GPS快速定位方程的病态性对整周模糊度及基线解的影响

The effect of ill-condition equations of GPS rapid positioning on the GPS baseline solution

GPS快速定位的数据处理一般是基于整数最小二乘理论,参数估计通过浮点解、整周模糊度的搜索、固定解三个步骤实现。当观测时间较短时,观测量间具有较强的相关性,用LS估计未知数的法方程严重病态,导致模糊度及基线浮点解与其正确值差距较大。本文通过实例研究了不同观测时间的GPS快速定位方程的病态性程度及其对模糊度和基线解的影响,计算结果表明当观测时间少于2分钟时,采用LS结合LAMBDA法难以求出可靠的固定解。

The data processing of GPS rapid positioning is usually based on integer least-squares principle,and parameter estimation consists of three steps:float-solution,search of integer ambiguities and fixed-solution.But in case of short observational time spans,the normal equations are seriously ill-conditional,which cause float-solution has large deflection compared with accurate solution.In this paper,the ill-condition extent of normal equations and the effect on the GPS baseline solution in different observational time spans is studied by examples.The results show that it is difficult to acquire reliable solution with LS and LAMBDA method in case of less than two minutes spans.