Moving horizon state estimation for linear discrete-time singular systems

In this study, the moving horizon recursive state estimator for linear singular systems is derived from the least squares estimation problem. It will be shown that this procedure yields the same state estimate as the Kalman filter for descriptor systems when the noises are Gaussian. The obtained results are applied to the state and the unknown inputs estimation for discrete-time systems with unknown inputs. A numerical example is presented to illustrate the proposed method.