一种拟合GPS高程异常的新方法

A new way of GPS height anomaly fitting

针对GPS高程异常拟合中观测数据存在粗差和系数矩阵存在误差的情况,提出采用一种新的RTLS迭代算法,同时构造基于标准化残差的IGGIII权函数.RTLS迭代算法顾及了系数矩阵中的常数列不存在误差的特性,仅考虑存在误差的列向量部分.以某市城区的80组GPS水准联测数据为例,设计两种实验方案证该方法的精度和稳健性,其中,拟合数据有43组(四组GPS数据含有粗差),外符合检验数据37组.在拟合数据不含粗差的情况下,RLTS和抗差LS估计效果一致;而在拟合数据存在粗差的情况下,RTLS拟合二次曲面的效果明显抗差LS算法.结果表明:利用RTLS拟合GPS高程异常拟合的二次曲面是最优选择.

Aiming at the situation of errors in observation data and coefficient matric in GPS Height anomaly,a robust total least squares(RTLS) is proposed with a IGGIII weight function based on standardized residuals.The method only takes the parts containing deviation in coefficient matrix into consideration.Taking the 80 groups GPS observation of benchmark as an example,the feasibility and accuracy of TRLS is analyzed compared with two kinds of experiment including 43 groups of data for fitting(4 groups of data with gross error) and 37 groups of data for testing.If the data have no robust,the result of RTLS is equal with robust LS.If the data have robust,the result of RTLS is better than robust LS.The experiment shows that the method of RTLS is the best choice when fitting GPS height anomaly.