This study considers the parameter estimation of a multi‐variable output‐error‐like system with autoregressive moving average noise. In order to solve the problem of the information vector containing unknown variables, a least squares‐based iterative algorithm is proposed by using the iterative search. The original system is divided into several subsystems by using the decomposition technique. However, the subsystems contain the same parameter vector, which poses a challenge for the identification problem, the approach taken here is to use the coupling identification concept to cut down the redundant parameter estimates. In addition, the recursive least squares algorithm is provided for comparison. The simulation results indicate that the proposed algorithms are effective.

By combining the coupling identification concept with the gradient search, this study develops a partially coupled generalised extended projection algorithm and a partially coupled generalised extended stochastic gradient algorithm to estimate the parameters of a multivariable output‐error‐like system with autoregressive moving average noise from input–output data. The key is to divide the identification model into several submodels based on the hierarchical identification principle and to establish the parameter estimation algorithm by using the coupled relationship between these submodels. The simulation test results indicate that the proposed algorithms are effective.

The parameter estimation problem of multivariable output‐error‐like systems with autoregressive moving average noises is investigated in this study, and the primary system is segregated into some subsystems and a subsystem generalised extended gradient‐based iterative algorithm is presented according to the decomposition technique. Nevertheless, there exists the common parameter vector in each subsystem, which increases the calculation. By taking the mean value of the common parameter estimation vectors of the subsystems as the optimal estimate of the current iteration, and substituting it into the next iteration, a partially coupled subsystem generalised extended gradient‐based iterative algorithm is proposed. Furthermore, in the cause of further deepening the coupled relationships between the common parameter estimation vectors of two subsystems and to reduce the computational cost and the redundant estimates, a partially coupled generalised extended gradient‐based iterative algorithm is presented by making use of the coupling identification concept. Finally, the simulation results show that the coupled gradient‐based iterative algorithms are effective.

This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.