Orbit determination modeling analysis by GPS including perturbations due to geopotential coefficients of high degree and order, solar radiation pressure and luni-solar attraction

Pardal, Paula C. P. M.; Moraes, Rodolpho Vilhena de; Kuga, Helio K.

doi:10.5028/jatm.2011.03010611

Abstract

The purpose of this paper was to analyze the modeling of an artificial satellite orbit, using signals of the GPS constellation and least squares algorithms as the method of estimation, with the aim of analyzing the performance of the orbit estimation process. One pursues to verify how differences of modeling can affect the final accuracy of orbit determination. To accomplish that, the following effects were considered: high degree and order for the geopotential coefficients; direct solar radiation pressure; and Sun-Moon attraction. The measurements were used to feed the batch least squares orbit determination process, in order to yield conclusive results about the orbit modeling issue. An application has been done, using GPS data of the TOPEX/Poseidon satellite, whose accurate ephemeris are available on the Internet. It is shown that from a poor but acceptable modeling up to all effects included, the accuracy can vary from 28 to 9 m in the long-period analysis.

Keywords:
Orbit determination; GPS; Orbit perturbations; Geopotential; Solar radiation pressure; Luni-solar gravitational attraction

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REFERENCES

Antreasian, P.G., Rosborough, G.W., 1992, "Prediction of Radiant Energy Forces on the Topex/Poseidon Spacecraft", Journal of Spacecraft and Rockets, Vol. 29, No. 1, p. 81-90. doi: 10.2514/3.26317.
» https://doi.org/10.2514/3.26317
Binning, P.W., 1996, "GPS, Dual Frequency, SA Free Satellite Navigation. Navigation Technology for the 3rd Millennium", Proceedings of the 52nd Annual Meeting of the Institute of Navigation, June 19-21, Cambridge, MA, USA, pp. 803-812.
Chiaradia, A.P.M., Kuga, H.K. and Prado, A.F.B.A., 2000, "Investigation on Ionospheric Correction Models for GPS Signals", Proceedings of the 9^th Colóquio Brasileiro de Dinâmica Orbital, Advances in Space Dynamics, Prado, A.F.B.A., Editor, Águas de Lindoia, Brazil, pp. 214-219.
CNES, 2007, Topex/Poseidon. The beginnings of satellite oceanography, Available at: http://www.cnes.fr/web/1461-topexposeidon.php Access on May 10, 2007.
» http://www.cnes.fr/web/1461-topexposeidon.php
Givens, J.W., 1958, "Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular Form", SIAM Journal on Applied Mathematics, Vol. 6, pp. 26-50.
Kaula, W.M., 1966, "Theory of Satellite Geodesy: Applications of Satellites to Geodesy", Blaisdell Publ. Co., Waltham, MA, USA.
Kuga, H.K., 2005, "Noções Práticas de Técnicas de Estimação", Class Notes of Optimization on Dynamical Systems II", INPE, São José dos Campos, Brazil.
Kuga, H.K., 1989, "Determinação de órbitas de satélites artificiais terrestres através de técnicas de estimação combinadas a técnicas de suavização de estado". (INPE-4959-TDL/079). Ph.D. Thesis, National Institute for Space Research, São José dos Campos, Brazil, 249 p.
Marshall, J.A., Antreasian, P.G., Rosborough, G.W. and Putney, B.H., 1991, "Modeling radiation forces acting on satellites for precision orbit determination", Advances in Astronautical Sciences, Astrodymanics Conference, AAS 91-357, Vol. 76, Part I, p. 72-96.
Marshall, J.A., Luthcke, S.B., 1994, "Modelling radiation forces acting on TOPEX/Poseidon for precision orbit determination", Journal of Spacecraft and Rockets, Vol. 31, No. 1, p. 89-105.
Montenbruck, O., Suarez, M., 1984, "A Modular Fortran Library for Sequential Least-Squares Estimation Using QR-Factorization", DLR, German Space Operations Center, Oberpfaffenhofen, Germany (DLR-GSOC IB 94-05).
Pardal, P.C.P.M., 2007, "Determinação de Órbita via GPS Considerando Modelo de Pressão de Radiação Solar para o Satélite Topex/Poseidon", Masters Dissertation, National Institute for Space Research, São José dos Campos, Brazil.
Prado, A.F.B.A., Kuga, H.K. (Eds), 2001, "Fundamentos de Tecnologia Espacial", National Institute for Space Research, São José dos Campos, Brazil, 220 p. ISBN: 85-17-00004-8.
Silva, A.A., 2001, "Determinação de Órbitas com o GPS através de Mínimos Quadrados Recursivo com Rotações de Givens", Masters Dissertation, São Paulo State University, Guaratinguetá, Brazil.
Soyka, M.T., Davis, M.A., 2001, "Estimation of Periodic Accelerations to Improve Orbit Ephemeris Accuracy", Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Advances in the Astonautical Sciences, Vol. 108, Part II, California, USA, pp. 1123-1140.
Vilhena de Moraes, R., Raimundo, P.C.P. and Kuga, H.K., 2008, "Orbit Determination Using GPS Including Perturbations due to Geopotential Coefficients of Higher Degree and Order and Solar Radiation Pressure", Advances in the Astronautic Sciences, Galveston, Proceedings of the 18^th AAS/AIAA Space Flight Meeting, Vol. 130, San Diego: American Astronautical Society, p. 923-933.
Pardal, P.C.P.M., Kuga, H.K. and Vilhena de Moraes, R., 2010, "Comparing the Extended and the Sigma Point Kalman Filters for Orbit Determination Modeling Using GPS Measurements". In: 23^rd International Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR. Proceedings of the 23^rd International Meeting of the Satellite Division of the Institute of Navigation (under publication).

