Performance analysis of auxiliary model based Stochastic gradient parameter estimation for MIMO systems under weak conditions

This paper presents an auxiliary model based stochastic gradient (AMSG) parameter estimation algorithm for output error multivariable systems. The basic idea is to establish an auxiliary model and to replace the unmeasurable variables in the information vector by the outputs of the auxiliary model. Convergence analysis using the stochastic martingale theory indicates that the AMSG algorithms have good performance: the parameter estimation converges to the true parameters only assuming that the input-output is persistently exciting and that the process noises are zero mean and uncorrelated. The main convergence results in the paper do not assume that the noise variances and high-order moments exist and are finite. These results remove the strict assumptions, made in existing references, that the noise variances and high-order moments exist and that processes are stationary and ergodic.