Convergence analysis of MISG algorithms for MIMO systems

This paper develops a multi-innovation stochastic gradient (MISG) algorithm for multi-input, multi-output systems. The convergence analysis using the martingale convergence theorem shows that the parameter estimates by the MISG algorithm consistently converge to the true parameters under the persistent excitation condition. The MISG algorithm uses not only the current innovation but also the past innovation at each iteration and repeatedly utilizes the available input-output data, thus the parameter estimation accuracy can be improved. The simulation example confirms the theoretical results.