Optimal recursive estimation for discrete-time descriptor systems

In this paper, we revisit the optimal recursive estimation problem for general time-variant descriptor systems. Instead of the standard stochastic formulation, the estimates are derived using deterministic arguments in a completely self-contained way. We show that the filter recursions can be obtained as a solution of appropriate deterministic data-fitting problems. Two data-fitting problems are considered in this paper: the first involves the entire trajectory, and the second is performed taking into account a one-step correction. A numerical example is presented to illustrate the performance of the filtered and predicted estimators.