单频干扰逼近误差分析

Error analysis of mono-frequency interference approximation

在各种单频干扰识别与消除方法中,首先要准确估算出单频干扰的振幅、频率和时延三个参数,才能有效消除单频干扰。这三个参数的估算误差会引起单频干扰的估算误差。在余弦函数逼近中,由于频率和时延两个参数估算误差,可以引起振幅的计算误差和单频干扰的计算误差。而在正余弦函数逼近中,由于频率参数估算误差,可以引起正余弦函数振幅的计算误差和单频干扰的计算误差。为此本文定量计算了三个参数误差引起的单频干扰计算误差,以及频率、时延参数估算误差引起的振幅参数计算误差。理论和实际数据的单频干扰逼近误差分析结果表明:为准确估算余弦函数振幅和单频干扰,频率估算精度至少应为0.01Hz,时延估算精度为0.1;准确估算正余弦函数振幅和单频干扰,频率估算精度至少应为0.01Hz。

In a variety of the identification and elimination methods of the mono-frequency interference(MFI) approximation,three parameters of the amplitude,frequency,and phase would first be accurately estimated,and then the MFI could be effectively eliminated.So the estimation errors for those three parameters would also result in an estimation error of the MFI.In the cosine function approximation,the amplitude and the MFI computation errors could be brought by the estimation error for the frequency and the time-delay parameters,and in the sine-cosine function approximation,the estimation error of the frequency would also result in the computation errors of the amplitude and the MFI.So in this paper,a quantitative error is performed about the MFI estimation error induced by three parameter estimation errors and the amplitude computation error induced by the frequency or time-delay estimation errors.The error analysis results of the MFI approximations for the synthetic and field data examples have illustrated that in order to estimate the cosine function amplitude and MFI exactly and precisely,the accuracy of the frequency should not be less than 0.01Hz,and one of the time-delay should be 0.1,and at the same time to estimate the sine-cosine function amplitudes and MFI exactly and precisely,the accuracy of the frequency should not be less than 0.01Hz.