PRARE及其应用于ERS-2精密定轨的研究
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摘要
PRARE（Precise Range And Range-rate Equipment）是二十世纪九十年代由德国发展
的一种双频、双程、空基、微波卫星跟踪系统，可以为人造卫星提供精密的距离和距离变化率两
种观测，单次观测精度分别为2.5-6.5cm和0.1mm/s，标准点精度为1cm和0.015mm/s.
PRARE系统具有全天候、全自动、观测数据密集、地面站易于流动等优点．其空间部分自1995
年4月起搭载在欧洲空间局的第二颗资源遥感卫星ERS-2上，并正常工作至今．
本文分析了PRARE提供的跟踪数据，并将其用于ERS-2卫星的精密定轨．主要内容如下：
1.介绍了PRARE系统的构成和工作、测量原理，给出了PRARE系统的观测模型，重点是基
于空间的双程距离变化率模型。
2.分析了ERS-2卫星的表面几何模型和姿态变换特征，给出了卫星在任意方向上横截面积的计
算方法。
3.介绍了用于ERS-2卫星精密定轨的各种力学模型。重点分析了表面力（包括大气阻力和升
力、太阳光压、地球反照辐射压）模型，并针对实际情况作了适当的改进。在摄动量级估计的
基础上，对各种摄动因素作了取舍。
4.分析了PRARE观测的改正值．重点分析了对流层折射改正，对目前宣称精度较高的几个映
射函数作了比较，结果表明，在观测高度角5°以上，各映射函数相差无几。
5.分析了海洋负荷引起的台站水平位移对定轨计算的影响，认为在目前的解算精度水平上，海
洋负荷引起的台站水平位移不能忽略．
6.完成了精密定轨软件SHORDE的移植、调试，并将软件中的常数系统和各种模型按照IERS1996
规范作了更新，使定轨精度有了大幅度提高．将处理PRARE资料的功能和ERS-2卫星的
各种模型加入 SHORDE中，建立了综合利用SLR和PRARE资料进行ERS-2卫星精密
定轨的软件。
7.编写了数据剪辑程序PASEDT和DATEDT，对PRARE资料作了细致的预处理．
8.将方差分量估计（VCE）方法结合 Givens-Gentleman正交变换算法应用到卫星精密定轨
计算中，基本解决了多种资料综合定轨时观测资料的合理加权问题。同时，在对Helmert方
差分量估计方法深入分析的基础上，提出利用待估参数的先验信息来消除VCE结果中可能
出现的负方差，效果显著．讨论了先验约束强弱的设置和非整数自由度的问题．在此基础上，
编写了适用于人造卫星精密定轨的方差分量估计程序VACE。
1
＜n＞
9．根据试验计算，拟定了详细的 ERS－2定轨计算方案，计算了 1997年 ERS－2卫星的轨道。经
过多方面的检验，估计轨道的径向精度为3—5厘米，完全可以满足利用测高资料对海洋表
面研究的需要，法向精度为10—20厘米，可以满足合成孔径雷达干涉测量的需要．
PRARE (Precise Range And Range-rate Equipment) is a space-borne, two-way, two-
frequency microwave satellite tracking system developed by Germany in 1990's. PRARE can
automatically provide precise range and range-rate measurements under all weather condi-
tions, with full-rate precision 2.5 - 6.5 cm for range and 0.1 mm/s for Doppler, normal-point
precision 1 cm and 0.015 mm/s, respectively. Its space segment has been carried by the 2nd
European Remote Sensing satellite ERS-2 since April, 1995 and works normally up to now.
This dissertation analyzed the tracking data provided by PRARE, and applied the data
to precision orbit determination (POD) for ERS-2. In summary, the main contents are as
follow:
1. Introducing the system composition and measurement principle of PRARE. Presenting
measurement models for PRARE observations, especially the space-based two-way range-
rate model.
2. Analyzing the surface geometric model and attitude transformation characteristics of
ERS-2. Presenting the computational formula of cross-sectional area in any direction for
the satellite.
3. Introducing dynamic models used in ERS-2 POD, analyzing surface force models in
emphasis, including atmospheric drag and lift, solar radiation pressure, Earth albedo
and emissivity. Some proper modifications on the models were made. Based on the
magnitude estimation of each perturbing factors, made a choice among the perturbation
models.
4. Analyzing the corrections of PRARE observations, and tropospheric delay corrections in
emphasis. The comparisons among several mapping functions with high nominal preci-
sion showed, that the mapping functions are all similar in accuracy above 5°elevation.
5. Analyzing the effect of horizontal station displacement due to ocean loading on POD
cWutation, conc1uded that the horizontal station disp1acement caused by ocean loading
should not be neglected in current computational accuxacy.
6. Updating the constants and models in the POD software SHORDE according to IERS
Convention (1996). Adding PRARE and ERS-2 models into SHORDE, made the com-
bination of SLR and PRARE data for ERS-2 POD possible.
7. Editing the PRARE data carefully by using data-edit program PASEDT and DATEDT.
8. App1ying the Relmert method of variance-comPonent-estimation to POD comPutation
considering Givens-Gentleman orthogonal transfOrmation method simultaneous1y. This
made the data-weighting moe prOPer in POD comPutation while combiaing several
kinds of observations. Moreover, based on the deep analysis of Helmert VCE method,
we brought forward a the improved Helinert VCE method n which remove the possible
negative variance esthaation by using the a priori infOrmation of solved-for parameters.
The experAnenis showed that the twroved method was effective in avoiding the negative
variance. The probIems about the strength of a priori constraints and noninteger degree
of freedom were discussed.
9. Detendning the scheme fOr ERS-2 POD computation according to experimental com-
putations and comPuting ERS-2 orbits in 1997. According to the accuracy assessment
from several aspects, the accuracy estAnation of 3 -- 5 cm in radial direction and 10 -- 20
cm in normal direction are given. This precision can comP1etely satisfy the requlrement
of ocean surface research by using altAnetry, and basically satisfy the requlrement of
InSAR measuxement.
的一种双频、双程、空基、微波卫星跟踪系统，可以为人造卫星提供精密的距离和距离变化率两
种观测，单次观测精度分别为2.5-6.5cm和0.1mm/s，标准点精度为1cm和0.015mm/s.
