A Risk Sensitive Estimator for Nonlinear Problems using the Adaptive Grid Method

Abstract

An Adaptive Grid Method based on the well-known point-mass approximation has been developed for computation of risk-sensitive state estimates in non-linear non-Gaussian problems. Risk-sensitive estimators, believed to have increased robustness compared to their risk neutral counterparts, admit closed form expressions only for a very limited class of models including linear Gaussian models. The Extended Risk-Sensitive Filter (ERSF) which uses an EKF-like approach fails to take care of non-Gaussian problems or severe non-linearities. Recently, a particle-filter based approach has been proposed for extending the range of applications of risk-sensitive techniques. The present authors have developed the adaptive grid risk-sensitive filter (AGRSF), which was partially motivated by the need to validate the particle filter based risk-sensitive filter and uses a set of heuristics for the adaptive choice of grid points to improve the numerical efficiency. The AGRSF has been cross-validated against closed-form solutions for the linear Gaussian case and against the risk-sensitive particle filter (RSPF) for fairly severe non-linear problems which create a multi-modal posterior distribution. Root mean square error and computational cost of the AGRSF and the RSPF have been compared.