ABSTRACT This article investigates the identification issue of multivariable ARX systems with colored noise. To address the bias caused by colored noise, a data filtering method is applied to whiten the original multivariable system, which filters the input–output data without altering their inherent dynamics and yields a filtered identification model. Considering the computational complexity and burden in multivariable system identification, a three‐stage filtered stochastic gradient algorithm is proposed based on the filtered identification model with a hierarchical strategy. In addition, the historical innovations are utilized to further improve estimation accuracy and convergence performance, resulting in a three‐stage filtered multi‐innovation stochastic gradient algorithm. The numerical examples verify the effectiveness of the proposed algorithms in identifying multivariable ARX systems.
Xing et al. (Sun,) studied this question.