Adaptive background estimation using an information theoretic cost for hidden state estimation

Hidden state estimation in linear systems is a popular and broad research topic which became a mainstream research area after Rudolf Kalman´s seminal paper. The Kalman Filter (KF) gives the optimal solution to the estimation problem in a setting where all the processes are Gaussian random processes. However because of the suboptimal behavior of the KF in non-Gaussian settings, there is a need for a new filter that can extract higher order information from the signals. In this paper we propose using an information theoretic cost function utilizing the similarity measure Correntropy as a performance index. This results in a different perspective on hidden state estimation. We present the superior performance of the new filter on both synthetic data and on adaptive background estimation problem and discuss future research directions.