PRARE系统具有全天候、全自动、观测数据密集、地面站易于流动等优点．其空间部分自1995
年4月起搭载在欧洲空间局的第二颗资源遥感卫星ERS-2上，并正常工作至今．
本文分析了PRARE提供的跟踪数据，并将其用于ERS-2卫星的精密定轨．主要内容如下：
1.介绍了PRARE系统的构成和工作、测量原理，给出了PRARE系统的观测模型，重点是基
于空间的双程距离变化率模型。
2.分析了ERS-2卫星的表面几何模型和姿态变换特征，给出了卫星在任意方向上横截面积的计
算方法。
3.介绍了用于ERS-2卫星精密定轨的各种力学模型。重点分析了表面力（包括大气阻力和升
力、太阳光压、地球反照辐射压）模型，并针对实际情况作了适当的改进。在摄动量级估计的
基础上，对各种摄动因素作了取舍。
4.分析了PRARE观测的改正值．重点分析了对流层折射改正，对目前宣称精度较高的几个映
射函数作了比较，结果表明，在观测高度角5°以上，各映射函数相差无几。
5.分析了海洋负荷引起的台站水平位移对定轨计算的影响，认为在目前的解算精度水平上，海
洋负荷引起的台站水平位移不能忽略．
6.完成了精密定轨软件SHORDE的移植、调试，并将软件中的常数系统和各种模型按照IERS1996
规范作了更新，使定轨精度有了大幅度提高．将处理PRARE资料的功能和ERS-2卫星的
各种模型加入 SHORDE中，建立了综合利用SLR和PRARE资料进行ERS-2卫星精密
定轨的软件。
7.编写了数据剪辑程序PASEDT和DATEDT，对PRARE资料作了细致的预处理．
8.将方差分量估计（VCE）方法结合 Givens-Gentleman正交变换算法应用到卫星精密定轨
计算中，基本解决了多种资料综合定轨时观测资料的合理加权问题。同时，在对Helmert方
差分量估计方法深入分析的基础上，提出利用待估参数的先验信息来消除VCE结果中可能
出现的负方差，效果显著．讨论了先验约束强弱的设置和非整数自由度的问题．在此基础上，
编写了适用于人造卫星精密定轨的方差分量估计程序VACE。
1
＜n＞
9．根据试验计算，拟定了详细的 ERS－2定轨计算方案，计算了 1997年 ERS－2卫星的轨道。经
过多方面的检验，估计轨道的径向精度为3—5厘米，完全可以满足利用测高资料对海洋表
面研究的需要，法向精度为10—20厘米，可以满足合成孔径雷达干涉测量的需要．
PRARE (Precise Range And Range-rate Equipment) is a space-borne, two-way, two-
frequency microwave satellite tracking system developed by Germany in 1990's. PRARE can
automatically provide precise range and range-rate measurements under all weather condi-
tions, with full-rate precision 2.5 - 6.5 cm for range and 0.1 mm/s for Doppler, normal-point
precision 1 cm and 0.015 mm/s, respectively. Its space segment has been carried by the 2nd
European Remote Sensing satellite ERS-2 since April, 1995 and works normally up to now.
This dissertation analyzed the tracking data provided by PRARE, and applied the data
to precision orbit determination (POD) for ERS-2. In summary, the main contents are as
follow:
1. Introducing the system composition and measurement principle of PRARE. Presenting
measurement models for PRARE observations, especially the space-based two-way range-
rate model.
2. Analyzing the surface geometric model and attitude transformation characteristics of
ERS-2. Presenting the computational formula of cross-sectional area in any direction for
the satellite.
3. Introducing dynamic models used in ERS-2 POD, analyzing surface force models in
emphasis, including atmospheric drag and lift, solar radiation pressure, Earth albedo
and emissivity. Some proper modifications on the models were made. Based on the
magnitude estimation of each perturbing factors, made a choice among the perturbation
models.
4. Analyzing the corrections of PRARE observations, and tropospheric delay corrections in
emphasis. The comparisons among several mapping functions with high nominal preci-
sion showed, that the mapping functions are all similar in accuracy above 5°elevation.
5. Analyzing the effect of horizontal station displacement due to ocean loading on POD
cWutation, conc1uded that the horizontal station disp1acement caused by ocean loading
should not be neglected in current computational accuxacy.
6. Updating the constants and models in the POD software SHORDE according to IERS
Convention (1996). Adding PRARE and ERS-2 models into SHORDE, made the com-
bination of SLR and PRARE data for ERS-2 POD possible.
7. Editing the PRARE data carefully by using data-edit program PASEDT and DATEDT.
8. App1ying the Relmert method of variance-comPonent-estimation to POD comPutation
considering Givens-Gentleman orthogonal transfOrmation method simultaneous1y. This
made the data-weighting moe prOPer in POD comPutation while combiaing several
kinds of observations. Moreover, based on the deep analysis of Helmert VCE method,
we brought forward a the improved Helinert VCE method n which remove the possible
negative variance esthaation by using the a priori infOrmation of solved-for parameters.
The experAnenis showed that the twroved method was effective in avoiding the negative
variance. The probIems about the strength of a priori constraints and noninteger degree
of freedom were discussed.
9. Detendning the scheme fOr ERS-2 POD computation according to experimental com-
putations and comPuting ERS-2 orbits in 1997. According to the accuracy assessment
from several aspects, the accuracy estAnation of 3 -- 5 cm in radial direction and 10 -- 20
cm in normal direction are given. This precision can comP1etely satisfy the requlrement
of ocean surface research by using altAnetry, and basically satisfy the requlrement of
InSAR measuxement.
