正弦波频率估计的牛顿迭代方法初始值研究

The Starting Point Problem of Sinusoid Frequency Estimation Based on Newton's Method

本文分析了Rife算法的性能,指出当信号频率位于量化频率点附近时它的精度降低,以它为初始值进行牛顿迭代会导致不收敛.针对此问题,本文提出了一种修正Rife(MRife)算法,通过对信号进行频移,使新信号的频率位于两个相邻量化频率点的中心区域,然后再利用Rife算法进行频率估计.仿真结果表明修正Rife算法性能不随被估计信号的频率分布而产生波动,以它为初始值进行一次迭代得到的频率估计值的方差在整个频段都接近克拉美-罗限,具有稳定的性能.

In this paper we analysis the performance of Rife algorithm and point out when the true frequency is much close to quantized frequency of DFT （discrete Fourier transform） Newton＇s iteration will be disconvergent because of decreasing of Rife algorithm＇ s precision. In order to solve the problem we present a modified Rife （MRife） algorithm by moving the signal frequency to the midpoint of two neighboring discrete frequencies and then estimate the frequency using the Rife algorithm. The simulation results show that the performance of MRife does not fluctuate with the distribution of signal frequency. The RMSE （root mean square error） of one iteration of Newton＇s method whose initialization is MRife is close to CRLB （ Cramer-Rao Lower Bound） throughout the frequency band and the performance is steady.