Myopic deconvolution combining Kalman filter and tracking control

In this paper, we propose a deconvolution method based on discrete-time optimal control. By combining Kalman filtering with optimal control, we state the problem in terms of a tracking problem. This leads to solve a set of recurrent equations, including in particular a matrix Riccati equation. We present a method that transforms the solution of these recurrent equations in that of a linear system of equations. Once the linear system has been set up, the deconvolution procedure becomes very fast, and permits on-line deconvolution. It is also possible to use the discrete impulse response, and perform blind deconvolution. This technique includes an L₂ or H_∞ optimal filter. Numerical examples illustrate the robustness of the procedure