle filters. These methods implement Bayes' rule using a continuous transition between prior and posterior. The feedback particle filter (FPF) is one of them. The FPF uses feedback gains to adjust each particle according to the measurement, which is in contrast to conventional particle filters based on importance sampling. The gains are found as solutions to partial differential equations. This paper contains an evaluation of the FPF on two highly nonlinear estimation problems. The FPF is compared with conventional particle filters and the unscented Kalman filter. Sensitivity to the choice of gains is discussed and illustrated. We demonstrate that with a sensible approximation of the exact gain function, the FPF can decrease tracking errors with more than one magnitude while significantly improving the quality of the particle distribution.

[1]  Tao Ding,et al.  Implementation of the Daum-Huang exact-flow particle filter , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[2]  Simon J. Godsill,et al.  An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo , 2007, Proceedings of the IEEE.

[3]  Karl Berntorp.  Particle filter for combined wheel-slip and vehicle-motion estimation , 2015, 2015 American Control Conference (ACC).

[4]  J. Guermond,et al.  Theory and practice of finite elements , 2004 .

[5]  Sean P. Meyn,et al.  A mean-field control-oriented approach to particle filtering , 2011, Proceedings of the 2011 American Control Conference.

[6]  Fred Daum,et al.  Nonlinear filters with particle flow , 2009, Optical Engineering + Applications.

[7]  Fredrik Gustafsson,et al.  Statistical Sensor Fusion , 2013 .

[8]  Jeffrey K. Uhlmann,et al.  Corrections to "Unscented Filtering and Nonlinear Estimation" , 2004, Proc. IEEE.

[9]  F Gustafsson,et al.  Particle filter theory and practice with positioning applications , 2010, IEEE Aerospace and Electronic Systems Magazine.

[10]  Uwe D. Hanebeck,et al.  S2KF: The Smart Sampling Kalman Filter , 2013, Proceedings of the 16th International Conference on Information Fusion.

[11]  Sean P. Meyn,et al.  Multivariable feedback particle filter , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[12]  Simon J. Godsill,et al.  Particle filtering with progressive Gaussian approximations to the optimal importance density , 2013, 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[13]  Rudolph van der Merwe,et al.  The unscented Kalman filter for nonlinear estimation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[14]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

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

[16]  Uwe D. Hanebeck,et al.  Semi-analytic Gaussian Assumed Density Filter , 2011, Proceedings of the 2011 American Control Conference.

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

[18]  Tao Yang,et al.  The continuous-discrete time feedback particle filter , 2014, 2014 American Control Conference.

[19]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[20]  Fred Daum,et al.  Particle degeneracy: root cause and solution , 2011, Defense + Commercial Sensing.

[21]  Wolfram Burgard,et al.  Improved Techniques for Grid Mapping With Rao-Blackwellized Particle Filters , 2007, IEEE Transactions on Robotics.

[22]  Fred Daum,et al.  Particle flow with non-zero diffusion for nonlinear filters , 2013, Defense, Security, and Sensing.

[23]  Tao Yang,et al.  Feedback particle filter and its applications , 2014 .

[24]  Uwe D. Hanebeck,et al.  Progressive Bayes: a new framework for nonlinear state estimation , 2003, SPIE Defense + Commercial Sensing.

[25]  J. Zabczyk,et al.  Wong-Zakai approximations of stochastic evolution equations , 2006 .

[26]  Thomas B. Schön,et al.  Marginalized particle filters for mixed linear/nonlinear state-space models , 2005, IEEE Transactions on Signal Processing.

[27]  Simo Särkkä,et al.  On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear Systems , 2007, IEEE Trans. Autom. Control..

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

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

[30]  Karl-Erik Årzén,et al.  Rao–Blackwellized Particle Filters With Out-of-Sequence Measurement Processing , 2014, IEEE Transactions on Signal Processing.

[31]  Prashant G. Mehta,et al.  A comparative study of nonlinear filtering techniques , 2013, Proceedings of the 16th International Conference on Information Fusion.

[32]  Fred Daum,et al.  Exact particle flow for nonlinear filters , 2010, Defense + Commercial Sensing.

[33]  Sean P. Meyn,et al.  Feedback Particle Filter , 2013, IEEE Transactions on Automatic Control.

[34]  Wolfram Burgard,et al.  Particle Filters for Mobile Robot Localization , 2001, Sequential Monte Carlo Methods in Practice.

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