Highly-efficient filtered hierarchical identification algorithms for multiple-input multiple-output systems with colored noises

Multiple -input multiple -output (MIMO) systems have extensive applications in industrial processes and systems engineering. This letter applies the filtering identification idea to establish a filtered identification model and investigate a filtered auxiliary model -based recursive least squares (F-AM-RLS) algorithm for parameter identification of MIMO systems with colored noises. To improve the computational efficiency, this work further proposes a four -stage filtered auxiliary model -based recursive least squares (4S-F-AM-RLS) algorithm by means of the hierarchical identification principle. Then, by incorporating the forgetting factor, a four -stage filtered auxiliary model -based forgetting factor recursive least squares (4S-F-AM-FF-RLS) algorithm is given to improve the convergence speed and the estimation accuracy. Additionally, the computational complexity analysis of the proposed algorithms indicates that the 4S-F-AM-RLS algorithm effectively reduces the computational burden and improves computational efficiency. Finally, the effectiveness of the F-AM-RLS, 4S-F-AM-RLS and 4S-F-AM-FF-RLS algorithms is validated through a numerical example.