基于自相关函数相位的频率估计方法方差分析

Variance analysis on sinusoid frequency estimators based on the argument of the sample autocorrelation function

为了分析基于自相关函数相位频率估计方法的性能,推导了加性高斯白噪声背景中正弦信号观测数据的相关函数相位噪声的表示式,得到了相位噪声方差的计算公式和基于自相关函数相位的频率估计方差的计算公式,给出了此类频率估计方法的估计方差与信噪比、观测数据长度以及对相关函数相位差进行平滑时利用的相关函数的点数关系.仿真结果与该文给出的公式计算结果吻合很好.

Frequency estimators based on the argument of the sample autocorrelation function outperform those based on the phase of the samples of the sinusoid signal in additive white Gaussian noise background. The expression of the noise in the argument of the sarnple autocorrelation function was given to investigate the performance of these estimators. And formulas for evaluating the variance of sample autocorrelation argument noise and the variance of frequency estimation based on the sample autocorrelation argument were derived. The relations among frequency estimation variance and signal-to-noise ratio, length of the measurement time, and sample numbers used in smoothing the autocorrelation function can be determined using these formulas. Computer simulation results confirm the correctness of the proposed formulas.