Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 49781, 8 pages
Research Article

Simple Orbit Determination Using GPS Based on a Least-Squares Algorithm Employing Sequential Givens Rotations

Rodolpho Vilhena de Moraes,1 Aurea Aparecida da Silva,2 and Helio Koiti Kuga2

1Departamento de Matemática, UNESP Campus de Guaratinguetá, Guaratinguetá 12516-410, SP, Brazil
2Divisão de Mecânica Espacial e Controle, Instituto Nacional de Atividades Espaciais, São José dos Campos 12227-010, SP, Brazil

Received 21 September 2006; Revised 4 June 2007; Accepted 13 July 2007

Academic Editor: José Manoel Balthazar

Copyright © 2007 Rodolpho Vilhena de Moraes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A low-cost computer procedure to determine the orbit of an artificial satellite by using short arc data from an onboard GPS receiver is proposed. Pseudoranges are used as measurements to estimate the orbit via recursive least squares method. The algorithm applies orthogonal Givens rotations for solving recursive and sequential orbit determination problems. To assess the procedure, it was applied to the TOPEX/POSEIDON satellite for data batches of one orbital period (approximately two hours), and force modelling, due to the full JGM-2 gravity field model, was considered. When compared with the reference Precision Orbit Ephemeris (POE) of JPL/NASA, the results have indicated that precision better than 9 m is easily obtained, even when short batches of data are used.