Filtered auxiliary model recursive generalized extended parameter estimation methods for Box–Jenkins systems by means of the filtering identification idea

• Published in: International journal of robust and nonlinear control Vol. 33; no. 10; pp. 5510 - 5535
• Main Authors: Ding, Feng, Xu, Ling, Zhang, Xiao, Zhou, Yihong
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.07.2023
• Subjects: Autoregressive moving average; auxiliary model identification; filtering identification; Filtration; gradient search; Identification methods; Innovations; Least squares; multi‐innovation identification; Parameter estimation; Stochastic systems
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6657

For equation‐error autoregressive moving average systems, that is, Box–Jenkins systems, this paper presents a filtered auxiliary model generalized extended stochastic gradient identification method, a filtered auxiliary model multi‐innovation generalized extended stochastic gradient identification method, a filtered auxiliary model recursive generalized extended gradient identification method, a filtered auxiliary model multi‐innovation recursive generalized extended gradient identification method, a filtered auxiliary model recursive generalized extended least squares identification method, and a filtered auxiliary model multi‐innovation recursive generalized extended least squares identification method by using the filtering identification idea and the auxiliary model identification idea. The proposed filtered auxiliary model recursive generalized extended identification methods can be generalized to other linear and nonlinear multivariable stochastic systems with colored noises.