对称a稳定分布中预处理的分数低阶协方差时差估计

Preprocessed Fractional Lower-order Covariance Time Delay Estimation under Symmetric a-stable Conditions

该文针对传统算法中预处理函数类型有限,对预处理函数所带来的性能改进分析不足及分数低阶协方差时差估计算法精度不够高的缺点进行改进,提出一类预处理函数,指出其需要满足的一组条件;并理论推导得到接收信号通过任意满足该组条件的函数处理后,其分数低阶协方差的方差减小且是无偏估计,从而提高了分数低阶协方差的峰值检测精度,提高了时差估计精度。最后提出了两种满足条件的预处理函数,仿真验证了在对称a稳定分布噪声中该文算法提高时差估计精度的有效性及在高斯噪声环境下的适用性。

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.