An optimal deconvolution smoother for systems with random parametric uncertainty and its application to semi-blind deconvolution

This paper develops a Kalman smoother to estimate white noise input for systems with random parametric uncertainties in the observation equation. The derived input estimator is optimal in terms of the mean square error (MSE) criterion. Convergence analysis for the derived Kalman smoother is provided, which shows that stability of the Kalman filter cannot guarantee that of the designed fixed-point Kalman smoother. Furthermore, the designed smoothing estimator is applied to the semi-blind deconvolution problem, and an optimal solution is obtained. Numerical examples are given to demonstrate the performance of the proposed method in comparison with two typical deconvolution methods.