稳健加权整体最小二乘法在GPS高程拟合中的应用

Application of Robust Weighted Total Least Squares Method for GPS Height Fitting

由于GPS测量技术获取的大地高与国家采用的正常高之间存在高程异常的问题,为此,通常采用高程拟合的方式进行高程异常的计算,从而将大地高转换为正常高。针对采用加权整体最小二乘法估计GPS高程拟合中的多项式系数时,并没有考虑到观测数据中可能存在粗差的情况。采用稳健加权整体最小二乘法求解GPS高程平面拟合参数,并与最小二乘法、加权整体最小二乘法和稳健最小二乘法的结果进行对比,结果表明稳健加权整体最小二乘法的平面拟合结果最优。

Due to the problem of the height anomaly between the geodetic height obtained by the global positioning system ( GPS) surveying technology and the normal height adopted by the country, the height fitting method is usually adopted to calculate the height anomaly and convert the geodetic height to the normal height.Weighted total least squares ( WTLS) method was adopted to estimate polynomial coefficients of GPS height fitting.However,the possible gross errors in the observations are not taken into account.In order to solve this problem,in this study,robust weighted total least squares method is employed to estimate polynomial coefficients for GPS height fitting.A comparison with least squares method,weighted total least squares method and robust least squares method is conducted,the results show that robust weighted total least squares method is most reasonable.