引文
[1] Andersen, P. H., K. Aksnes. H. Skonnord. ERS-2 Orbit Determination. XXII Gen. Assembly of the EGS, Vienna, 21-25 April 1997．
[2] Andersen, P.H., K. Aksnes, H. Skonnord, Precise ERS-2orbit determination using SLR, PRARE, and RA observations. Journal of Geodesy. 72:421-429． 1998．
[3] Bedrich S, Flechtner F, Teubel A. EGS(European Geophysical Socienty) XXII General Assembly, Vienna, 1997 (retrieved from Internet: http://florence97． ers-symposium.org/data/flechtner/)
[4] Bedrich S., F. Flechtner, Ch. Fdrste, Ch. Reigber. and A. Teubel. PRARE system performance. In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence. Italy. ESA SP-414, Vol 3． pp. 1637-1642, 1997
[5] Bedrich, S., A New Method for Highly Precise Two Way Common-View Time Transfer between Ground-Based Atomic Clocks with PRARE. XXII Gen. Assembly of the EGS. Vienna, 21-25 April 1997．
[6] Bordi, J. J., Analysis of the Precise Range and Range-Rate Equipment (PRARE) and its application to precise orbit determination. Center for Space Research Report. CSR-99-01． 1999．
[7] Chao, C. C., the tropospheric calibration model for .Mariner Mars 1971． Tech. Rep. 32-1587． pp. 61-76, Jet Propul. Lab., Pasadena. Calif.. 1974．
[8] Davis J. L., T.A. Herring, I.I. Shapiro et al.. Geodesy by radio interferometry: Effects of atmospheric modeling errors on the estimates of baseline length. Radio Science. 20． 1593-1607, 1985．
[9] Dong, D.N., T.A. Herring, R.W. King. Estimating Regional Deformation from a Combination of Space and Terrestrial Geodetic Data. Journal of Geodesy. Vol 72． Iss 4． pp 200-214． 1998．
[10] Eanes R.J. and Bettadpur S.. The CSR 3． 0 Global Ocean Tide Model: Diurnal and Semi-diurnal Ocean Tides from TOPEX/Poseidon Altimetry. Center for Space Research. University of Texas at Austin, Austin, Texas, Technical Memorandum. CSR-TM-96-05． December 1996．
[11] Enninghorst, K., F. H. Massmann. K. H. Neumayer. and J.C. Raimondo. ERS-2 precise orbit determination with PRARE, paper presented at EGS (European Geophysical Society) XXII General Assembly, Vienna, G17． 24 April. 1997．
[12] Estefan, J.A., and O.J. Stovers, A Comparative Survey of Current and Proposed Tropospheric Refraction-Delay Models for DSN Radio Metric Data Calibration. JPL Publication 94-24． October 1994．
[13] Estefan, J.A., TDA Progress Report 42-120． Jet Propulsion Laboratory. USA. 1995．
[14] Fadrique F. M. M., Dow J. M., Zandbergen R. C. A. et al.. ERS-2 Orbit Determination with PRARE. ESA/ESOC, Robert Bosch Str. 5． D-64293． Darmstadt. Germany. 1997
[15] Flechtner, F., S. Bedrich, F. H. Massmann. PRARE/ERS-2: System Status and Results. CSTG Bull. 13, Munich:DGFI, 1997:67-71．
[16] Th. Gruber and A. Bode and Ch. Reigber and P. Schwintzer. D-PAF Global Earth Gravity Models Based on ERS, In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence, Italy. ESA SP-414, Vol 3, pp. 1661-1668． 1997
[17] Hartl Ph, Reigber Ch. CSTG Bull. 8． Munich:DGFI. 1985:124-134
[18] Hedin A. E., 1987, MSIS-86 thermospheric model. J. Geophys. Res. 92: 4649-4662
[19] Herring, T. A., Modeling Atmospheric Delays in the Analysis of Space Geodetic Data, in "Refraction of Transatmospheric Signals in Geodesy". Netherlands Geodetic Commission, Edited by J.C.De Munck and T.A.Th. Spoelstra. New Seris No.36． p157． 1992．
[20] Hu X. G., X. H. Liao, C. Huang, Data weighting and solution assessment in combination. Journal of Geodesy, 73:391-397． 1999．
[21] Klokocnik, J., F.G. Lemoine and J. Kostelecky. Reduction of Crossover Errors in the Earth Gravity Model (EGM) 96, Marine Geodesy. 21:219-239． 1998．
[22] Lemoine F.G., D.E. Smith, et al.. The development of NASA GSFC and DMA Joint Geopoten-tial Model, Proceedings of IAG Symposium: Gravity. Geoid and Marine Geodey. Tokyo 1996． Berlin: Springer-Verlag, 1997．
[23] Lemoine, F.G., N.K.Pavlis, et al.. New high-resolution model developed for Earth's gravitational field, EOS Trans AGU, 79:9．
[24] Lemoine, F.G., et al.. The development of the NASA GSFC and NTMA Joint Geopotential Model, in International Association of Geodesy Symposia. Vol. 117: Segawa et al. (eds.), Gravity, Geoid and Marine Geodesy, pp.461-469． Springer-Verlag. Berlin Heidelberg. 1997．
[25] Le Traon, P.Y., P. Gaspar. F. Ogor, and J. Dorandeu. Satellites work in tandem to improve accuracy of data, Eos Trans. AGU. 7(5(39) . 385． 389． 1995．
[26] P.-Y. Le Traon and F. Ogor, ERS-1/2 orbit improvement using TOPEX/POSEIDON: The 2 cm challenge, Journal of Geophysical Research. Vol. 103． No. C4． Pages 8045-8057． 1998．
[27] Marini,J.W., Correction of satellite tracking data for an arbitrary atmospheric profile. Radio Science, 7, 223-231, 1972．
[28] Marini and Murray, correction to laser range tracking data for atmospheric refraction at elevations above 10 degrees, GSFC report x-591-73-351． Nov. 1973．
[29] Marshall, J.A., N.P. Zelensky, S.M.Klosko. D.S.Chinn. S.B.Luthcke. and K.E. Rachlin, The temporal and spatial characteristics of TOPEX/POSEIDON radial orbit error, J. Geophys. Res., 100(C12) , 25,331-25,352, 1995．
[30] Massmann F H, Flechtner F. Raimondo J C et al. Impact of PRARE on ERS-2 POD. (retrieved from Internet:http://www.gfz-potsdam.de )
[31] Massmann, F. H.. K. H. Neumayer, J. C. Raimondo. K. Enninghorst.H. Li. Quality of the D-PAF ERS Orbits Before and After Inclusion of PRARE Data. In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence. Italy. ESA SP-414． Vol 3． pp. 1655-1660, 1997．
[32] McCarthy, D. D., US Naval Observatory. IERS Standards (1992) . IERS TECHNICAL NOTE 13, Central Bureau of IERS-Observatoire de Paris. July 1992．
[33] McCarthy, D. D.. US Naval Observatory. IERS Conventions (1996) . Central Bureau of IERS, Observatoire de Paris. July 1996．
[34] Moyer, T. D., 1971, Mathematical Formulation of the Double-precision Orbit Determination Program, JPL Technical Report 32-1527．
[35] Niell, A.E., Global mapping functions for the atmosphere delay at radio wavelengths. Journal of Geophysical Research, Vol. 101． No. B2． pp 3227-3246． February 10． 1996．
[36] Raimondo, J.C., A. Bode, K. Enninghorst. F.H. Massmann. K.H. Neumayer, Point Positioning and Earth Parameters derived from ERS-2 PRARE Data. EGS XXII General Assembly Vienna. 21-25 April 1997．
[37] Reigber, Ch., F. H. Massmann. F. Flechtner. The PRARE System and the Data Analysis Procedure. CSTG Bull. 14． Munich:DGFI. 11-19． 1997．
[38] Ries, J. C., J. J. Bordi. C. K. Shum. and B. D. Tapley. Precise orbit determination for ERS-2． European Geophysical Society XXII Genaral Assembly. Vienna. Austria. April 21-25． 1997．
[39] Ries, J.C., J. Bordi and T. Urban, Precise Orbits for ERS-2 using laser ranging and PRARE tracking, Center for Space Research. University of Texas at Austin. Austin, Texas, Technical Memorandum, CSR-TM-99-03, May 1999．
[40] Ries, J.C.,个人通信，1999年9月1日.
