SPODS软件GPS/GNSS网解的模糊度解算方法
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摘要
为了尽可能多地固定模糊度,需要定义一组"最容易被固定"的独立双差模糊度,当前最优的方法(传统方法)是分基线层和网层对候选双差模糊度进行独立性检验,其中候选模糊度按照其综合固定成功概率进行排列。考虑到通常的网解中,测站数量远多于卫星数量,提出了先星座层再网层的分层独立模糊度选取方法以及基于更新协方差阵上三角平方根的序贯模糊度固定方法,并应用于西安测绘研究所自主设计和开发的SPODS软件中。采用包含64个IGS监测站的实测GPS数据进行单天解算试验,验证了该方法的正确性。试验结果表明,该方法和传统方法得到的单天GPS轨道解与IGS最终综合轨道比较的1DRMS都约为0.012m,独立双差模糊度成功固定的比例约为92%,两种方法仅有非常细微的差异。不同测站数量的进一步试验表明,该方法和传统方法在网层需要采用Grams-Schmidt方法进行独立性检验的候选双差模糊度数量的比约等于卫星和测站的数量比,这与理论分析结论一致。对于实际应用中更为普遍的测站数量大于卫星数量的情况,该方法将减少独立双差模糊度选取的计算时间,且测站数越多,其优势越明显。
Ambiguity resolution plays an essential role in global GPS/GNSS network solution.In order to fix as many double-difference(DD)ambiguities to the nearest integers as possible,a set of"most-easy-to-fix"independent DD-ambiguities has to be defined.The most usable state-of-art method(the"traditional"method)at present is to make the independency checking on two levels firstly on the baseline level and then the network level,in which the DD-ambiguity candidates are sorted by their fixing probabilities on both levels.Considering the fact that,in general global network solution,the number of stations involved is usually times larger than that of satellites,a new approach for independent DD-ambiguities selection was presented,which makes the independency checking in an analogous two-level way firstly on the constellation level and then the network level.Together with a new procedure for sequential ambiguity fixing based on updating the upper triangular square root of covariance matrix,the new approach is implemented in the satellite positioning and orbit determination system(SPODS)software which is designed and developed at Xi'an Research Institute of Surveying & Mapping.Validation experiment with GPS observation data collected from about 64 IGS stations was carried out,which demonstrate that 1DRMSs for daily orbit solution,compared with IGS final combined solution,are about 0.012 m,and about 92%of DD-ambiguities were fixed,with only neglectable tiny difference tetween the new and traditional method.Another experiment with varied number of stations indicates that the ratio of the number of DD-ambiguities candidates to be checked for independency on the network level between the new and the traditional approach is nearly equal to the ratio of satellites to stations involved.For the cases that more stations are involved than satellites,which are common in actual GPS/GNSS network solution,the computation time for independent DD-ambiguities selection is reduced with the new approach,the more stations involved,the greater advantage is exhibited.
Ambiguity resolution plays an essential role in global GPS/GNSS network solution.In order to fix as many double-difference(DD)ambiguities to the nearest integers as possible,a set of"most-easy-to-fix"independent DD-ambiguities has to be defined.The most usable state-of-art method(the"traditional"method)at present is to make the independency checking on two levels firstly on the baseline level and then the network level,in which the DD-ambiguity candidates are sorted by their fixing probabilities on both levels.Considering the fact that,in general global network solution,the number of stations involved is usually times larger than that of satellites,a new approach for independent DD-ambiguities selection was presented,which makes the independency checking in an analogous two-level way firstly on the constellation level and then the network level.Together with a new procedure for sequential ambiguity fixing based on updating the upper triangular square root of covariance matrix,the new approach is implemented in the satellite positioning and orbit determination system(SPODS)software which is designed and developed at Xi'an Research Institute of Surveying & Mapping.Validation experiment with GPS observation data collected from about 64 IGS stations was carried out,which demonstrate that 1DRMSs for daily orbit solution,compared with IGS final combined solution,are about 0.012 m,and about 92%of DD-ambiguities were fixed,with only neglectable tiny difference tetween the new and traditional method.Another experiment with varied number of stations indicates that the ratio of the number of DD-ambiguities candidates to be checked for independency on the network level between the new and the traditional approach is nearly equal to the ratio of satellites to stations involved.For the cases that more stations are involved than satellites,which are common in actual GPS/GNSS network solution,the computation time for independent DD-ambiguities selection is reduced with the new approach,the more stations involved,the greater advantage is exhibited.
引文
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[11]GE M,GENDT G,ROTHACHER M,et al.Resolution of GPS Carrier-phase Ambiguities in Precise Point Positioning(PPP)with Daily Observations[J].Journal of Geodesy,2008,82:389-399.
[12]TEUNISSEN P J G.The Least-squares Ambiguity Decorrelation Adjustment:A Method for Fast GPS Integer Ambiguity Estimation[J].Journal of Geodesy,1995,70(1-2):65-82.
[13]WEI Ziqing,RUAN Rengui,JIA Xiaolin,et al.Satellite Positioning and Orbit Determination System SPODS:Theory and Test[J].Acta Geodaetica et Cartographica Sinica,2014,43(1):1-4.(魏子卿,阮仁桂,贾小林,等.卫星定位定轨系统SPODS:理论与测试[J].测绘学报,2014,43(1):1-4).
