GPS高程转换的总体最小二乘方法研究

摘要

Curve surface fitting methods have been extensively utilized for the task of conversion GPS elevation to normal elevation.However,errors of the coordinates of GPS observations maybe propagate into the transformed normal elevation during estimating the curve surface parameters.To analyze the influence of these errors in the observation data on the transformed elevation,we employed three models:the quadratic polynomial curve surface,cubic polynomial curve surface and moving quadratic curve surface,to study the accuracy of the converted normal elevation.Least-Squares and two algorithms:Total Least-Squares and Weighted Total Least-Squares to estimate the parameters of these curve surfaces.The results from numerical experiments confirm that the accuracy of normal elevation have been considerably improved when errors of the coordinates of GPS observations data were modeled during the process of transformation.%利用曲面拟合对GPS高程进行转换时,GPS观测数据中的误差会通过曲面参数的解算过程传播到转换后的高程数据中.为分析观测误差对高程数据的影响,分别对二次多项式曲面、三次多项式曲面、移动二次多项式曲面的拟合模型进行研究,利用最小二乘估计、总体最小二乘和加权总体最小二乘算法进行高程转换.数值试验表明,在考虑观测数据中的误差后,采用总体最小二乘估计方法进行高程转换,精度明显提高.