System parameter estimation methods using template functions.

Abstract

Abstract.This paper presents a system parameter estimation method for correlated noise systems by using template functions and conjugate equations. The so-called extended template function estimator is developed on the basis of the conjugate equation theory. Under some weak conditions the parameter estimates obtained with the extended template function method are asymptotically Gaussian distributed. The covariance matrix of this distribution can then be used as a measure of the accuracy. In this paper it will be shown that this matrix can be optimized with respect to the vector of template functions and to the prefilter and that an optimal vector of template functions really do exist.With the optimal choice of the template function vector and of the prefilter, the proposed extended template function estimator reduces to the optimal instrumental variable estimator. When implementing the optimal template function method, a multistep algorithm consisting of four simple steps is proposed to estimate the system parameters and the parameters describing the noise characteristics.Tom tlit. Bai nay trlnh bay mot phiro'ng ph ap danh gia thOng so h~thong doi vo'i cac h~on nhieu c6 ttro'ng quan tren co-so' cac ham m~u v a cac phtrc'ng trrnh lien ho'p. Bi? danh gia dung ham mill mo' ri?ng duo c ph at trie'n du'a treri ly thuyet cac phtro'ng trmh lien ho'p, Trong mo t so di'eu kien ygu, cac dan h gia thong s6 rih an diro'c bang phtrc'ng ph ap ham m~u mo: rong c6 ph an bo Gauss ti~m c~n. Ma tr~n h iep bign cd a ph an bo nay co the' dU'(?,cdung nhu' mot thtro'c do di? chirih xac , Trong bai bao nay, ch ung toi se chimg to ding ma tr~n nay c6 the' du'o'c toi Ul1 h6a doi voi vecto: cac ham mill, doi voi bi? ti'en 19C v a chirng minh s~' ton ta.i ciia vecto: toi U'U cac ham m~u. VO'i viec chon toi Ul1 vecto cac ham m~u va bi? tien 19C, bi? darih gia dung cac ham mill mo: ri?ng ducc de xuat qui ve bi? danh gia bien dung c~toi Ul1. Khi thtrc hien phiro'ng ph ap ham mill t6i Ul1, mot thuat gi<lj bao gom bon birc'c do'n gian d a dtro'c d'e xufit de' d arih gia cac thong so M th6ng v a cac thOng so mo ta cac d~c trung cii a on nhie u.