バイアス補償拡張最小相関法に基づく変数誤差モデルの同定

抄録

In this paper, the methods of consistent estimation for identification of linear discrete-time system in the presence of input and output noises, which is usually called “errors-in-variables” (EIV) models, are studied. It is well known that the least squares (LS) method gives biased parameter estimates for EIV situations. To solve this bias problem, the instrumental variable (IV) methods and the least correlation (LC) method are often used. The IV and LC based methods can be applied in more general noise conditions, but these methods suffer from poor accuracy of the estimated parameters because the coefficient matrix of these methods may often become ill-conditioned. In order to obtain numerically stable estimates, the methods presented in this paper use the biased extended LC (XLC) estimates. The biased XLC estimates can be defined by using the extended vectors and the pre-filters. According to the bias compensation principle (BCP) technique, the proposed bias-compensated XLC (BCXLC) methods are developed. The way to reduce the computational load is examined. The results of simulated examples indicate that the proposed methods provide numerically stable and good estimates.