CARMA模型多新息增广随机梯度参数估计算法的收敛性

将多新息辨识理论用于研究CARMA模型的参数估计问题。首先用估计残差来代替信息向量中的不可测噪声项,导出了CARMA模型的增广随机梯度算法,进一步把标量新息推广为新息向量,导出了相应的多新息增广随机梯度辨识算法,并利用鞅收敛定理分析了多新息增广随机梯度算法的收敛性。最后的仿真结果验证了该算法的有效性。

Convergence of multi-innovation ESG parameter estimation algorithms for CARMA models

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.