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Abstract-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 sub-optimal 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. We present the superior performance of the new filter on both synthetic data and on adaptive background estimation problem and discuss future research directions.

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The auditory cortex in the brain does effortlessly a better job of extracting information from the acoustic world than our current generation of signal processing algorithms. Abstracting the principles of the auditory cortex, the proposed architecture is based on Kalman filters with hierarchically coupled state models that stabilize the input dynamics and provide a representation space. This approach extracts information from the input and self-organizes it in the higher layers leading to an algorithm capable of clustering time series in an unsupervised manner. An important characteristic of the methodology is that it is adaptive and self-organizing, i.e. previous exposure to the acoustic input is the only requirement for learning and recognition, so there is no need of selecting the number of clusters.