Abstract: The parameter estimation problem of CARMA models is studied by using the multi-innovation identification theory.The basic idea is to obtain the extended stochastic gradient algorithm by replacing the unmeasurable noise terms in the information vector with the estimated residuals and to derive the multi-innovation extended stochastic gradient(ESG) algorithm by expanding the scalar innovation to an innovation vector.The convergence properties of the proposed multi-innovation ESG algorithm are analyzed by using the martingale convergence theorem.The simulation example indicates that the multi-innovation ESG algorithm is effective.