一种新的外测数据随机误差分离方法∗

摘要

The problem of random error separation of tracking data was considered. The method of building mathematical models to fit the trend part is complicated. The wavelets transform method is required to determine the wavelet basis and the number of decomposition in ad-vance. The empirical mode decomposition method has the problem of mode mixing and it always overestimates the number of modes, the re-sidual of EMD may not necessarily closely approach the trend parts. On the basis of EMD based measurement data error extraction method, an ensemble EMD based measurement data error separation method was proposed. According to the property of frequency and energy of each mode of EMD, an energy-ratio method was used to determine the number of mode that can represent the trend, thus extracting the measurement data error. Simulations and measured data prove the practicality and effectiveness of this method.%主要研究了外测数据随机误差分离问题。利用模型函数逼近趋势项的方法建模较为复杂，小波变换的方法需预先确定小波基和分解层数。基于经验模式分解( EMD)的趋势项消除方法由于EMD分解可能会有模态混叠效应和分解的本征模态函数层数冗余的特性，导致该方法分解的余项不一定能准确逼近趋势项。在此方法基础上提出了基于总体经验模式分解( EEMD)的随机误差分离方法，利用EMD分解的频率特性和能量特性，提出了利用能量比例法来确定用来逼近趋势项的本征模态的层数，进而分离随机误差的方法。理论仿真和实测数据证明了该算法的有效性和实用性。