Data-Based Filters for Non-Gaussian Dynamic Systems with Unknown Output Noise Covariance

This paper proposes linear and nonlinear filters for a non-Gaussian dynamic system with an unknown nominal covariance of the output noise. The challenge of designing a suitable filter in the presence of an unknown covariance matrix is addressed by focusing on the output data set of the system. Considering that data generated from a Gaussian distribution exhibit ellipsoidal scattering, we first propose the weighted sum of norms (SON) clustering method that prioritizes nearby points, reduces distant point influence, and lowers computational cost. Then, by introducing the weighted maximum likelihood, we propose a semi-definite program (SDP) to detect outliers and reduce their impacts on each cluster. Detecting these weights paves the way to obtain an appropriate covariance of the output noise. Next, two filtering approaches are presented: a cluster-based robust linear filter using the maximum a posterior (MAP) estimation and a cluster-based robust nonlinear filter assuming that output noise distribution stems from some Gaussian noise resources according to the ellipsoidal clusters. At last, simulation results demonstrate the effectiveness of our proposed filtering approaches.