基于岭估计的北斗系统双差整周模糊度解算方法

An Approach for Double-differenced Integer Ambiguity Resolution of BeiDou Navigation Satellite System Based on Ridge Regression

针对北斗卫星导航系统中高轨卫星角速度较慢引起的基线网络实时动态差分法模型病态性减弱较慢而造成的模糊度收敛较慢的问题,提出一种适用于网络实时动态差分法参考站间双差整周模糊度快速解算的新方法。首先,在分析北斗系统快速定位模型中法矩阵结构病态性的基础上,基于岭估计的原理提出一种减弱法矩阵病态性的新方法。该方法只需几个历元的北斗系统载波相位观测值,就可得到比较准确的模糊度浮动解及其相应的均方误差矩阵。利用最小二乘相关分解法方法,用与模糊度浮点解相应的均方误差矩阵代替协方差阵,可准确、快速地搜索固定整周模糊度。结合算例,将新方法和最小二乘法分别结合最小二乘相关分解法方法解算的整周模糊度结果进行比较,结果证明新方法能实现北斗系统双差整周模糊度的固定。

A new scheme which responses to the high-orbit satellites in BeiDou navigation satellite system(BDS)is proposed for ill-conditioned problems in estimating long-baseline ambiguity between reference stations of Network RTK in this paper.First,based on ridge regression,a new approach is chosen to mitigate the ill-condition of the normal matrix.The accurate float ambiguity solutions and their corresponding mean square error matrix(MSEM)are obtained using several epoch phase observations.Then combined with least-square ambiguity decorrelation adjustment method,a new approach can fix the ambiguities correctly and quickly using MSEM instead of the covariance matrix to determine the ambiguity search space.At last,the effect of the new algorithm and least square method is illustrated by one numerical example,combining with least-square ambiguity decorrelation adjustment method to fix the integer ambiguities respectively.The result proves that the new solution can achieve double-differenced integer ambiguity of BDS fast fixed.