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.