一种总体最小二乘算法及在Volterra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，提出了一种鲁棒的总体最小二乘自适应算法．该算法利用滤波器的增广权向量的瑞利商为损失函数，导出了其自适应迭代公式，并利用随机离散学习规律对权向量模的分析进行算法梯度修正，提高了算法的噪声鲁棒性，而且使得算法简单，稳定性好，收敛精度高．将该算法应用于Volterra滤波器，可使滤波器在非线性系统中的信噪比达到10dB，在学习因子为0．01时，算法仍然能够保持良好的收敛性．仿真结果表明，即使在高噪声环境或使用较大学习因子的情况下，该算法的鲁棒抗噪性能和稳态收敛精度均明显高于其他总体最小二乘方法．

Total Least Square Algorithm and Its Application to Volterra Filter

Aiming at the filter problem that exists when the input and output signal are both corrupted by noise, a robust total least square adaptive algorithm is proposed. Taking the minimum Rayleigh quotient as the loss function, the recursive formula of weight vector is derived, the stochastic discrete laws are applied to the analysis of the rule of the norm of the weight vector and the gradient is modified, and the robust anti-noise performance is improved. The algorithm is more simple and has excellent stability and high accuracy. The algorithm is applied to the Volterra filter; it still keeps nice convergent performance in the nonlinear systems even when the signal-noise-ratio is 10dB and learning rate is 0.01. The simulation results have also shown that, the robust anti-noise performance and the stable convergence precision of the proposed algorithm are remarkably better than other total least square adaptive algorithms when the signal-noise-ratio is lower or a larger learning factor is used.