Difference equation reconstruction algorithms based on maximum likelihood method

Abstract

The possibilities and singularities of use of the maximum likelihood method for an improvement of the estimations of denominator polynomial factors at reconstruction of an 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. The special iterative algorithm of a solution of the indicated system is offered, in which for 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 enough choice of transfer function order of the shaping filter and by the iterative character of a nonlinear system solution. The procedure of indirect monitoring of the obtained estimations effectiveness by means of inspection of indexes of centrality, whiteness and normality of generating noise estimation is offered.