Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems

Abstract

This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.

Parameter estimation for time‐delay systems based on the frequency responses and harmonic balance methods

“…The simulation results validate the performance of the presented algorithms. The algorithm in this article is proposed for linear time-delay systems but the idea can extended to other linear and nonlinear time-delay stochastic systems [65][66][67][68][69][70][71][72][73][74][75] and can be applied to other literature studies [76][77][78][79][80][81][82][83][84][85][86][87][88] such as signal processing and vibration analysis.…”

Two‐stage recursive identification algorithms for a class of nonlinear time series models with colored noise

“…The proposed algorithms in this article are based on this identification model in (2). Many identification methods are derived based on the identification models of the systems [40][41][42][43][44] and can be used to estimate the parameters of other linear systems and nonlinear systems [45][46][47] and can be applied to fields such as chemical process control systems. Note that y(t) is highly nonlinear with respect to the parameter , the LS method cannot be used directly for the ExpARMA model.…”

“…Equations (34)- (46) form the 2S-LS-ESG algorithm for the ExpARMA model. Form the information vectors (t), s (̂(t − 1), t),̂n(t) and̂(̂(t − 1), t) by (41), (42), (43), (44).…”

“…When p = 1, the 2S-LS-MIESG algorithm reduces to the 2S-LS-ESG algorithm. Similar to the 2S-LS-ESG algorithm in (34)- (46), the 2S-LS-MIESG algorithm computes the parameter estimateŝ(t) and̂(t) by an interactive way. Moreover, the recursion computation of 2S-LS-MIESG algorithm involves more innovations and data.…”

Parameter identification of a nonlinear radial basis function‐based state‐dependent autoregressive network with autoregressive noise via the filtering technique and the multiinnovation theory

“…The colored noise comes in different forms, including the autoregressive (AR) process, the moving average (MA) process and the ARMA process. 32,33 This article studies the parameter estimation methods of the RBF-AR model with AR noise (RBF-ARAR model for short). According to the RBF-ARAR model, a special filter is selected to filter the observed data based on the data filtering technique, and then a filtered identification model and a noise identification model are obtained.…”