Optimal filtering for systems with unknown inputs

Abstract

An optimal filtering formula is derived for linear time-varying discrete systems with unknown inputs. By making use of the well-known innovations filtering technique, the derivation is an extension of a new observer design method for time-invariant deterministic systems with unknown inputs. The systems under consideration have the most general form. The derived optimal filter has a similar form to the standard Kalman filter with some modified covariance and gain matrices.