一种基于窄带自相关的实信号频率估计算法

单频含噪实正弦信号的自相关函数和其原信号的频率一致,且自相关可去除一部分噪声影响,因此基于自相关的频率估计算法一直备受关注。由于自相关可以从时域获得也可以从频域获得,基于自相关的频率估计算法有比较简单的基于时域的方法和性能比较好的基于频域的算法。结合时域和频域自相关的特点,提出一种基于窄带自相关的实信号频率估计算法,该算法在频域进行谱峰搜索后,利用信号的窄带功率谱来计算自相关,进而用简单的时域自相关的改进协方差算法(modified covariance,MC)来得到频率估计,推导出频率估计闭式解。仿真结果表明该算法性能优于传统的自相关时域算法和频域算法,在信噪比高于-7 dB时就能逼近CRB界。

A Narrow-band Autocorrelation-based Frequency Estimator for a Noisy Sinusoid

Frequency estimation based on autocorrelation function of the real sinusoid embedded in white Gaussian noise has been received extensive attention, because the sample autocorrelation sequence has the same frequency as the original signal, but with less noise effect. The method of the frequency estimation based on autocorrelation function can be divided into two categories: the time-domain and frequency-domain methods. The former are relatively simple while the latter have better estimation performance. In this paper, a narrow-band autocorrelation-based method for real sinusoid frequency estimation was proposed, by combining the characteristics of time domain with frequency domain autocorrelation. Firstly, spectral peak searching in frequency domain was applied to provide a coarse frequency estimate. Then, the narrow-band power spectrum of the signal was used to calculate the autocorrelation, from which the fine frequency estimate was obtained based on the simple modified covariance (MC) method. Finally, a closed-form frequency estimator was derived. Simulation results show that the performance of the proposed algorithm, when compared with several existing time-domain autocorrelation-based estimators and frequency-domain autocorrelation-based estimators, is closer to the Cramer-Rao Bound (CRB) when the signal to noise ratio (SNR) exceeds -7dB.