加权总体最小二乘法及其在 GPS 高程拟合中的应用

摘要

Polynomial function is a commonly used method in GPS elevation fitting .For the conventional least-squares solution method does not consider the errors of coefficient matrix , this paper analyzes the different forms polynomial functions and unequal accuracy of observation elements in the coefficient ma -trix, introduces the weighted total least-squares method in GPS elevation fitting based on the quadric function method, and gives the weight value in accordance with the law of error propagation and the ob-served precision circumstances.Using the iterative solution method of weighted total least-squares prob-lem, after the example calculation, the calculated results are compared and analyzed among weighted to-tal least-squares method ,total least-squares method and least-squares method, and it verifies that the weighted total least-squares method is more reasonable to solve more accurate model parameters .%　　多项式函数法是GPS高程拟合的常用方法，而常规的最小二乘解算方法没有考虑系数矩阵误差这一问题。该文分析了不同形式的多项式函数以及系数矩阵中观测元素之间的不等精度性，在基于二次曲面函数的GPS高程拟合中引入加权总体最小二乘的方法，并依据误差传播定律、实际观测精度情况定权。采用加权总体最小二乘问题的迭代解算方法，经过实例计算，对比分析加权总体最小二乘法与总体最小二乘法、最小二乘法的计算结果，验证了加权总体最小二乘法更加合理，可以求得更准确的模型参数。