象限判别与移动拟合结合的信号频率估计方法

Signal frequency estimation method combining quadrant discriminant and moving fitting

正弦信号的频率估计广泛应用于通信、雷达和声呐等领域,针对正弦信号频率精确估计,提出了一种基于象限判别与移动拟合的正弦信号频率估计方法,首先采用象限判别法对采样序列数据进行周期或相位步距的初步估计,再利用初估参数对序列数据进行正弦移动拟合,最后直接根据移动拟合的各序列点的相位精确计算信号周期或频率。与现有的3种基于离散傅里叶变换(DFT)插值算法进行的仿真精度对比,其结果表明,在设计信噪比分别为-5,0,5 dB,测量频率为11.432 Hz左右6个离散频率,采样频率为2 222.22 Hz以及数据量为5 112个的条件下,该方法的频率估计均方根误差(RMSE)平均值分别为2.048×10^(-3),1.290×10^(-3),0.870×10^(-3)Hz,平均绝对误差(MAE)的平均值分别为1.823×10^(-3),1.209×10^(-3),0.687×10^(-3)Hz,低于其他3种算法的误差,具有更高的精度,更加接近克拉美罗界(CRLB),而且对频率取值范围不敏感,性能稳定。

Frequency estimation of sinusoidal signal is widely used in communication, radar and sonar, etc. Forasmuch as accurate estimation of sinusoidal signal frequency, an frequency estimation method for sinusoidal signals based on quadrant discriminating and moving fitting is proposed. The period or phase step of the sampled signal is estimated preliminarily using the quadrant discriminating method. Then, the move sine fitting method and the estimated parameters are applied to processing of sequence data further. Finally, the signal period or frequency is calculated directly according to the fitted phase of corresponding sequence point. The proposed algorithm is compared with simulation accuracy of three existing interpolation algorithms based on discrete Fourier transform(DFT), The simulation results show that when the design SNR is-5,0,5 dB, measuring frequency is about 11.432 Hz with six discrete frequencies, sampling frequency is 2 222.22 Hz and data quantity is 5 112, the mean root mean square error(RMSE) of frequency estimation of this method is respectively 2.048×10^(-3),1.290×10^(-3),0.870×10^(-3)Hz. The mean of mean absolute error(MAE) is respectively 1.823×10^(-3),1.209×10^(-3),0.687×10^(-3)Hz, which is lower than the errors of the other three algorithms. The proposed algorithm has higher accuracy and is closer to the Cramer-Rao lower bound(CRLB). The proposed algorithm is stable performance due to insensitive to the range of frequency.