Decomposition and composition modeling algorithms for control systems with colored noises

Summary This article proposes a novel identification framework for estimating the parameters of the controlled autoregressive autoregressive moving average (CARARMA) models with colored noise. By means of building an auxiliary model and using the hierarchical identification principle, this article investigates a highly‐efficient parameter estimation algorithm. In order to meet the need for identifying the systems with large‐scale parameters, the whole parameters of the CARARMA system is separated into two parameter sets and a decomposition and composition recursive identification algorithm (i.e., hierarchical generalized extended least squares algorithm or decomposition‐based recursive generalized extended least squares algorithm) is presented. Moreover, this article analyzes the convergence of the proposed decomposition and composition recursive identification algorithm. The performance analysis shows that the proposed decomposition and composition identification algorithm can reduce the complexity of the identification algorithm compared with the algorithm without decomposition.