Linear estimation for discrete-time periodic systems with unknown measurement input and missing measurements

This paper considers the estimation problem for periodic systems with unknown measurement input and missing measurements. The missing measurements phenomenon is described by an independent and identically distributed Bernoulli process. The quality of the estimation achieved by an admissible filter is measured by a performance criterion described by the Cesaro limit of the mean square of the deviation between the remote signal and the estimated signal. By employing the minimum variance unbiased estimation technique, the periodic unbiased estimator is obtained, where the estimator gain is designed in terms of the unique periodic solution of a Lyapunov equation together with the periodic stabilizing solution of a Riccati equation. Finally, a numerical example is provided to show the effectiveness of the proposed estimation approach.