基于CGA初选和Helmert加权优化的北斗/GNSS选星算法研究

It is the vital technology to select the reasonable and visible satellites in the real-time and high precision navigation for BeiDou Navigation Satellite System/Global Navigation Satellite System (BDS/GNSS). But the traditional satellite selection methods cannot meet the requirements of the more visible satellites of the multisystem. Using the advantages of conformal geometric algebra (CGA) about space representation and operation, combining the characters of Helmert variance component estimation, and considering the problem about the selection satellite and the weighted coefficients of the navigation multisystem together, a satellite selection algorithm for BDS/GNSS by grouping based-on CGA and optimization weighted based-on Helmert variance component estimation is proposed in this project. The main contents of this project including: (1) Using geocenter as the vector-end, taking the direction of the preliminary coordinates of the observation station as the zenith direction, and considering the mean radius of the navigation satellites, the zenith center point or domain is fitted. Then the fusion weighted coefficients of the satellite navigation systems are designed. And then the threshold values about observation elevating angle and azimuth angle are set. Thus the umbrella shape model based-on CGA is constructed. This model can be regarded as the matched reference model; (2) Using the space coordinates information of the visible satellites, on the basis of CGA theory, the zenith center point or domain’s point, the multiple vector set about the visible satellites is built. The visible satellite group is selected by using the spatial topological arithmetic and matching based-on CGA; (3) The observation weighted matrix about visible satellite group is optimized by using Helmert variance component estimation. The precision about the visible satellite group can be evaluated by using the threshold of GDOP value. Moreover the Optimization Weighted model based-on Helmert variance component estimation and the satellite selection model are fused together. The research results of this project are vital important to the defense/economic construction.

合理选取导航解算星是实现北斗/GNSS快速高精度导航的关键，但现行算法难以满足多系统多可见星的选星需求。利用共形几何代数CGA的运算优势，结合Helmert方差估计的特点，将选星和多系统权重融合统一考虑，提出基于CGA初选和Helmert加权优化的选星算法。主要研究内容：（1）以地球质量中心为矢端，以测站概略坐标为天顶指向，结合导航星的平均轨道高度，拟合天顶中心点或中心域。设定各卫星系统的权重、观测高度角和方位角阈值，构建基于CGA的伞状多面体模型，为选星提供匹配的基准模型；（2）利用可见星、测站天顶方向的中心点或中心域点的空间坐标信息，构建基于CGA的可见星多重矢量集，通过CGA空间拓扑运算与匹配，筛选出可见星组；（3）利用Helmert优化可见星组的观测权阵，通过设置的GDOP阈值判断所选可见星组是否满足精度要求，进而与基于CGA的选星模型有机地结合。研究成果对国防/经济建设意义重大。

从北斗/GNSS多系统可见星中快速选取空间几何分布良好的导航星，以其相应数据进行导航定位解算，是进一步改善导航实时性、可靠性、精确性等性能指标的关键。项目主要从构建选星算法模型和实验验证平台开发着手，开展和取得的主要研究内容和成果如下：.（1）规划了基于CGA初选和Helmert加权优化的北斗/GNSS选星算法的总体方案规划，细化了课题研究内容，构建了以北斗星通的和芯星通芯片UB4B0-MINI为主的四模数据实验硬件系统，开发了VC++平台和MatLab平台的数据的实时传输软件；.（2）提出了利用Herlmert方差估计加权优化北斗/GNSS多系统观测值权阵的方法。Herlmert加权融合方法减少了数据处理中的迭代次数，有效提高了数据处理效率，且Herlmert加权融合方法通过权阵优化，合理分配北斗/GNSS多系统观测值在定位解算中的权值，使得未知参数的方差达到最小，从而改善了导航定位的精度；.（3）利用主成分分析理论对北斗/GNSS多系统可见星的GDOP贡献率进行排序，基于Sherman-Morrison公式进一步评价选星数量的合理性，并设置合理阈值，在合理确定选星数量的基础上，实现了无人工干预下的自主选星；.（4）构建了基于CGA的低仰角伞状选星模型和可见星多重矢量集，根据预设的总选星数目和顶座星数目，计算匹配阈值角，基于CGA向量角度运算，进行可见星多重矢量集与伞状模型的匹配筛选，实现基于CGA理论的快速选星。实测数据处理结果表明：当选星数目达到13时，该算法的GDOP值优于2，且其计算耗时大大优于最小GDOP法；.（5）采用小波去噪对伪距观测值进行降噪处理，然后联合电离层残差 (Phase Ionospheric residual, PIR) 法，构成PIR-GFPMP (Geometry-Free Pseudorange Minus Phase）组合模型，选出其最优组合以解决不敏感周跳探测困难和PIR法探测结果多值性的问题。实验结果表明：该方法对各类周跳均具备良好的探测修复效果；.（6）提出一种改进的M-Cholesky分解法求解GNSS整周模糊度。该方法利用四角规则法逐步消元计算合成矩阵各元素，减少了计算和存储空间，提高了计算效率。实验结果表明：相对Cholesky分解法，该方法计算效率提高了15%左右，计算矩阵的维数越大，其效率的改善越明显。