[41] Ries, J. C., C. K. Shum. and B. D. Tapley. Surface Force Modeling for Precision Orbit Determination, Geophysical Monograph 73． IUGG Vol. 13． 111-124． 1993．
[42] RUMMEL, R., 1993, Principle of satellite altimetry and elimination of radial orbit errors. In Satellite Altimetry in Geodesy and Oceanography. Lecture Notes in Earth Sciences. Vol.50, edited by R. Rummel and F. Sanso (Berlin Heidelberg: Springer-Verlag). pp. 189-241．
[43] Saastamoinen, J., Atmospheric Correction for the Troposphere and Stratosphere in Radio Rang-ing of Satellites, The Use of Artificial Satellites for Geodesy. Geophysics Monograph Series, Vol. 15, American Geophysical Union, Washington D.C.. 1972．
[44] Sahin, M., P. A. Cross, and P. C. Sellers, Variance component estimation applied to satellite laser ranging, Bull. Geod., 66． 284-295, 1992．
[45] Schafer W., Shumann W., PRARE-2-Building On the Lessons from ERS-1． 1997 (retrieved from Internet: http://esapub.esrin.esa.it/ bullet83/schaf83． htm)
[46] Scharroo R., PNAM Visser, ERS Tandem Mission orbits: is 5cm still a challenge? In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence, Italy. ESA SP-414, Vol 3, pp 1643-1648, 1997
[47] Scharroo R. and P. Visser, Precise orbit determination and gravity field improvement for the ERS satellites. Journal of Geophysical Research. Vol.103． No.C4． Pages 8113-8127, April 15． 1998
[48] Schwintzer, P., Ch. Reigber, A. Bode, Z. Kang. S.Y. Zhu. F.-H. Massmann. J.C. Raimondo, R. Biancale, G. Balmino, J.M. Lemoine, B. Moynot. J.C. Marty. F. Barlier, Y. Boudon, Long-wavelength global gravity field models: GRIM4-S4． GRIM4-C4． Journal of Geodesy 71:189-208, 1997．
[49] Sillard P., Z. Altamimi, C. Boucher. The ITRF96 realization and its associted Velocity field, Geophysical Research Letters. Vol.25． No.17． Pages 3223-3226． September 1． 1998
[50] Stovers, O.J., and G.E. Lanyi, Evaluation of Current Tropospheric Mapping Functions by Deep Space Network Very Long Baseline Interferometry. TDA Progress Report 42-119． pp 1-11． November 15, 1994．
[51] TAI, C.K., and KUHN, J., 1995． Orbit and tide error reduction for the first 2 years of TOPEX/POSEIDON data, Journal of Geophysical Research 100． C12． 25353-25363．
[52] Tapley B.D., Statistical Orbit Determination Theory. Proceedings of NATO Advanced Study Institute in Dynamical Astronomy. Cortina d'Ampezzo. Italy. Reidel Publishing Co. Dordrecht, 1976
[53] Tapley, B.D., G.H.Born, Statistical Orbit Determination Theory.统计定轨理论，李济深译，《航天测控技术》编辑部,1990．
[54] Tapley, B.D., TOPEX/POSEIDON precision orbit determination standards, memorandum. Bur. of Eng. Res., Univ. of Tex. at Austin. 1992．
[55] Tapley, B. D., J. C. Ries, G. VV. Davis, R. J. Eanes. B. E. Schutz, C. K. Shum, M. M. Watkins, J. A. Marshall, R. S. Nerem, B. H. Putney. S. M. Klosko. S. B. Luthcke. D. Pavlis. R. G. Williamson, and N. P. Zeiensky, Precision Orbit Determination for TOPEX/POSEIDON.J.Geophys. Res., Vol. 99, No. C12, 24． 383-24． 404． 1994．
[56] Tapley, B. D., B. E. Schutz, R. J. Eanes. J. C. Ries. and M. M. Watkins , Lageos laser ranging contributions to geodynamics. geodesy, and orbital dynamics, in Contributions of Space Geodesy to Geodynaniics: Earth Dynamics. Geodyn. Ser.. vol. 24． edited by D. E. Smith and D. L. Turcotte, pp.147-173． AGU. Washington. D.C.. 1993
[57] Tapley, B. D., M. M. Watkins, J. C. Ries. G. W. Davis. R. J. Eanes. S. R. Poole. H. J. Rim, B. E. Schutz, C. K. Shum, R. S. Nerem. F. J. Lerch. J. A. Marshall. S. M. Klosko, N. K. Pavlis, and R. G. Williamson, The Joint Gravity Model 3, J. Geophys. Res., Vol. 101． No. B12, 28,029-28,049, December 10, 1996．
[58] Tapley, B. D., C. K. Shum, J. C. Ries. S. R. Poole. P.A.M. Abusali. S. V. Battadpur, R. J. Eanes, M. C. Kim, H. J. Rim, and B. E. Schutz. The TEG-3 Geopotential Model. Gravity, Geoid and Marine Geodesy, 453-460． J. Seagwa, H. Fujimoto. and S. Okubo (Ed.), Springer-Verlag. 1997．
[59] Visser, P. N. A. M., Evaluation of ERS-2 POD using PRARE: preliminary results, paper presented at AFRICAR Scientific Meeting. Delft. Faculty of Geodesy. 1996 (retrieved from Inter-net:http://dutlru8． lr.tudelft.nl)
[60] Visser, P.N.A.M., R. Scharroo. B.A.C. Ambrosius and R. Noomen. Incorporation of PRARE data in ERS-2 orbit computation, paper presented at European Geophysical Society XXII Genaral Assembly, Vienna, Austria. April 21-25． 1997．
[61] Visser, P. N. A. M., R. Scharroo, R. Floberghagen. B. Ambrosius. Impact of PRARE on ERS-2 Orbit Determination. Proceedings of 12th International Symposium on Space Flight Dynamics, ESOC, Darmstadt, Germany. 2-6 June 1997． Space Agency Spec. Publ.. ESA SP 3-403． pp.115-120, 1997
