网络RTK参考站间模糊度动态解算中病态方程的一种解算方法

A method of ill-posed equation resolution for ambiguity resolution on-the-fly in network RTK reference station

在网络RTK参考站间的模糊度估计中,若误差方程严重病态,将导致模糊度解与其准确值偏差较大或整周模糊度无法固定,因此提出了一种适于网络RTK模糊度动态解算的新方案:1)法方程病态性的判断;2)Tikhonov正则化解算病态方程;3)LAMBDA方法搜索固定整周模糊度。同时,深入研究了Tikhonov正则化矩阵的构造方法和正则化参数的选取准则。最后以实例验证了采用此方案解算病态方程是可行的,通过选取合适的正则化参数可以解得准确的整周模糊度;详细讨论了选择不同的正则化参数对模糊度解算结果的影响。

In estimating ambiguity between reference stations in Network RTK, if error equations are ill-posed, they will lead to larger error in ambiguity float solution and incapability of fixing integer ambiguity. In order to solve this problem, this paper presents a novel scheme to solve the ambiguity on-the-fly based on the features of Network RTK： 1） Judge whether normal equation is ill-posed or not; 2） Resolve ill-posed equation using Tikhonov Regularization Principle; 3） Search and Fix integer ambiguity by LAMBDA（Least-square AMBiguity De-correlation Adjustment）. Meanwhile, it studied the method of constructing Tikhonov regularization matrix and how to choose regularization parameter. At last, the experiment are made which proves that the method is feasible. This method can acquire exact Integer Ambiguity by choosing an appropriate regularization parameter. The paper also discusses the effect of different regularization parameters on ambiguity resolution.