باقی مانده های تعاملی مبتنی بر حداقل مربعات الگوریتم ها و مطالعات شبیه سازی

This paper presents a two-stage least squares based iterative algorithm, a residual based interactive least squares algorithm and a residual based recursive least squares algorithm for identifying controlled autoregressive moving average (C-ARMA) models. The simulation studies indicate that the proposed algorithms can effectively estimate the parameters of the C-ARMA models.

The time series contains three basic models: autoregressive (AR) model, moving average (MA) model and autoregressive moving average (ARMA) model. This paper considers the least squares identification problem of controlled autoregressive moving average (C-ARMA) model. Compared with least squares (LS) algorithm, the stochastic gradient (SG) algorithm has small computational load but slow convergence rate [1]. Recently, Ding, Yang and Liu analyzed the consistency of the multivariable SG algorithm [2]; Ding and Chen presented a hierarchical SG algorithm for multivariable systems [3] and an auxiliary model based SG algorithm for dual-rate systems [4]; Ding et al. studied the performances of the SG algorithms for dual-rate systems based on the polynomial transformation technique [5] and [6]. In order to improve the convergence rate of the SG algorithm, Ding and Chen developed a multi-innovation SG identification algorithm for linear regression model [7] and an extended stochastic gradient algorithm with a forgetting factor for Hammerstein nonlinear systems [8]; Ding and Wang discussed the gradient based identification algorithm for Hammerstein–Wiener ARMAX systems [9]. Finally, Zhang, Ding and Shi presented a multi-innovation SG parameter estimation based self-tuning control algorithm [10]. Because of the fast convergence rate of the least squares identification, it has received much attention in many areas, including signal processing [11], system identification and parameter estimation [12], [13], [14], [15], [16], [17], [18] and [19], adaptive control [5], [20] and [21]. For example, Ding and Chen presented a hierarchical LS algorithm for multivariable systems [22], whose consistency was studied in [23]; Ding and Chen proposed an auxiliary model based LS algorithm for dual-rate systems [24]; Ding, Liu and Shi studied the performances of the polynomial transform based LS algorithm for dual-rate systems [25].

The paper presents a residual based least squares algorithm and a residual based interactive least squares algorithm for C-ARMA models. The methods in this paper can be extended to finite impulse response Hammerstein nonlinear systems with autoregressive moving average noise [12] and [8].