一种全最小二乘算法及其在非线性滤波器中的应用

针对输入输出观测数据均含有噪声的滤波问题,提出了一种稳定的总体最小二乘自适应算法。该算法以系统的增广权向量的瑞利商(RQ)与对增广权向量的最后元素的约束的和作为总损失函数,利用梯度最陡下降原理导出权向量的自适应迭代算法,并将该算法应用于非线性Volterra滤波器。研究了算法的稳定性能,提出的算法不仅有良好的收敛性能,而且在权向量的自适应迭代时不需要标准化处理,使得算法的实施更为简单。仿真实验表明,无论在线性系统或非线性系统,本文算法的收敛性能,鲁棒抗噪性能和稳态收敛精度明显高于其它同类总体最小二乘算法。

A Total Least Square Adaptive Algorithm and Its Application to the Nonlinear Filter

Aiming at the filter problem when the input and output signal are both corrupted by noise, a stable total least square adaptive algorithm is proposed in this paper. Taking the Rayleigh Quotient of the augmented weight vectors for the system and a constraint to the last element of the augmented weight vectors via a LaGrange multiplier as the overall cost function, by the steepest descent principle, the adaptive updating formula os the weight vector is derived, and the algorithm is applied to the nonlinear Volterra filter. The stability property of the algorithm is analyzed. The proposed algorithm possesses fine convergence, and does not require normalization. The simulation results have shown that, in addition to the fine convergence, the robust anti-noise performance and the stable convergence precision of the proposed algorithm are remarkably higher than other congener algorithms in whether the linear system or the nonlinear system.