This study applies the filtering technique to system identification to study the data filtering-based parameter estimation methods for multivariable systems, which are corrupted by correlated noise – an autoregressive moving average process. To solve the difficulty that the identification model contains the unmeasurable variables and noise terms in the information matrix, the authors present a hierarchical gradient-based iterative (HGI) algorithm by using the hierarchical identification principle. To improve the convergence rate, they apply the filtering technique to derive a filtering-based HGI algorithm and a filtering-based hierarchical least squares-based iterative (HLSI) algorithm. The simulation examples indicate that the filtering-based HLSI algorithm has the highest computational efficiency among these three algorithms.