【摘要】 针对输入输出观测数据均含有噪声的系统辨识问题,提出了一种鲁棒的总体最小二乘自适应辨识算法.该算法在对总体最小二乘问题与向量的瑞利商及其性质研究的基础上,以被辨识系统的增广权向量的瑞利商(RQ)作为损失函数,利用梯度最陡下降原理导出权向量的自适应迭代算法,并利用随机离散学习规律对权向量模的分析修正了算法梯度,提高了算法的噪声鲁棒性,构成了一种噪声鲁棒的总体最小二乘自适应辨识算法.文中研究了该算法的收敛性能.仿真实验结果表明该算法的鲁棒抗噪性能和稳态收敛精度明显高于其它同类方法,而且可使用较大的学习因子,在较高的噪声环境下仍然保持良好的收敛性.更多还原

【Abstract】 The system identification problem is researched when the input and output signal are both corrupted by noise, a robust total least mean square adaptive identification algorithm is proposed in this paper. The algorithm, after the analysis of the total least mean square problem and the Rayleigh Quotient of the vectors and its property, is based on the minimum Rayleigh Quotient of the augmented weight vectors for the system and the steepest descent principle, the adaptive updating formula of the weight vector is educed, and the stochastic discrete law is applied to the analysis of the rule of the norm for the augmented weight vectors and the gradient is modified, the robust anti-noise performance is improved and the robust total least mean square adaptive identification algorithm is formed. The convergent performance of the algorithm is studied. The simulation results have shown that the robust anti-noise performance and the stable convergence precision of the proposed algorithm are remarkably higher than other congener algorithms when the noise is strong and a larger learning factor is used.更多还原