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. 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.