Unbiased steady minimum-variance estimation for systems with measurement-delay and unknown inputs

Abstract This paper considers the problem of simultaneously estimating the state and the unknown input for linear discrete-time systems with measurement delay. Firstly, the reorganized innovation analysis approach is applied to deal with measurement delay and the measurement delay model is converted into a measurement delay free model. A recursive filter where the estimation of the state and the input are interconnected is proposed. Then we utilize the innovation to obtain the unknown input estimator by least-squares estimation and the optimal state estimator is constructed by transforming into a standard Kalman filtering in terms of two Riccati equations with the same dimension as the state model. Further, the infinite horizon asymptotic stability of proposed filter is discussed. Finally we give a numerical example to show that our estimation approach is effective.