The linearized dynamic equations used for on-board orbit determination of Sun-synchronous satellite are derived. Sun-synchronous orbits are orbits with the secular rate of the right ascension of the ascending node equal to the right ascension rate of the mean sun. Therefore the orbit is no more a closed circle but a tight helix about the Earth. In the paper, instead of treating the orbit as a closed circle, the actual helix orbit is taken as nominal trajectory. The details of the linearized equations of motion for the satellite in the Sun-synchronous orbit are derived. The linearized equations are obtained by perturbing the Keplerian motion with the J2 correction and the effect of sun's attraction being neglected. Combined with the GPS navigation equations, the Kalman filter formulation is given. The particular application considered is the circular Sun-synchronous orbit with the altitude of View the MathML source and inclination of 98.6°. The numerical example simulated by MATLAB® shows that only the pseudo-range data used in the algorithm still gives acceptable results. Based on the simulation results, we can use the on-board GPS receivers’ signal only as an alternative to determine the orbit of Sun-Synchronous satellite and therefore circumvents the need for extensive ground support.