基于不等式约束算法改善高纬度地区GNSS电离层建模精度
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摘要
由于当前国际GNSS服务组织(IGS)跟踪站在高纬度区域分布不均,用于电离层拟合建模的观测数据不均匀、不全面,导致在利用这些IGS跟踪站观测数据建立电离层拟合模型时该区域的电离层电子总含量拟合模型精度不够,电离层拟合模型格网输出值甚至出现了大量有悖于电离层实际物理意义的负值和零值现象。针对此问题,利用不等式约束算法,对拟合模型电离层格网输出的负值点、零值点加入不等式约束条件,采用附加不等式约束条件的最小二乘法对参数的解算进行优化,并用实测GNSS数据进行验证。实验结果表明,该算法对测站分布稀疏的高纬度地区出现大量零值和负值的情况有明显改善。此外,该算法对全球电离层模型的建模精度也有一定程度的提高。
Due to uneven distribution of the international GNSS service(IGS) organization tracking stations in high latitudes, the observation data used for ionospheric fitting modeling are uneven and incomplete, leading to inadequate modeling accuracy of the total ionospheric content in this region. When the ionospheric fit model is established using observation data from these IGS tracking stations, the grid output values of the ionospheric fitting model contain a large number of negative and zero values, which are contrary to the actual physical meaning of the ionosphere. Aiming at this problem, we adopt the ionospheric grid output negative point, zero point to join inequality constraint conditions, and the inequality constraint least square method, to calculate parameters of optimization. Experimental results show that the algorithm shows a significant improvement in reducing the large number of zeros and negative values in the sparse high-latitude areas, and modeling accuracy of the global ionosphere model is also improved.
Due to uneven distribution of the international GNSS service(IGS) organization tracking stations in high latitudes, the observation data used for ionospheric fitting modeling are uneven and incomplete, leading to inadequate modeling accuracy of the total ionospheric content in this region. When the ionospheric fit model is established using observation data from these IGS tracking stations, the grid output values of the ionospheric fitting model contain a large number of negative and zero values, which are contrary to the actual physical meaning of the ionosphere. Aiming at this problem, we adopt the ionospheric grid output negative point, zero point to join inequality constraint conditions, and the inequality constraint least square method, to calculate parameters of optimization. Experimental results show that the algorithm shows a significant improvement in reducing the large number of zeros and negative values in the sparse high-latitude areas, and modeling accuracy of the global ionosphere model is also improved.
引文
[1] 李征航,张小红.卫星导航定位新技术及高精度数据处理方法[M].武汉:武汉大学出版社,2009(Li Zhenghang,Zhang Xiaohong.New Technology of Satellite Navigation and Positioning and High Precision Data Processing Method[M].Wuhan:Wuhan University Press,2009)
[2] 中国卫星导航系统管理办公室.北斗卫星导航系统空间信号接口控制文件(1.0)[Z].北京,2012(China Satellite Navagation System Management Office.Beidou Satellite Navagation System Spatial Signal Interface Control File 1.0 [Z].Beijing,2012)
[3] 韩文慧.不等式约束算法在地基GNSS全球电离层延迟建模中的应用[D].武汉:武汉大学,2012(Han Wenhui.The Application of Inequality Constraints Least Squares in Global Ionospheric Mapping with IGS Ground based GNSS Network[D].Wuhan:Wuhan University,2012)
[4] Remodi B W.Real-Time Centimeter-Accurary GPS:Initial While in Motion (Warm Startversus Cold Start)[J].Journal of the Institute of Navigation,1993,40(2):199-208
[5] Zhu J,Santerre R,Chang X W.A Bayesian for Linear,Inequality-Constrained Adjustment and Its Application to GPS Positioning[J].Journal of Geodesy,2005,78:528-524
