System modelling is important for studying the motion laws of dynamical systems. Parameters of the system models can be estimated through identification methods from measurement data. This paper develops a gradient-based and a least-squares-based iterative estimation algorithms to estimate the parameters for a multi-input multi-output (MIMO) system with coloured auto-regressive moving average (ARMA) noise from input–output data, based on the gradient search and least-squares principles, respectively. The key is to replace the unknown noise terms and residuals contained in the information vector with their corresponding estimates at the previous iteration. The simulation test results indicate that the proposed algorithms are effective.
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