Optimal time-delayed joint input and state estimation for systems with unknown inputs

This paper addresses the time-delayed joint input and state estimation for discrete-time linear stochastic systems with unknown inputs. The objective is to derive an optimal joint (unknown) input and state delayed estimator to relax the unbiasedness conditions of the recently developed extended recursive three-step filter (ERTSF). The conventional rank condition for designing an unbiased minimum-variance state estimator for systems with unknown inputs can be relaxed through this new filter. The relationship with the existing literature results is also addressed. Illustrative examples are provided to verify the usefulness of the proposed results.