ℒ2 optimization in discrete FIR estimation: Exploiting state-space structure

This paper studies the ℒ² (mean-square) optimal design of discrete-time FIR estimators. A solution procedure, which reduces the problem to a static matrix optimization problem admitting a closed-form solution, is proposed. In the latter solution, a special state-space structure of the associated matrices is exploited to obtain efficient formulae with the computational complexity proportional to the length of the impulse response of the estimator. This is a considerable improvement over Levinson-like algorithms. The proposed procedure can also handle interpolation constraints on the unit circle, which facilitates the inclusion of steady-state performance requirements.