Identification of Non Stationary ARMA Models Based on Matrix Forgetting

Abstract

Abstract. To identify time-varying matrix parameter participating in ARMAX-model description, a new recursive procedure is suggested in this thesis. This algorithm presents a combination of recursive version of Instrumental Variable procedure together with Matrix Forgetting Factor. The asymptotic value of the identification error "in average" is shown to have a bound which turns out to be dependent on the rate of parameter changing as well as on the variance of noise to be applied. By Monte-Carlo method it was shown that identification performance index has a minimum within the set of matrix forgetting with a norm less then 1. The optimum value as well as the corresponding optimal matrix forgetting are dependent on unknown parameters of a given ARMAX model and also on statistic characteristics of the applied noises.