[14]BONDY J A,MURTY U S R.Graph Theory with Applications[M].New York:Elsevier Science Pubblishing Co Inc,1976.
[15]BIERMAN G J.Factorization Methods for Discrete Sequential Estimation[M].New York:Academic Press,1977:81-103.
[16]TAPLEY B D,SCHUTZ B E,BORN G H.Statistical Orbit Determination[M].Burlington:Elsevier Inc,2004:330-339.
[17]FU Mengyin.Kalman Filtering Theory and Its Applications in Navigation Systems[M].Beijing:Science Press,2003:199-202.(付梦印.Kalman滤波理论及其在导航系统中的应用[M].北京:科学出版社,199-202.)
[18]BLEWITT G.An Automatic Editing Algorithm for GPS Data[J].Geophysical Research Letter,1990,17(3):199-202.
[19]BEUTLER G,MERVART L,VERDUN A.Methods of Celestial Mechanics Volume I:Physical,Mathematical,and Numerical Principles[M].Berlin:Springer-Verlag,2005.
[20]SPRINGER T A.Modeling and Validating Orbits and Clocks Using the Global Positioning System[D].Berne:University of Berne,1999:169.
[2]BLEWITT G.Carrier Phase Ambiguity Resolution for the Global Positioning System Applied to Geodetic Baselines up to 2000km[J].Journal of Geophysical Research,1989,94(B8):187-203.
[3]DONG D N.BOCK Y.Global Positioning System Network Analysis with Phase Ambiguity Resolution Applied to Crustal Deformation Studies in California[J].Journal of Geophysical Research,1989,94(B4):3949-3966.
[4]GE M,GENDT G,DICK G,et al.Improving Carrier-phase Ambiguity Resolution in Global GPS Network Solutions[J].Journal of Geodesy,2005,79(1):103-110.
[5]GE M,GENDT G,DICK G,et al.A New Data Processing Strategy for Huge GNSS Global Networks[J].Journal of Geodesy,2006,80(4):199-203.
[6]MERVART L.Ambiguity Resolution Techniques in Geodetic and Geodynamic Applications of the Global Positioning System[D].Berne:University of Berne,1995.
[7]GENG J,SHI C,GE M,et al.Improving the Estimation of Fractional-cycle Biases for Ambiguity Resolution in Precise Point Positioning[J].Journal of Geodesy,2012,86(8):579-589.
[8]LOYER S,PEROSANZ F,MERCIER F,et al.Zerodifference GPS Ambiguity Resolution at CNES-CLS IGS Analysis Center[J].Journal of Geodesy,2012,86(11):991-1003.
[9]ZHANG Xiaohong,LI Pan,LI Xingxing,et al.An Analysis of Time-varying Property of Widelane Carrier Phase Ambituity Fractional Bias[J].Acta Geodaetica et Cartographica Sinica,2013,42(6):798-803(张小红,李盼,李星星,等.宽巷载波相位模糊度小数偏差时变特性分析[J].测绘学报,2013,42(6):798-803).
[10]COLLINS P,LAHAYE F,HEROUX P,et al.Precise Point Positioning with Ambiguity Resolution Using the Decoupled Clock Model[C]∥Proceedings of the 21st International Technical Meeting of the Satellite Division of the Institute of Navigation.Savannah:ION,2008:1315-1322.
[11]GE M,GENDT G,ROTHACHER M,et al.Resolution of GPS Carrier-phase Ambiguities in Precise Point Positioning(PPP)with Daily Observations[J].Journal of Geodesy,2008,82:389-399.
[12]TEUNISSEN P J G.The Least-squares Ambiguity Decorrelation Adjustment:A Method for Fast GPS Integer Ambiguity Estimation[J].Journal of Geodesy,1995,70(1-2):65-82.
[13]WEI Ziqing,RUAN Rengui,JIA Xiaolin,et al.Satellite Positioning and Orbit Determination System SPODS:Theory and Test[J].Acta Geodaetica et Cartographica Sinica,2014,43(1):1-4.(魏子卿,阮仁桂,贾小林,等.卫星定位定轨系统SPODS:理论与测试[J].测绘学报,2014,43(1):1-4).
[14]BONDY J A,MURTY U S R.Graph Theory with Applications[M].New York:Elsevier Science Pubblishing Co Inc,1976.
[15]BIERMAN G J.Factorization Methods for Discrete Sequential Estimation[M].New York:Academic Press,1977:81-103.
[16]TAPLEY B D,SCHUTZ B E,BORN G H.Statistical Orbit Determination[M].Burlington:Elsevier Inc,2004:330-339.
[17]FU Mengyin.Kalman Filtering Theory and Its Applications in Navigation Systems[M].Beijing:Science Press,2003:199-202.(付梦印.Kalman滤波理论及其在导航系统中的应用[M].北京:科学出版社,199-202.)
[18]BLEWITT G.An Automatic Editing Algorithm for GPS Data[J].Geophysical Research Letter,1990,17(3):199-202.
[19]BEUTLER G,MERVART L,VERDUN A.Methods of Celestial Mechanics Volume I:Physical,Mathematical,and Numerical Principles[M].Berlin:Springer-Verlag,2005.
[20]SPRINGER T A.Modeling and Validating Orbits and Clocks Using the Global Positioning System[D].Berne:University of Berne,1999:169.