Three‐Stage Filtered Gradient Identification Methods for Multivariable ARX Systems With Colored Noise

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.