[62] Whar, J. M., 1981, "The Forced Nutations of an Elliptical. Rotating, Elastic, and Oceanless Earth," Geophys. J. Roy. Astron. Soc.. 64． pp. 705-727
[63] Yan, H. J. and J. S. Ping, The generator function method of the tropespheric refraction corrections, The Astron. J., 110(2) , 934-939． 1995．
[64] Yuan, D. N., The determination and error assessment of the Earth's gravity field model, Ph.D. diss., Univ. of Tex. at Austin, 1991
[65] Zandbergen, R., J.M. Dow, F. Martinez Fadrique, M. Romay Merino and R. Piriz, Progress in ERS Orbit and Tracking Data Analysis. In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp., Florence, Italy. ESA SP-414． Vol 3． pp 1669-1680． 1997
[66] Zhang F.P., C. Huang. C.G. Feng. X.J. Dong. Accuracy Assessment of PRARE via Variance Component Estimation, submitted to International Journal of Remote Sensing.
[67]Zhu S Y, Ch. Reigber, F.-H. Massmann. ERS Standards used at D-PAF. Technical Report of The German PAF for ERS. Oberpfaffenhofen: D-PAF. 1991
[68]崔希璋，於宗俦，陶本藻，刘大杰，于正林，广义测量平差(第二版)，测绘出版社，第86-89页，北京，1992
[69]丁晓利，陈永奇，李志林，刘国祥，章国宝，合成孔径雷达干涉技术及其在地表形变监测中的应用，“1999天体力学和天体测量学术年会”论文，(紫金山天文台台刊将出版会议文集)。
[70]何昌礼，解病态线性方程组的奇异值分解法及其应用，中国地质大学出版社，第116页，1990
[71]CAPS(Covariance Analysis Program Developed at Shanghai observatory) 的原理、结构和使用，中国科学院上海天文台年刊，No．20，1999
[72]黄城，利用LAGEOS激光测距资料精确测定地球自转参数。博士论文，上海：中国科学院上海天文台，1985
[73]李济深，人造卫星精密轨道确定，解放军出版社，北京，1995
[74]刘林，人造地球卫星轨道力学，高等教育出版社，北京，1992
[75]米兰尼，A．，A．M．诺比利，P．法里内拉，非引力摄动和卫星大地测量，夏汉林译，解放军出版社，北京，1990
[76]沈镜祥，施品浩，刘基余，何妙福，钱志瀚等，空间大地测量，中国地质大学出版社，1990
[77]陶本藻，测量数据统计分析，测绘出版社，第83-161页，北京，1992
[78]吴晓清，Helmert-WF(权因子)方差分量估计，武汉测绘科技大学学报，Vol．17，No．4．1992。
[79]希洛夫，最小二乘法，朱新美，郑景乾，朱栋译，测绘出版社，第51-54页，北京，1957。
[80]严豪健，对流层大气折射延迟改正(Ⅰ)：经典理论，天文学进展，Vol．13，No．4，p380-391，1995。
[81]严豪健，对流层大气折射延迟改正(Ⅱ)：当前主要研究方向和进展，天文学进展，Vol．14，No．3，p181-191，1996。
[82]严豪健，李凤凤，吴海南，有限距离目标的大气折射改正，中国科学院上海天文台年刊，No．18，1997。
[83]严豪健，林钦畅，全球大气折射延迟映射函数的可能性问题，中国科学院上海天文台年刊，No．20，1999。
[84]杨福民，私人通讯，1999年1月
[85]张飞鹏，冯初刚，黄城，李雅勤，改进的Helmert方差分量估计方法在统计定轨中的应用，测绘学报，第29卷，第2期，2000．(待发表)
[86]张飞鹏，黄城，李雅勤，冯初刚，统计定轨中随机模型的验后估计，天文学报，第41卷，第2期，2000．(待发表)
[87]、张飞鹏，黄城，张忠平，精密测距测速系统的研究与应用，天文学进展，Vol．17，No．1，1999．
[88]张飞鹏，黄城，冯初刚，董晓军，廖新浩，方差分量估计方法在ERS-2卫星精密定轨中的应用，巳投天文学报。
[89]张万鹏，方差分量估计理论及其在边角网平差中的应用，武汉测绘科技大学学报，Vol．13，No．1，1988
[90]张忠平，刘乃苓．测绘通报，1997，第1期，27
[91]张忠平，谭德同．中国科学院上海天文台年刊，1997，18：107
[92]赵长印，引力场模型引起的卫星轨道径向误差的估计结果，天文学报研究快报
[93]朱圣源，私人通讯，1997年5月
[2] Andersen, P.H., K. Aksnes, H. Skonnord, Precise ERS-2orbit determination using SLR, PRARE, and RA observations. Journal of Geodesy. 72:421-429． 1998．
[3] Bedrich S, Flechtner F, Teubel A. EGS(European Geophysical Socienty) XXII General Assembly, Vienna, 1997 (retrieved from Internet: http://florence97． ers-symposium.org/data/flechtner/)
[4] Bedrich S., F. Flechtner, Ch. Fdrste, Ch. Reigber. and A. Teubel. PRARE system performance. In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence. Italy. ESA SP-414, Vol 3． pp. 1637-1642, 1997
[5] Bedrich, S., A New Method for Highly Precise Two Way Common-View Time Transfer between Ground-Based Atomic Clocks with PRARE. XXII Gen. Assembly of the EGS. Vienna, 21-25 April 1997．
[6] Bordi, J. J., Analysis of the Precise Range and Range-Rate Equipment (PRARE) and its application to precise orbit determination. Center for Space Research Report. CSR-99-01． 1999．
[7] Chao, C. C., the tropospheric calibration model for .Mariner Mars 1971． Tech. Rep. 32-1587． pp. 61-76, Jet Propul. Lab., Pasadena. Calif.. 1974．
[8] Davis J. L., T.A. Herring, I.I. Shapiro et al.. Geodesy by radio interferometry: Effects of atmospheric modeling errors on the estimates of baseline length. Radio Science. 20． 1593-1607, 1985．
[9] Dong, D.N., T.A. Herring, R.W. King. Estimating Regional Deformation from a Combination of Space and Terrestrial Geodetic Data. Journal of Geodesy. Vol 72． Iss 4． pp 200-214． 1998．
[10] Eanes R.J. and Bettadpur S.. The CSR 3． 0 Global Ocean Tide Model: Diurnal and Semi-diurnal Ocean Tides from TOPEX/Poseidon Altimetry. Center for Space Research. University of Texas at Austin, Austin, Texas, Technical Memorandum. CSR-TM-96-05． December 1996．
[11] Enninghorst, K., F. H. Massmann. K. H. Neumayer. and J.C. Raimondo. ERS-2 precise orbit determination with PRARE, paper presented at EGS (European Geophysical Society) XXII General Assembly, Vienna, G17． 24 April. 1997．
[12] Estefan, J.A., and O.J. Stovers, A Comparative Survey of Current and Proposed Tropospheric Refraction-Delay Models for DSN Radio Metric Data Calibration. JPL Publication 94-24． October 1994．
