Adaptive risk-sensitive filter for Markovian jump linear systems

Abstract

In this paper, we present divergence-based minimax methods to derive the adaptive risk-sensitive filter for Markovian jump linear systems with parameter uncertainties. The risk-sensitive parameter is treated as a random variable rather than chosen as a prior, which reflects the hypothesis merging property. To tackle the proposed joint probability density function due to the introduction of the random variable, a method that projects orthogonally the original probability measure into a new independent conditional probability space in the Kullback–Leibler (KL) sense is then presented. The exact close-form expression can be obtained via optimization that is of a form suitable in a recursive procedure. The proposed filter can improve robustness by increasing the mixed covariance, whose risk-sensitive like parameter can be updated adaptively using the measurements to fit different situations well. Simulation examples illustrate that the proposed methods can be regarded as competitive alternatives to existing robust approaches against modeling uncertainties.