Multi-Observations Initial Orbit Determination based on Angle-Only Measurements

Document Type : Research Article


1 Associate Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

2 Assistant Professor, Department of Civil Engineering, Imam Hossein University (IHU) , Tehran, Iran

3 Assistant Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran


A new approach with the ability to use the multiple observations based on the least square approach has been proposed for initial orbit determination. This approach considers the Earth’s Oblateness by using the developed Lagrange coefficients. The efficiency of the proposed method has been tested in two scenarios. The first scenario is to use the simulated and the second one is to utilize the real angle-only observations for the GRACE-like and GPS-like satellites. Under the first scenario, the ground-based observations are produced using the reduced-dynamic orbit generated by GFZ. Then, various error levels were added to the produced azimuth and elevation observations. The results show that considering the Earth’s oblateness could improve the accuracy of the initial orbit determination by six times for a GRACE-like satellite, and by 60 times for a GPS-like satellite. Afterward, under the second scenario, the real observations of the SLR station were used. In view of increasing in the number of observation tests, by increasing the numbers of the observations from 3 to 15, the accuracy of initial orbit determination was improved from 1496 to 8 m using the SLR data for the GRACE-A satellite.


Main Subjects

Bate, R. R., Mueller, D. D., Saylor, W. W., and White, J. E., 2013, Fundamentals of astrodynamics: (dover books on physics): Dover publications.
Celletti, A. and Pinzari, G., 2005, Four classical methods for determining planetary elliptic elements: a comparison. Celestial Mechanics and Dynamical Astronomy, 93(1-4), 1-52.
Celletti, A. and Pinzari, G., 2006, Dependence on the observational time intervals and domain of convergence of orbital determination methods Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications, pp. 327-344, Springer.
Cerri, L., Berthias, J., Bertiger, W., Haines, B., Lemoine, F., Mercier, F. and Ziebart, M., 2010, Precision orbit determination standards for the Jason series of altimeter missions. Marine Geodesy, 33(S1), 379-418.
Curtis, H. D., 2005, Orbital Mechanics for Engineering Students (Third edition. ed.).
Doscher, D. P., 2018, Orbit Determination for Space-Based Near Co-planar Observations of Space Debris Using Gooding's Method and Extended Kalman Filtering.
Escobal, P. R., 1965, Methods of Orbit Determination. New York: Wiley, 1965, 1.
Farnocchia, D., Tommei, G., Milani, A. and Rossi, A., 2010, Innovative methods of correlation and orbit determination for space debris. Celestial Mechanics and Dynamical Astronomy, 1071-2, 169-185.
Gauss, C. F., 2004, Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections: Courier Dover Publications.
Gooding, R., 1996, A new procedure for the solution of the classical problem of minimal orbit determination from three lines of sight. Celestial Mechanics and Dynamical Astronomy, 6(64), 387-423.
Gronchi, G. F., 2009, Multiple solutions in preliminary orbit determination from three observations. Celestial Mechanics and Dynamical Astronomy, 103(4), 301-326.
Hu, J., Li, B. and Li, J., 2019, Initial orbit determination utilizing solution group optimization. IEEE Transactions on Aerospace and Electronic Systems.
Jäggi, A., Hugentobler, U., Bock, H. and Beutler, G., 2007, Precise orbit determination for GRACE using undifferenced or doubly differenced GPS data. Advances in Space Research, 39(10), 1612-1619.
Karimi, R. R. and Mortari, D., 2011, Initial orbit determination using multiple observations. Celestial Mechanics and Dynamical Astronomy, 109(2), 167-180.
Karimi, R. R. and Mortari, D., 2013, A performance based comparison of angle-only initial orbit ‎determination methods. Adv. Astronaut. Sci., AAS/AIAA, Hilton Head Island, South Carolina, 150, 1793-‎‎1809.‎
Kristensen, L. K., 2007, N-observations and radar orbits. Celestial Mechanics and Dynamical Astronomy, 98(3), 203-215.
Kristensen, L. K., 2009, Single lunation N-observation orbits. Celestial Mechanics and Dynamical Astronomy, 105(4), 275-287.
Laplace, P. S., 1780, Memoires de l' Académie royale des sciences de Paris. Collected Works, 10.
Lin, L. and Xin, W., 2003, A method of orbit computation taking into account the earth's oblateness. Chinese Astronomy and Astrophysics, 27(3), 335-339. doi:
McCarthy, D. D. and Petit, G., 2003, IERS conventions. Paper presented at the IAU Joint Discussion.
McCutcheon, S. and McCutcheon, B., 2005, Space and astronomy: Infobase Publishing.
Merton, G., 1925, A modification of Gauss's method for the determination of orbits. Monthly Notices of the Royal Astronomical Society, 85, 693.
Milani, A. and Gronchi, G., 2010, Theory of orbit determination: Cambridge University Press.
Milani, A., Gronchi, G. F., Farnocchia, D., Knežević, Z., Jedicke, R., Denneau, L., and Pierfederici, F., 2008, Topocentric orbit determination: algorithms for the next generation surveys. Icarus, 195(1), 474-492.
Montenbruck, O. and Gill, E., 2000, Satellite orbits: Springer.
Sharifi, M. A. and Seif, M. R., 2011, Dynamic orbit propagation in a gravitational field of an inhomogeneous attractive body using the Lagrange coefficients. Advances in Space Research, 48(5), 904-913, doi:
Taff, L. G., 1984, On initial orbit determination. The Astronomical Journal, 89, 1426-1428.
Tommei, G., Milani, A. and Rossi, A., 2007, Orbit determination of space debris: admissible regions. Celestial Mechanics and Dynamical Astronomy, 97(4), 289-304.
Vallado, D. A., 2001, Fundamentals of Astrodynamics and Applications (Vol. 12): Springer.
Van Helleputte, T. and Visser, P., 2008, GPS based orbit determination using accelerometer data. Aerospace Science and Technology, 12(6), 478-484.