[13] Estefan, J.A., TDA Progress Report 42-120． Jet Propulsion Laboratory. USA. 1995．
[14] Fadrique F. M. M., Dow J. M., Zandbergen R. C. A. et al.. ERS-2 Orbit Determination with PRARE. ESA/ESOC, Robert Bosch Str. 5． D-64293． Darmstadt. Germany. 1997
[15] Flechtner, F., S. Bedrich, F. H. Massmann. PRARE/ERS-2: System Status and Results. CSTG Bull. 13, Munich:DGFI, 1997:67-71．
[16] Th. Gruber and A. Bode and Ch. Reigber and P. Schwintzer. D-PAF Global Earth Gravity Models Based on ERS, In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence, Italy. ESA SP-414, Vol 3, pp. 1661-1668． 1997
[17] Hartl Ph, Reigber Ch. CSTG Bull. 8． Munich:DGFI. 1985:124-134
[18] Hedin A. E., 1987, MSIS-86 thermospheric model. J. Geophys. Res. 92: 4649-4662
[19] Herring, T. A., Modeling Atmospheric Delays in the Analysis of Space Geodetic Data, in "Refraction of Transatmospheric Signals in Geodesy". Netherlands Geodetic Commission, Edited by J.C.De Munck and T.A.Th. Spoelstra. New Seris No.36． p157． 1992．
[20] Hu X. G., X. H. Liao, C. Huang, Data weighting and solution assessment in combination. Journal of Geodesy, 73:391-397． 1999．
[21] Klokocnik, J., F.G. Lemoine and J. Kostelecky. Reduction of Crossover Errors in the Earth Gravity Model (EGM) 96, Marine Geodesy. 21:219-239． 1998．
[22] Lemoine F.G., D.E. Smith, et al.. The development of NASA GSFC and DMA Joint Geopoten-tial Model, Proceedings of IAG Symposium: Gravity. Geoid and Marine Geodey. Tokyo 1996． Berlin: Springer-Verlag, 1997．
[23] Lemoine, F.G., N.K.Pavlis, et al.. New high-resolution model developed for Earth's gravitational field, EOS Trans AGU, 79:9．
[24] Lemoine, F.G., et al.. The development of the NASA GSFC and NTMA Joint Geopotential Model, in International Association of Geodesy Symposia. Vol. 117: Segawa et al. (eds.), Gravity, Geoid and Marine Geodesy, pp.461-469． Springer-Verlag. Berlin Heidelberg. 1997．
[25] Le Traon, P.Y., P. Gaspar. F. Ogor, and J. Dorandeu. Satellites work in tandem to improve accuracy of data, Eos Trans. AGU. 7(5(39) . 385． 389． 1995．
[26] P.-Y. Le Traon and F. Ogor, ERS-1/2 orbit improvement using TOPEX/POSEIDON: The 2 cm challenge, Journal of Geophysical Research. Vol. 103． No. C4． Pages 8045-8057． 1998．
[27] Marini,J.W., Correction of satellite tracking data for an arbitrary atmospheric profile. Radio Science, 7, 223-231, 1972．
[28] Marini and Murray, correction to laser range tracking data for atmospheric refraction at elevations above 10 degrees, GSFC report x-591-73-351． Nov. 1973．
[29] Marshall, J.A., N.P. Zelensky, S.M.Klosko. D.S.Chinn. S.B.Luthcke. and K.E. Rachlin, The temporal and spatial characteristics of TOPEX/POSEIDON radial orbit error, J. Geophys. Res., 100(C12) , 25,331-25,352, 1995．
[30] Massmann F H, Flechtner F. Raimondo J C et al. Impact of PRARE on ERS-2 POD. (retrieved from Internet:http://www.gfz-potsdam.de )
[31] Massmann, F. H.. K. H. Neumayer, J. C. Raimondo. K. Enninghorst.H. Li. Quality of the D-PAF ERS Orbits Before and After Inclusion of PRARE Data. In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence. Italy. ESA SP-414． Vol 3． pp. 1655-1660, 1997．
[32] McCarthy, D. D., US Naval Observatory. IERS Standards (1992) . IERS TECHNICAL NOTE 13, Central Bureau of IERS-Observatoire de Paris. July 1992．
[33] McCarthy, D. D.. US Naval Observatory. IERS Conventions (1996) . Central Bureau of IERS, Observatoire de Paris. July 1996．
[34] Moyer, T. D., 1971, Mathematical Formulation of the Double-precision Orbit Determination Program, JPL Technical Report 32-1527．
[35] Niell, A.E., Global mapping functions for the atmosphere delay at radio wavelengths. Journal of Geophysical Research, Vol. 101． No. B2． pp 3227-3246． February 10． 1996．
[36] Raimondo, J.C., A. Bode, K. Enninghorst. F.H. Massmann. K.H. Neumayer, Point Positioning and Earth Parameters derived from ERS-2 PRARE Data. EGS XXII General Assembly Vienna. 21-25 April 1997．
[37] Reigber, Ch., F. H. Massmann. F. Flechtner. The PRARE System and the Data Analysis Procedure. CSTG Bull. 14． Munich:DGFI. 11-19． 1997．
[38] Ries, J. C., J. J. Bordi. C. K. Shum. and B. D. Tapley. Precise orbit determination for ERS-2． European Geophysical Society XXII Genaral Assembly. Vienna. Austria. April 21-25． 1997．
[39] Ries, J.C., J. Bordi and T. Urban, Precise Orbits for ERS-2 using laser ranging and PRARE tracking, Center for Space Research. University of Texas at Austin. Austin, Texas, Technical Memorandum, CSR-TM-99-03, May 1999．
[40] Ries, J.C.,个人通信，1999年9月1日.
