Available online at www.sciencedirect.com Acta Astronautica 53 (2003) 123–133 www.elsevier.com/locate/actaastro Single frequency GPS measurements in real-time articial satellite orbit determination  A.P.M. Chiaradia ∗; 1 , H.K. Kuga, A.F.B.A. Prado INPE-Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas, 1758-Jardim da Granja, S˜ ao Jos e dos Campos, SP CEP 12 227-010, Brazil Received 26 April 2000; received in revised form 21 May 2002 Abstract A simplied and compact algorithm with low computational cost providing an accuracy around tens of meters for articial satellite orbit determination in real-time and on-board is developed in this work. The state estimation method is the extended Kalman lter. The Cowell’s method is used to propagate the state vector, through a simple Runge–Kutta numerical integrator of fourth order with xed step size. The modeled forces are due to the geopotential up to 50th order and degree of JGM-2 model. To time-update the state error covariance matrix, it is considered a simplied force model. In other words, in computing the state transition matrix, the eect of J2 (Earth attening) is analytically considered, which unloads dramatically the processing time. In the measurement model, the single frequency GPS pseudorange is used, considering the eects of the ionospheric delay, clock osets of the GPS and user satellites, and relativistic eects. To validate this model, real live data are used from Topex/Poseidon satellite and the results are compared with the Topex/Poseidon Precision Orbit Ephemeris (POE) generated by NASA/JPL, for several test cases. It is concluded that this compact algorithm enables accuracies of tens of meters with such simplied force model, analytical approach for computing the transition matrix, and a cheap GPS receiver providing single frequency pseudorange measurements. c  2002 Published by Elsevier Science Ltd. 1. Introduction The orbit determination process consists of ob- taining values of the parameters, which completely  Based on paper IAF-99-A.7.03 presented at the 50th Interna- tional Astronautical Congress, Amsterdam, Holland, 1–5 October 1999. ∗ Corresponding author. E-mail addresses: chiara@ief.ita.br (A.P.M. Chiaradia), hkk@dem.inpe.br (H.K. Kuga), prado@dem.inpe.br (A.F.B.A. Prado). 1 Departamento de Matem atica,ITA/CTA, Praca Marechal Ed- uardoGomes,50-S˜ aoJos edosCampos,SP,CEP12228-900,Brazil. specify the motion of an orbiting object, like a satel- lite, based on a set of observations of the object. It involves system models, measurement models that de- pend on the measurement system, and estimation tech- niques. One of the evolutions of this process has been themeasurementsystem.Inprinciple,theobservations may be obtained from ground station networks using laser, radar, Doppler, or by space navigation systems as the global positioning system (GPS). The choice of the measurement system depends on a compromise between the goals of the mission and the tools avail- able. In the case of GPS, the advantages are global coverage, high precision, low cost, and autonomous 0094-5765/03/$-see front matter c  2002 Published by Elsevier Science Ltd. PII:S0094-5765(02)00198-4