一种稳定的总体最小二乘自适应滤波算法

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与增广权向量最后元素的约束项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,并通过对算法稳定性的分析确定了算法中学习因子的取值范围.所提出的算法稳定,计算复杂度低,既没有平方根运算,也不需要标准化处理.仿真实验表明,该算法的收敛性能、鲁棒抗噪性能和稳态收敛精度均明显高于同类其他总体最小二乘算法.

Stable Total Least Mean Square Adaptive Filter Algorithm

Aiming at the filter problem that the input and output signal are both corrupted by noise, a stable total least mean square (LMS) adaptive algorithm was proposed. Taking the sum of Rayleigh quotient of the augmented weight vectors of the system and a constraint to the last element of the augmented weight vectors via a LaGrange multiplier as an overall cost function, using the steepest descent principle, the (adaptive) updating formula of the weight vector was derived, the stability of the algorithm was analyzed, and the range of the learning factor to which the stability is guaranteed was educed. The proposed (algorithm) is stable and its computation complexity is lower, which can be realized neither calculating the squares root, nor normalization is required. The simulation results show that the convergence performance, the robust against noise and the convergence precision of the proposed algorithm are remarkably higher than other total LMS algorithms.