Risk-Sensitive Particle Filters for Mitigating Sample Impoverishment

Risk-sensitive filters (RSF) put a penalty to higher-order moments of the estimation error compared to conventional filters as the Kalman filter minimizing the mean square error (MSE). The result is a more cautious filter, which can be interpreted as an implicit and automatic way to increase the state noise covariance. On the other hand, the process of jittering, or roughening, is well known in particle filters to mitigate sample impoverishment. The purpose of this contribution is to introduce risk-sensitive particle filters (RSPF) as an alternative approach to mitigate sample impoverishment based on constructing explicit risk functions from a general class of factorizable functions. It is first shown that RSF can be done in nonlinear systems using a recursion of an infinite dimensional information state which involves general risk functions. Then, this information state calculation is carried out using particle approximations. Some alternative approaches, generalizations, specific cases, comparison to existing methods of sample impoverishment mitigation and issues related to the selection of risk functions and parameters are examined. Performance of the resulting filter using various risk functions is illustrated on a simulated scenario and compared with the roughening method.

[1]  Robert J. Elliott,et al.  Risk-sensitive generalizations of minimum variance estimation and control , 1997 .

[2]  Arnaud Doucet,et al.  Particle filters for state estimation of jump Markov linear systems , 2001, IEEE Trans. Signal Process..

[3]  Simon J. Godsill,et al.  On sequential simulation-based methods for Bayesian filtering , 1998 .

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

[5]  S. Sadhu,et al.  Alternative Formulation of Risk-Sensitive Particle Filter (Posterior) , 2006, 2006 Annual IEEE India Conference.

[6]  J. Speyer,et al.  Optimal stochastic estimation with exponential cost criteria , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[7]  S. Sadhu,et al.  Particle Methods for Risk Sensitive Filtering , 2005, 2005 Annual IEEE India Conference - Indicon.

[8]  John B. Moore,et al.  Finite-dimensional risk-sensitive filters and smoothers for discrete-time nonlinear systems , 1999, IEEE Trans. Autom. Control..

[9]  John Langford,et al.  Risk Sensitive Particle Filters , 2001, NIPS.

[10]  Fredrik Gustafsson,et al.  Risk Sensitive Particle Filters for Mitigating Sample Impoverishment , 2007 .

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

[12]  Lakhdar Aggoun,et al.  Measure Theory and Filtering : Introduction with Applications , .

[13]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[14]  Pravin Varaiya,et al.  Stochastic Systems: Estimation, Identification, and Adaptive Control , 1986 .

[15]  Vahid Reza Ramezani,et al.  Product Estimators for Hidden Markov Models , 2001 .

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

[17]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[18]  Ian R. Petersen,et al.  Robustness and risk-sensitive filtering , 2002, IEEE Trans. Autom. Control..

[19]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

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

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

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

[23]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[24]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[25]  S. Dey,et al.  Risk-sensitive filtering and smoothing via reference probability methods , 1995, Proceedings of 1995 American Control Conference - ACC'95.