[6] 聂文峰,胡伍生.利用GPS双频数据进行区域电离层TEC提取[J].武汉大学学报:信息科学版,2014,39(9):1 022-1 027(Nie Wenfeng,Hu Wusheng.Extraction of Regional Ionospheric TEC from GPS Dual Observation[J].Geomatics and Information Science of Wuhan University,2014,39(9):1 022-1 027)
[7] 龚阳昭,蔡昌盛.一种利用北斗GNSS三频观测值计算绝对电离层TEC的方法[J].大地测量与地球动力学,2017,37(2):205-208(Gong Yangzhao,Cai Changsheng.A Calculation Method of Ionospheric TEC Using Triple-Frequency GNSS Observation[J].Journal of Geodesy and Geodynamics,2014,37(2):205-208)
[8] 袁运斌.基于GPS的电离层监测及其延迟改正理论与方法的研究[D].武汉:中国科学院测量与地球物理研究所,2002(Yuan Yunbin.Study on Theories and Methods of Correcting Ionospheric Delay and Monitoring Ionosphere Based on GPS[D].Wuhan:Institute of Geodesy and Geophysics,CAS,2002)
[9] 宋迎春,朱建军,罗德仁,等.附非负约束平差模型的最小二乘估计[J].武汉大学学报:信息科学版,2008,33(9):907-909(Song Yingchun,Zhu Jianjun,Luo Deren,et al.Least-Squares Estimation of Nonnegative Constrained Adjustment Model[J].Geomatics and Information Science of Wuhan University,2008,33(9):907-909)
[10] 章红平.基于地基GPS的中国区域电离层监测与延迟改正研究[D].上海:中国科学院上海天文台,2006(Zhang Hongping.Study on Regional Ionospheric Monitoring and Delay Correction in China Based on Ground-Based GPS[D].Shanghai:Shanghai Astronomical Observatory,CAS,2006)
[11] 任晓东.多系统GNSS电离层TEC高精度建模及差分码偏差精确估计[D].武汉:武汉大学,2017(Ren Xiaodong.Theory and Methodology of Ionospheric TEC Modeling and Differential Code Biases Estimation with Multi-GNSS[D].Wuhan:Wuhan University,2017)
[2] 中国卫星导航系统管理办公室.北斗卫星导航系统空间信号接口控制文件(1.0)[Z].北京,2012(China Satellite Navagation System Management Office.Beidou Satellite Navagation System Spatial Signal Interface Control File 1.0 [Z].Beijing,2012)
[3] 韩文慧.不等式约束算法在地基GNSS全球电离层延迟建模中的应用[D].武汉:武汉大学,2012(Han Wenhui.The Application of Inequality Constraints Least Squares in Global Ionospheric Mapping with IGS Ground based GNSS Network[D].Wuhan:Wuhan University,2012)
[4] Remodi B W.Real-Time Centimeter-Accurary GPS:Initial While in Motion (Warm Startversus Cold Start)[J].Journal of the Institute of Navigation,1993,40(2):199-208
[5] Zhu J,Santerre R,Chang X W.A Bayesian for Linear,Inequality-Constrained Adjustment and Its Application to GPS Positioning[J].Journal of Geodesy,2005,78:528-524
[6] 聂文峰,胡伍生.利用GPS双频数据进行区域电离层TEC提取[J].武汉大学学报:信息科学版,2014,39(9):1 022-1 027(Nie Wenfeng,Hu Wusheng.Extraction of Regional Ionospheric TEC from GPS Dual Observation[J].Geomatics and Information Science of Wuhan University,2014,39(9):1 022-1 027)
[7] 龚阳昭,蔡昌盛.一种利用北斗GNSS三频观测值计算绝对电离层TEC的方法[J].大地测量与地球动力学,2017,37(2):205-208(Gong Yangzhao,Cai Changsheng.A Calculation Method of Ionospheric TEC Using Triple-Frequency GNSS Observation[J].Journal of Geodesy and Geodynamics,2014,37(2):205-208)
[8] 袁运斌.基于GPS的电离层监测及其延迟改正理论与方法的研究[D].武汉:中国科学院测量与地球物理研究所,2002(Yuan Yunbin.Study on Theories and Methods of Correcting Ionospheric Delay and Monitoring Ionosphere Based on GPS[D].Wuhan:Institute of Geodesy and Geophysics,CAS,2002)
[9] 宋迎春,朱建军,罗德仁,等.附非负约束平差模型的最小二乘估计[J].武汉大学学报:信息科学版,2008,33(9):907-909(Song Yingchun,Zhu Jianjun,Luo Deren,et al.Least-Squares Estimation of Nonnegative Constrained Adjustment Model[J].Geomatics and Information Science of Wuhan University,2008,33(9):907-909)
[10] 章红平.基于地基GPS的中国区域电离层监测与延迟改正研究[D].上海:中国科学院上海天文台,2006(Zhang Hongping.Study on Regional Ionospheric Monitoring and Delay Correction in China Based on Ground-Based GPS[D].Shanghai:Shanghai Astronomical Observatory,CAS,2006)
[11] 任晓东.多系统GNSS电离层TEC高精度建模及差分码偏差精确估计[D].武汉:武汉大学,2017(Ren Xiaodong.Theory and Methodology of Ionospheric TEC Modeling and Differential Code Biases Estimation with Multi-GNSS[D].Wuhan:Wuhan University,2017)