辅助变量最小二乘辨识的均方收敛性

Mean Square Convergence of Instrumental VariableLeast Square Identification

利用随机过程理论 ,首次证明了递推辅助变量最小二乘 (RIVL S)的收敛性 ,研究了 RIVL S算法的收敛速率 ,给出估算 RIVL S算法均方参数估计误差上界的计算公式。分析表明 ,当辅助矩阵与信息矩阵的乘积是非奇异阵 ,且关于辅助向量的弱持续激励条件成立时 ,均方参数估计误差以 (1/ t)的速率收敛于零。这一研究结果对于提高 RIVL S算法的实际应用效果具有重要意义。

The mean square convergence of recursive instrumental variable least square identification (RIVLS), using stochastic process theory, is proved and the convergence rates of the RIVLS algorithms are studied. The analysis indicates that when the instrumental vector is persistently excited and the product of the instrumental matrix and information matrix is nonsingular, the mean square parameter estimation error converges to zero at the rate of (1/t). Simulation results show the correctness of the conclusions.