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

This paper considers the problem of simultaneously estimating the slate 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. Finally we give a numerical example to show that our estimation approach is effective.