A Systematic Approach for Kalman-type Filtering with non-Gaussian Noises

Abstract

For nonlinear systems there exist several Kalman filter extensions that linearize or do moment matching to approx- imate 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.