基于数学形态学和改进Prony算法的谐波与间谐波参数估计

Harmonic and inter-harmonic parameter estimation based on mathematical morphology and improved Prony algorithm

由于传统Prony算法对谐波与间谐波的检测易受噪声影响,为了提高参数估计精度,准确提取谐波和间谐波的频率、幅值和相位,提出了一种基于数学形态学和改进Prony算法的谐波与间谐波参数估计方法。该方法主要思路是先用数学形态学构建形态滤波器去除噪声,可以克服传统Prony算法对噪声敏感的不足;然后再将去噪拟合后的谐波信号进行改进Prony分析。该方法针对原始Prony方法优化了实际阶数和线性参数的求解过程,对比小波消噪求解谐波各参数的方法优化了去噪效果。通过MATLAB对谐波信号进行编程分析,发现该方法在噪声情况下仍能得到较高精度的谐波与间谐波幅值、频率和相位参数估计,验证了该方法的可行性和有效性。

The detection of harmonic and inter-harmonic by the traditional Prony algorithm is sensitive to noise. In order to improve the parameter accuracy,and extract the characteristic parameters of frequency,amplitude and phase of harmonics and inter-harmonics accurately,a harmonic and inter-harmonic parameter estimation method based on mathematical morphology and improved Prony algorithm is proposed in this paper. The main idea of this method is to construct morphological filter with mathematical morphology to de-noise,and the shortcomings of the traditional Prony algorithm for noise sensitivity can be overcome. Then,the harmonic signal after noise removal is underway by improved Prony.Aimed at original Prony algorithm,this method optimized the actual order number and linear parameter solving process,as well as optimized the de-noising effect comparing with the wavelet de-noising method. The programming analysis of harmonic signal is conducted through MATLAB,it is found that this method can get high-accuracy amplitude,frequency and phase parameters under noises. The feasibility and effectiveness of the proposed method are verified.