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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。数字仿真例子表明了该结论的正确性
The stochastic process theory is used to prove the convergence of RIVL S for the first time. The convergence rate of RIVL S algorithm is studied, and the formula for calculating the upper bound of estimation error of RLSL algorithm is given. The analysis shows that the mean square parameter estimation error converges to zero at the rate of (1 / t) when the product of the auxiliary matrix and the information matrix is a nonsingular matrix and the weakly continuous excitation condition for the auxiliary vector is established. The result of this study is of great significance for improving the practical application of RIVL S algorithm. The numerical simulation example shows the correctness of the conclusion