Optimal Linear Filtering for Stochastic non-Gaussian Descriptor Systems

Stochastic linear discrete-time singular systems, also named descriptor systems, have been widely investigated in recent years and important results on optimal filtering according to the maximum likelihood (ML) criterion have been achieved in the Gaussian framework. The ML approach cannot be easily extended to non-Gaussian systems. In this paper, the estimation problem for non-Gaussian descriptor systems is studied by following the minimum error variance criterion and the optimal linear filter is developed by constructing the best estimator among a suitable class of linear output transformations. It is shown that, when applied in the Gaussian case, the proposed filter gives back the ML filter. Simulations support the theoretical results.