The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique

•The parameter estimation of multivariable systems with colored noise are discussed.•An auxiliary model based hierarchical stochastic gradient (HSG) method is proposed.•A filtering based auxiliary model HSG algorithm is proposed through filtering data.•The filtering based algorithm can generate higher accurate parameter estimates.•The convergence theorems of the proposed estimation algorithms are established.

On the basis of the auxiliary model identification idea, this paper studies the filtering based parameter estimation issues for a class of multivariable control systems with colored noise. An auxiliary model based hierarchical stochastic gradient (AM-HSG) algorithm is given for comparison and a data filtering AM-HSG identification algorithm is derived by using the data filtering technique. Its main key is to decompose a multivariable system into two subsystems and to coordinate the associate items between two subsystem identification algorithms. The convergence analysis indicates that the parameter estimates given by the presented algorithms converge to the true values under proper conditions by using the stochastic process theory. The simulation results show that the proposed hierarchical stochastic gradient estimation algorithms are effective.