| Résumé : |
(Auteur) Spacecraft formation flying is currently considered as a key technology for advanced space missions. Compared to large individual spacecraft, the distribution of Sensor systems amongst multiple platforms offers improved flexibility and redundancy, shorter times to mission and the prospect of being more cost effective. Besides these advantages, satellite formations in low Earth orbit provide advanced science opportunities that cannot, or not easily, be realized with single spacecraft. One of the fundamental issues of spacecraft formation flying is the determination of the relative state (position and velocity) between the satellite vehicles within the formation. Knowledge of these relative states in (near) real-time is important for operational aspects. In addition, some of the scientific applications, such as high resolution interferometry, require an accurate post-facto knowledge of these States. The goal of this dissertation is therefore to develop, implement and test a method for high precise post-facto relative positioning of formation flying spacecraft, using GPS observation data. The need for such a methodology comes from scientific satellite formation flying missions that are currently being planned. A good example here is the Synthetic Aperture Radar (SAR) interferometry formation consisting of the TerraSAR-X and TanDEM-X satellites. The primary mission objective here requires the relative position to be known within a 2 mm precision (1-dimensional).
GPS receivers are often considered as the primary instruments for precise relative navigation in future satellite formation flying missions. As is commonly known, precise relative positioning between GPS receivers in geodetic networks is exercised on a routine basis. Furthermore, GPS receivers are already frequently used onboard satellites to perform all kinds of navigational tasks, are suitable for real-time applications and provide measurements with a 3-dimensional nature.
Previous studies carried out in this research area focussed on the real-time or operational aspects, and all used GPS data obtained from software or hardware-in-the-loop simulations. This dissertation clearly distinguishes itself due to the fact that the developed methodology has been tested using real-world GPS data from the GRACE mission, which in addition also provides a precise way to validate the obtained results by means of the GRACE K/Ka-Band Ranging System (KBR) observations.
One of the key aspects of any GPS positioning application is the quality of the observation data used. To this extent an in-flight performance analysis of the used GRACE (and CHAMP) GPS data bas been carried out. The results show that the GRACE GPS pseudorange observations, on the individual frequencies, are subject to systematic errors in the order of 10-15 cm. Furthermore, an assessment of the noise of both the GPS pseudorange and carrier phase data demonstrates that the noise of the GRACE B observation data is significantly lower.
When using GPS for precise relative spacecraft positioning, the trajectory or orbit of one of the spacecraft, serving as the reference, has to be known to the best possible extent. In order to facilitate this, a total of three precise orbit determination strategies, using undifferenced ionosphere free GPS pseudorange and carrier phase observations, have been implemented and tested. They comprise a kinematic and reduced dynamic batch LSQ estimation method, as well as an extended Kalman filter/smoother (EKF), that also form the conceptual basis for the relative spacecraft positioning strategies. Each of the precise orbit determination concepts has been tested using GPS data from the CHAMP and GRACE missions. The reduced dynamic batch LSQ orbits were validated with Satellite Laser Ranging data, where the residuals showed an RMS of 3-4 cm.
Out of a total of four possible processing strategies that have been identified for relative spacecraft positioning, only an extended Kalman filter/smoother has proven to work satisfactorily when tested on the real-world GRACE GPS data. The EKF processes single difference GPS pseudorange and carrier phase observations and uses (pseudo) relative spacecraft dynamics to propagate the relative satellite state over the observation epochs. Despite its single difference parametrization the EKF can still resolve and incorporate the integer double difference carrier phase ambiguities, which is commonly regarded as, and has proven to be in this dissertation, the key to precise GPS based relative positioning. Estimation of the integer ambiguities is accomplished by the well known Least Squares Ambiguity Decorrelation Adjustment (LAMBDA) method. Due to the presence of systematic errors in the GRACE GPS data, a relatively conservative validation of the estimated integer ambiguity parameters was found to be required prior to their incorporation in the filter. When validating the daily ambiguity fixed GRACE relative position solutions from the EKF with the KBR observations, it has been shown that an actual overall relative position precision of 0.9 mm (1-dimensional) over a 101 day data arc is achieved. This dissertation is the first that proves that such precision can be truly obtained for real-world relative spacecraft positioning applications. |
Precise relative positioning of formation flying spacecraft using GPS (2006)
