GPS/BDS分类组合定位的指数加权Helmert方差分量估计法

Exponential Weighted Helmert Variance Component Estimation for GPS/BDS Combined Positioning with Satellite Classification

针对北斗卫星导航系统(BDS)星座结构复杂、不同类型卫星观测值残差差异较大的不利条件,将BDS系统中IGSO、MEO、GEO 3种卫星的观测值进行分类定权,提出一种顾及历史权比的指数加权Helmert方差分量估计法来精确确定不同系统之间观测值的权阵。为了验证该方法在GPS/BDS组合定位中的有效性,采用单点定位模型分别进行静态和动态导航实验,并将其定位结果与等权模型以及不考虑指数加权的Helmert方差分量估计方法进行对比。结果表明,采用改进的加权方法,在东、北、天3个方向的定位精度均获得显著提高,在静态条件下,相对于等权模型,改进方法 3个方向的定位精度提高幅度分别达到50.0%、51.0%和42.0%;在动态条件下,定位精度提高幅度分别为10.0%、8.0%和9.0%。特别在卫星数量较少、卫星几何图形强度较差时,定位结果的改善效果更为明显。

There are disadvantages of the BDS Navigation Satellite System（BDS）,such as complicated constellation structure and large differences in residual errors of observed values from different types of satellites.In order to precisely determine the weight matrices of observed values between different systems,this paper studies the observed values from IGSO,MEO and GEO satellites in the BDS system through classification and weighting.It proposes an exponential weighting Helmert variance component estimation method that takes historical weight ratios into account.Static and dynamic navigation tests are carried out through a point positioning model to verify the effectiveness of this improved method in GPS/BDS combined positioning,and the results of this improved method are then compared with those of the equal weighting model,as well as of the Helmert variance component estimation method without exponential weighting.Results show that with the improved method,positioning precision in east,north and zenith directions is improved significantly.Under static conditions,compared with the equal weighting model,this improved method results in 50.0%,51.0%and 42.0%improvement in positioning precision in the above three directions respectively;under dynamic conditions,relevant positioning precision is improved by 10.0%,8.0%and 9.0%respectively.Especially under situations of fewer satellites and weaker intensity of satellite geometry,improvement in positioning results is even more significant.