L1范数与IQR统计量组合的GNSS坐标序列粗差探测算法

A New Method of Outlier Detection for GNSS Position Time Series Based on the Combination of L1-Norm and IQR Statistic

GNSS坐标时间序列中不可避免地含有粗差,未剔除的粗差将会导致参数估计有偏。因此,粗差探测与剔除是GNSS坐标序列分析中一项重要的数据预处理工作。针对GNSS坐标时间序列特点,提出了一种将L1范数(L1-norm)估计与四分位距统计量IQR(interquartile range)组合的移动开窗粗差探测算法,称之为L1_Mod IQR。该方法的主要思想是,首先利用L1范数估计得到较"真实"的残差,然后再对残差采用IQR统计量进行粗差探测。将L1_Mod IQR法与"3σ"法、基于最小二乘的τ检验法等粗差探测算法进行了模拟计算与对比,验证了该算法的有效性。进一步采用L1_Mod IQR算法对中国区域10个IGS站的高程时间序列进行了分析,结果表明中国区域IGS站高程序列的粗差剔除率最小为0.1%,最大为2.6%。并且以WUHN站为例与SOPAC提供的结果进行了对比,结果表明SOPAC提供的"Clean"数据仍含有大量的粗差,而L1_Mod IQR算法能够有效地剔除粗差。

The outliers ubiquitously exist in the GNSS position time series, and the undetected outliers will lead bi- ased parameters estimation. Therefore, outliers have to be detected and eliminated in the GNSS data preprocessing. According to the characteristic of GNSS position time series, a modified method which combines Ll-norm estima- tion and interquartile range （IQR） statistic with moving window to detect outliers is presented. This method named LI_ModIQR consists two procedures which use Ll-norm estimation to get more ＂real＂ residuals firstly, and then the IQR statistic is used to detect outliers in the residuals with moving window. The simulated example is performed to validated the reliability of this method by comparing it with ＂3σ＂method and r test based on least square. In the real data analysis, the outliers in height time series of 10 IGS station located in China have been identified and re- moved using this method. The results show that the minimum removal ratio is 0.1%, and the maximum removal ra- tio is 2.6%. Finally, the WUHN station is used as an example to illustrate the efficiency of LI_ModIQR method through comparing it with that of SOPAC （ scrips orbit and permanent array center）.