基于奇异值总体最小二乘法的间谐波估计算法

An Algorithm of Interharmonic Estimation Based on Singular Value Decomposition Total Least Square

通过分析噪声误差,提出采用奇异值总体最小二乘(singularvaluedecompositiontotalleastsquares,SVDTLS)算法进行间谐波频率估计,即同时考虑矩阵方程两边的噪声干扰,采用SVDTLS算法求解该情况下的最小范数解,通过对增广矩阵进行奇异值分解(singularvaluedecomposition,SVD),采用简单实用的与信噪比相关的主奇异值个数确定方法对分解的右奇异矩阵进行存储计算,得到了较精确的间谐波频率估计结果。仿真结果表明,该算法具有良好的抗噪性能和数值稳定性,在低信噪比情况下可准确提取信号的频率。

By means of analyzing the noise error, it is proposed to use an algorithm of singular value decomposition total least squares （SVDTLS） to conduct the interharmonics estimation, namely taking the noise interference at both sides of the matrix equation into account simultaneously and solving the minimum norm problem by least square method under such condition. In the proposed algorithm by means of singular value decomposition （SVD） of a new augmented matrix and by use of a simple and practical method to determine the number of principal singular value related to signal to noise ratio （SNR） the storage calculation of right singular matrix is performed, thus a more accurate frequency estimation of interharmonics can be obtained. Simulation results show that the proposed algorithm possesses good anti-interference performance and numerical stability, the signal frequency can be accurately extracted under low SNR.