[41] Ries, J. C., C. K. Shum. and B. D. Tapley. Surface Force Modeling for Precision Orbit Determination, Geophysical Monograph 73． IUGG Vol. 13． 111-124． 1993．
[42] RUMMEL, R., 1993, Principle of satellite altimetry and elimination of radial orbit errors. In Satellite Altimetry in Geodesy and Oceanography. Lecture Notes in Earth Sciences. Vol.50, edited by R. Rummel and F. Sanso (Berlin Heidelberg: Springer-Verlag). pp. 189-241．
[43] Saastamoinen, J., Atmospheric Correction for the Troposphere and Stratosphere in Radio Rang-ing of Satellites, The Use of Artificial Satellites for Geodesy. Geophysics Monograph Series, Vol. 15, American Geophysical Union, Washington D.C.. 1972．
[44] Sahin, M., P. A. Cross, and P. C. Sellers, Variance component estimation applied to satellite laser ranging, Bull. Geod., 66． 284-295, 1992．
[45] Schafer W., Shumann W., PRARE-2-Building On the Lessons from ERS-1． 1997 (retrieved from Internet: http://esapub.esrin.esa.it/ bullet83/schaf83． htm)
[46] Scharroo R., PNAM Visser, ERS Tandem Mission orbits: is 5cm still a challenge? In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp.. Florence, Italy. ESA SP-414, Vol 3, pp 1643-1648, 1997
[47] Scharroo R. and P. Visser, Precise orbit determination and gravity field improvement for the ERS satellites. Journal of Geophysical Research. Vol.103． No.C4． Pages 8113-8127, April 15． 1998
[48] Schwintzer, P., Ch. Reigber, A. Bode, Z. Kang. S.Y. Zhu. F.-H. Massmann. J.C. Raimondo, R. Biancale, G. Balmino, J.M. Lemoine, B. Moynot. J.C. Marty. F. Barlier, Y. Boudon, Long-wavelength global gravity field models: GRIM4-S4． GRIM4-C4． Journal of Geodesy 71:189-208, 1997．
[49] Sillard P., Z. Altamimi, C. Boucher. The ITRF96 realization and its associted Velocity field, Geophysical Research Letters. Vol.25． No.17． Pages 3223-3226． September 1． 1998
[50] Stovers, O.J., and G.E. Lanyi, Evaluation of Current Tropospheric Mapping Functions by Deep Space Network Very Long Baseline Interferometry. TDA Progress Report 42-119． pp 1-11． November 15, 1994．
[51] TAI, C.K., and KUHN, J., 1995． Orbit and tide error reduction for the first 2 years of TOPEX/POSEIDON data, Journal of Geophysical Research 100． C12． 25353-25363．
[52] Tapley B.D., Statistical Orbit Determination Theory. Proceedings of NATO Advanced Study Institute in Dynamical Astronomy. Cortina d'Ampezzo. Italy. Reidel Publishing Co. Dordrecht, 1976
[53] Tapley, B.D., G.H.Born, Statistical Orbit Determination Theory.统计定轨理论，李济深译，《航天测控技术》编辑部,1990．
[54] Tapley, B.D., TOPEX/POSEIDON precision orbit determination standards, memorandum. Bur. of Eng. Res., Univ. of Tex. at Austin. 1992．
[55] Tapley, B. D., J. C. Ries, G. VV. Davis, R. J. Eanes. B. E. Schutz, C. K. Shum, M. M. Watkins, J. A. Marshall, R. S. Nerem, B. H. Putney. S. M. Klosko. S. B. Luthcke. D. Pavlis. R. G. Williamson, and N. P. Zeiensky, Precision Orbit Determination for TOPEX/POSEIDON.J.Geophys. Res., Vol. 99, No. C12, 24． 383-24． 404． 1994．
[56] Tapley, B. D., B. E. Schutz, R. J. Eanes. J. C. Ries. and M. M. Watkins , Lageos laser ranging contributions to geodynamics. geodesy, and orbital dynamics, in Contributions of Space Geodesy to Geodynaniics: Earth Dynamics. Geodyn. Ser.. vol. 24． edited by D. E. Smith and D. L. Turcotte, pp.147-173． AGU. Washington. D.C.. 1993
[57] Tapley, B. D., M. M. Watkins, J. C. Ries. G. W. Davis. R. J. Eanes. S. R. Poole. H. J. Rim, B. E. Schutz, C. K. Shum, R. S. Nerem. F. J. Lerch. J. A. Marshall. S. M. Klosko, N. K. Pavlis, and R. G. Williamson, The Joint Gravity Model 3, J. Geophys. Res., Vol. 101． No. B12, 28,029-28,049, December 10, 1996．
