Abstract: This paper proposes a category of preprocessing functions and the conditions they should meet as to the problems that the type of traditional preprocessing functions is limited and the analysis for the performance improvement caused by the functions is inadequate. Through mathematical reasoning the conclusion is drawn that the variance of the received signals fractional lower-order covariance decreases and is unbiased by passing them through the preprocessing functions, improving the detection precision of the peak of the fractional lower-order covariance, that results in the improvement of precision of time delay estimation. Finally, two preprocessing functions are proposed. The simulation results indicat that the proposed method is effective and can be used under Gaussian noises.