Convergence properties of multi-innovation ESG algorithms for multi-input multi-output CARMA models

In this paper, we extend the residual based extended stochastic gradient (ESG) algorithm with a poor convergence rate for multi-input multi-output CARMA models and present multi-innovation ESG identification algorithm. Because the proposed multi-innovation ESG algorithm uses not only the current innovation but also the past innovation at each iteration, thus parameter estimation accuracy can be improved. Further, we analyze the convergence properties of the algorithm involved and show that the parameter estimation errors have faster convergence rate to zero than that of the ESG algorithm. The simulation results are included.