[58] Tapley, B. D., C. K. Shum, J. C. Ries. S. R. Poole. P.A.M. Abusali. S. V. Battadpur, R. J. Eanes, M. C. Kim, H. J. Rim, and B. E. Schutz. The TEG-3 Geopotential Model. Gravity, Geoid and Marine Geodesy, 453-460． J. Seagwa, H. Fujimoto. and S. Okubo (Ed.), Springer-Verlag. 1997．
[59] Visser, P. N. A. M., Evaluation of ERS-2 POD using PRARE: preliminary results, paper presented at AFRICAR Scientific Meeting. Delft. Faculty of Geodesy. 1996 (retrieved from Inter-net:http://dutlru8． lr.tudelft.nl)
[60] Visser, P.N.A.M., R. Scharroo. B.A.C. Ambrosius and R. Noomen. Incorporation of PRARE data in ERS-2 orbit computation, paper presented at European Geophysical Society XXII Genaral Assembly, Vienna, Austria. April 21-25． 1997．
[61] Visser, P. N. A. M., R. Scharroo, R. Floberghagen. B. Ambrosius. Impact of PRARE on ERS-2 Orbit Determination. Proceedings of 12th International Symposium on Space Flight Dynamics, ESOC, Darmstadt, Germany. 2-6 June 1997． Space Agency Spec. Publ.. ESA SP 3-403． pp.115-120, 1997
[62] Whar, J. M., 1981, "The Forced Nutations of an Elliptical. Rotating, Elastic, and Oceanless Earth," Geophys. J. Roy. Astron. Soc.. 64． pp. 705-727
[63] Yan, H. J. and J. S. Ping, The generator function method of the tropespheric refraction corrections, The Astron. J., 110(2) , 934-939． 1995．
[64] Yuan, D. N., The determination and error assessment of the Earth's gravity field model, Ph.D. diss., Univ. of Tex. at Austin, 1991
[65] Zandbergen, R., J.M. Dow, F. Martinez Fadrique, M. Romay Merino and R. Piriz, Progress in ERS Orbit and Tracking Data Analysis. In: T.D.Guyenne and D.Danesy(ed) Proc. 3rd ERS Symp., Florence, Italy. ESA SP-414． Vol 3． pp 1669-1680． 1997
[66] Zhang F.P., C. Huang. C.G. Feng. X.J. Dong. Accuracy Assessment of PRARE via Variance Component Estimation, submitted to International Journal of Remote Sensing.
[67]Zhu S Y, Ch. Reigber, F.-H. Massmann. ERS Standards used at D-PAF. Technical Report of The German PAF for ERS. Oberpfaffenhofen: D-PAF. 1991
[68]崔希璋，於宗俦，陶本藻，刘大杰，于正林，广义测量平差(第二版)，测绘出版社，第86-89页，北京，1992
[69]丁晓利，陈永奇，李志林，刘国祥，章国宝，合成孔径雷达干涉技术及其在地表形变监测中的应用，“1999天体力学和天体测量学术年会”论文，(紫金山天文台台刊将出版会议文集)。
[70]何昌礼，解病态线性方程组的奇异值分解法及其应用，中国地质大学出版社，第116页，1990
[71]CAPS(Covariance Analysis Program Developed at Shanghai observatory) 的原理、结构和使用，中国科学院上海天文台年刊，No．20，1999
[72]黄城，利用LAGEOS激光测距资料精确测定地球自转参数。博士论文，上海：中国科学院上海天文台，1985
[73]李济深，人造卫星精密轨道确定，解放军出版社，北京，1995
[74]刘林，人造地球卫星轨道力学，高等教育出版社，北京，1992
[75]米兰尼，A．，A．M．诺比利，P．法里内拉，非引力摄动和卫星大地测量，夏汉林译，解放军出版社，北京，1990
[76]沈镜祥，施品浩，刘基余，何妙福，钱志瀚等，空间大地测量，中国地质大学出版社，1990
[77]陶本藻，测量数据统计分析，测绘出版社，第83-161页，北京，1992
[78]吴晓清，Helmert-WF(权因子)方差分量估计，武汉测绘科技大学学报，Vol．17，No．4．1992。
[79]希洛夫，最小二乘法，朱新美，郑景乾，朱栋译，测绘出版社，第51-54页，北京，1957。
[80]严豪健，对流层大气折射延迟改正(Ⅰ)：经典理论，天文学进展，Vol．13，No．4，p380-391，1995。
[81]严豪健，对流层大气折射延迟改正(Ⅱ)：当前主要研究方向和进展，天文学进展，Vol．14，No．3，p181-191，1996。
[82]严豪健，李凤凤，吴海南，有限距离目标的大气折射改正，中国科学院上海天文台年刊，No．18，1997。
[83]严豪健，林钦畅，全球大气折射延迟映射函数的可能性问题，中国科学院上海天文台年刊，No．20，1999。
[84]杨福民，私人通讯，1999年1月
[85]张飞鹏，冯初刚，黄城，李雅勤，改进的Helmert方差分量估计方法在统计定轨中的应用，测绘学报，第29卷，第2期，2000．(待发表)
[86]张飞鹏，黄城，李雅勤，冯初刚，统计定轨中随机模型的验后估计，天文学报，第41卷，第2期，2000．(待发表)
[87]、张飞鹏，黄城，张忠平，精密测距测速系统的研究与应用，天文学进展，Vol．17，No．1，1999．
[88]张飞鹏，黄城，冯初刚，董晓军，廖新浩，方差分量估计方法在ERS-2卫星精密定轨中的应用，巳投天文学报。
[89]张万鹏，方差分量估计理论及其在边角网平差中的应用，武汉测绘科技大学学报，Vol．13，No．1，1988
[90]张忠平，刘乃苓．测绘通报，1997，第1期，27
[91]张忠平，谭德同．中国科学院上海天文台年刊，1997，18：107
[92]赵长印，引力场模型引起的卫星轨道径向误差的估计结果，天文学报研究快报
[93]朱圣源，私人通讯，1997年5月
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