IDENTIFICATION WITH SEQUENCE ESTIMATION

Abstract

Into the description of the black box internal system, it is needed to know the relationship generated between the response and the excitation, establishing a model that approximates its answer only for a specific condition. This requires the model to approach the parameters selection for each condition generated by the excitation signal and the response given. In spite of this consideration, the convergence level could be highest, but the model response never describes the internal system dynamics; instead of it, it is possible if is viewed through internal parameters of the model bounded by stability inputs and outputs. Based on this, a FIR (Finite Impulse Response) filter identification is composed of a set of parameters that accomplishes with the Markov parameters and besides, maintaining the filter stability. Therefore, the problem is the parameters estimation through of a sequence in the same time interval applying into identification developing the signal convergence response with respect to the reference interval evolution. Furthermore, the sequence estimation is performed dynamically and adapted to misidentification, achieving to minimize the convergence error at each interval. Thus the identifier, in addition to parameters estimation sequence, requires a gain that affects the innovation process minimizing the uncertainties generated after reaching the stationary condition. Unfortunately, this convergence occurs in a small region, which depends on the variances of the signals disturbances. Keywords: Estimator, sequence of matrices, functional error, stochastic gradient, pseudo-inverse, the second probability moment.