Publication Dates

Publication in this collection
Jan-Apr 2011

History

Received
24 Feb 2011
Accepted
21 Mar 2011

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Antreasian, P.G., Rosborough, G.W., 1992, "Prediction of Radiant Energy Forces on the Topex/Poseidon Spacecraft", Journal of Spacecraft and Rockets, Vol. 29, No. 1, p. 81-90. doi: 10.2514/3.26317.
» https://doi.org/10.2514/3.26317

[2] Binning, P.W., 1996, "GPS, Dual Frequency, SA Free Satellite Navigation. Navigation Technology for the 3rd Millennium", Proceedings of the 52nd Annual Meeting of the Institute of Navigation, June 19-21, Cambridge, MA, USA, pp. 803-812.

[3] Chiaradia, A.P.M., Kuga, H.K. and Prado, A.F.B.A., 2000, "Investigation on Ionospheric Correction Models for GPS Signals", Proceedings of the 9^th Colóquio Brasileiro de Dinâmica Orbital, Advances in Space Dynamics, Prado, A.F.B.A., Editor, Águas de Lindoia, Brazil, pp. 214-219.

[4] CNES, 2007, Topex/Poseidon. The beginnings of satellite oceanography, Available at: http://www.cnes.fr/web/1461-topexposeidon.php Access on May 10, 2007.
» http://www.cnes.fr/web/1461-topexposeidon.php

[5] Givens, J.W., 1958, "Computation of Plain Unitary Rotations Transforming a General Matrix to Triangular Form", SIAM Journal on Applied Mathematics, Vol. 6, pp. 26-50.

[6] Kaula, W.M., 1966, "Theory of Satellite Geodesy: Applications of Satellites to Geodesy", Blaisdell Publ. Co., Waltham, MA, USA.

[7] Kuga, H.K., 2005, "Noções Práticas de Técnicas de Estimação", Class Notes of Optimization on Dynamical Systems II", INPE, São José dos Campos, Brazil.

[8] Kuga, H.K., 1989, "Determinação de órbitas de satélites artificiais terrestres através de técnicas de estimação combinadas a técnicas de suavização de estado". (INPE-4959-TDL/079). Ph.D. Thesis, National Institute for Space Research, São José dos Campos, Brazil, 249 p.

[9] Marshall, J.A., Antreasian, P.G., Rosborough, G.W. and Putney, B.H., 1991, "Modeling radiation forces acting on satellites for precision orbit determination", Advances in Astronautical Sciences, Astrodymanics Conference, AAS 91-357, Vol. 76, Part I, p. 72-96.

[10] Marshall, J.A., Luthcke, S.B., 1994, "Modelling radiation forces acting on TOPEX/Poseidon for precision orbit determination", Journal of Spacecraft and Rockets, Vol. 31, No. 1, p. 89-105.

[11] Montenbruck, O., Suarez, M., 1984, "A Modular Fortran Library for Sequential Least-Squares Estimation Using QR-Factorization", DLR, German Space Operations Center, Oberpfaffenhofen, Germany (DLR-GSOC IB 94-05).

[12] Pardal, P.C.P.M., 2007, "Determinação de Órbita via GPS Considerando Modelo de Pressão de Radiação Solar para o Satélite Topex/Poseidon", Masters Dissertation, National Institute for Space Research, São José dos Campos, Brazil.

[13] Prado, A.F.B.A., Kuga, H.K. (Eds), 2001, "Fundamentos de Tecnologia Espacial", National Institute for Space Research, São José dos Campos, Brazil, 220 p. ISBN: 85-17-00004-8.

[14] Silva, A.A., 2001, "Determinação de Órbitas com o GPS através de Mínimos Quadrados Recursivo com Rotações de Givens", Masters Dissertation, São Paulo State University, Guaratinguetá, Brazil.

[15] Soyka, M.T., Davis, M.A., 2001, "Estimation of Periodic Accelerations to Improve Orbit Ephemeris Accuracy", Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Advances in the Astonautical Sciences, Vol. 108, Part II, California, USA, pp. 1123-1140.

[16] Vilhena de Moraes, R., Raimundo, P.C.P. and Kuga, H.K., 2008, "Orbit Determination Using GPS Including Perturbations due to Geopotential Coefficients of Higher Degree and Order and Solar Radiation Pressure", Advances in the Astronautic Sciences, Galveston, Proceedings of the 18^th AAS/AIAA Space Flight Meeting, Vol. 130, San Diego: American Astronautical Society, p. 923-933.

[17] Pardal, P.C.P.M., Kuga, H.K. and Vilhena de Moraes, R., 2010, "Comparing the Extended and the Sigma Point Kalman Filters for Orbit Determination Modeling Using GPS Measurements". In: 23^rd International Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR. Proceedings of the 23^rd International Meeting of the Satellite Division of the Institute of Navigation (under publication).

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