A Unified Solution to Unbiased Minimum-Variance Estimation for Systems with Unknown Inputs

Abstract

A parameterized three-stage Kalman filter (PTSKF) is proposed, serving as a unified solution to unbiased minimum-variance estimation for systems with unknown inputs that affect both the system and the outputs. The PTSKF is characterized by two design parameters and includes three parts: one is for the main system state estimate, the second is for the optimal unknown inputs estimate, and the last is added to further enhance the robust filtering performance. It is shown that the extended robust two-stage Kalman filter (ERTSKF), which is an extension of the previously proposed RTSKF, and the optimal two-stage Kalman filter (OTSKF) are special cases of this new filter. Simulation results show that not only the filtering performance of the PTSKF is compatible to that of the previous proposed parameterized minimum-variance filter (PMVF) but also the computational complexity of the former is less intensive than that of the latter.