Convergence of the auxiliary model based stochastic gradient algorithm for multiple-input single-output systems

This paper studies the convergence of the auxiliary model based stochastic gradient parameter estimation algorithm for multi-input output-error systems by using the martingale convergence theorem. The basic idea is to formulate a positive definite function of the parameter estimation error and to indicate that the parameter estimates converge to their true values under persistent excitation. The proposed algorithm has less computational burden that existing least squares identification algorithms. A simulation example is given.