Difference equation reconstruction algorithms based on generalized least square method

Abstract

The possibilities and singularities of the use of the maximum likelihood method, for an improvement in the estimation of denominator polynomial factors at reconstruction of object discrete transfer function on noisy estimation of its impulse response, are considered. The application of this method reduces the necessity of a nonlinear algebraic system solution. A special iterative algorithm of solution of the system is proposed, on which each step, the solution of two linear systems is made. In this case the reconstruction error of the required factors is generated by an arbitrary choice of shaping filter transfer function order, and by the iterative character of a nonlinear system solution. The procedure of indirect monitoring of the obtained estimation effectiveness, by means of inspection of indices of centrality, whiteness and normality of generating noise estimation, is proposed.