Intermediate-variable-based Kalman filter for linear time-varying systems with unknown inputs

This article proposes a systematic design methodology of unknown input estimation for time-varying systems in which unknown inputs exist in system dynamic and measurement simultaneously. By introducing intermediate variables, the relationship between unknown inputs and system states is modeled by an intermediate dynamic process, and then a modified Kalman filter is designed to estimate system states and unknown inputs. Moreover, the stability condition is derived such that the mean square error of the intermediate Kalman filter is bounded. An illustrative example is employed to demonstrate the effectiveness of the proposed methods.