Optimal recursive linear filtering for general discrete time singular systems

This paper deals with optimal recursive filtering for time-variant singular systems. The novelty of this paper is the functional developed to deduce this filter in which least squares and penalty functions approaches are combined in a unified way. The advantage of this new procedure will be emphasized in the paper. The nominal singular Kalman filter will be deduced in its most general formulation when the state and measurement noises are correlated. It presents simple and useful symmetric structure.