Onboard orbit determination using GPS observations based on the unscented Kalman filter

Abstract

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1 σ) and 0.5 m/s (1 σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites. The comparison of the orbit determination results using EKF and UKF shows that orbit determination using the UKF yields better results than that using the EKF. In addition, the estimation of the accuracy using the C/A code pseudorange is better than that using the navigation solutions. The absolute position and velocity accuracies of the UKF using GPS C/A code pseudorange were 12.098 m and 0.0159 m/s in the case of the CHAMP satellite, and 8.172 m and 0.0085 m/s in the case of the KOMPSAT-2 satellite. Moreover, the abnormal excursions of navigation solutions can be eliminated. These results verify that onboard orbit determination using GPS C/A code pseudorange, which is based on the UKF can provide more stable and accurate orbit information in the spaceborne GPS receiver.