A systematic approach for Kalman-type filtering with non-Gaussian noises

For nonlinear systems there exist several Kalman filter extensions that linearize or do moment matching to approximate the nonlinear update. These algorithms usually assume Gaussian measurement noises. The assumption of Gaussian noises degrades the performance when the data contain outliers or are otherwise non-Gaussian. In this paper, we present a new way of treating non-Gaussian noises in a Kalman-type filter. We propose to model non-Gaussian noise as a non-linear transformation of a Gaussian noise, and we develop an algorithm for estimation with this kind of models. Results show that the proposed algorithm can achieve similar estimation accuracy as state-of-the-art methods designed for a specific distribution. However, with some models the estimate diverges and there is still work to do in the development of a suitable Kalman filter extension.