Onboard Orbit Determination Using GPS Measurements for Low Earth Orbit Satellites by Ning Zhou B.S., Nanjing University, People’s Republic of China, 1997 M.S., Nanjing University, People’s Republic of China, 2000 A THESIS submitted to the Faculty of the Built Environment and Engineering in partial fulfilment of the requirement for the degree of Doctor of Philosophy Cooperative Research Centre for Satellite Systems Queensland University of Technology GP.O. Box 2434, QLD 4001, Australia December 2004 Abstract Recent advances in spaceborne GPS technology have shown significant advantages in many aspects over conventional technologies. For instance, spaceborne GPS can realize autonomous orbit determination with significant savings in spacecraft life cycle, in power, and in mass. At present, the onboard orbit determination in real time or near-real time can typically achieve 3D orbital accuracy of metres to tens metres with Kalman filtering process, but 21st century space engineering requires onboard orbit accuracy of better than 5 metres, and even sub-metre for some space applications. The research focuses on the development of GPS-based autonomous orbit determination techniques for spacecraft. Contributions are made to the field of GPS-based orbit determination in the following five areas: Techniques to simplify the orbital dynamical models for onboard processing have been developed in order to reduce the computional burden while retaining full model accuracy. The Earth gravity acceleration approximation method was established to replace the traditional recursive acceleration computations. Results have demonstrated that with the computation burden for a 5×5 spherical harmonic gravity model, we achieve the accuracy of a 70 × 70 model. Efforts were made for the simplification of solar & lunar ephemerides, atmosphere density model and orbit integration. All these techniques together enable a more accurate orbit integrator to operate onboard. Efficient algorithms for onboard GPS measurement outlier detection and measurement improvement have been developed. In addition, a closed-form single point position method was implemented to provide an initial orbit solution without any a priori information. The third important contribution was made to the development of sliding-window short-arc orbit filtering techniques for onboard processing. With respect to the existing Kalman recursive filtering, the short-arc method is more stable because i more measurements are used. On the other hand, the short-arc method requires less accurate orbit dynamical model information compared to the long-arc method, thus it is suitable for onboard processing. Our results have demonstrated that by using the 1 ~ 2 revolutions of LEO code GPS data we can achieve an orbit accuracy of 1 ~ 2 metres. Sliding-window techniques provide sub-metre level orbit determination solutions with 5~20 minutes delay. A software platform for the GPS orbit determination studies has been established. Methods of orbit determination in near-real time have been developed and tested. The software system includes orbit dynamical modelling, GPS data processing, orbit filtering and result analysis modules, providing an effective technical basis for further studies. Furthermore a ground-based near-real time orbit determination system has been established for FedSat, Australia’s first satellite in 30 years. The system generates 10-metre level orbit solution with half-day latency on an operational basis. This system has supported the scientific missions of FedSat such as Ka-band tracking and GPS atmosphere studies within the Cooperative Research Centre for Satellite System (CRCSS) community. Though it is different from the onboard orbit determination, it provides important test-bed for the techniques described in previous section. This thesis focuses on the onboard orbit determination techniques that were discussed in Chapter 2 through Chapter 6. The proposed onboard orbit determination algorithms were successfully validated using real onboard GPS data collected from Topex/Poseidon, CHAMP and SAC-C satellites. ii Table of Contents Abstract................................................................................................................................................. i List of Figures..................................................................................................................................... ix List of Tables .................................................................................................................................... xiii List of Symbols .................................................................................................................................. xv List of Acronyms .............................................................................................................................. xix Statement of Authorship................................................................................................................. xxii Acknowledgements......................................................................................................................... xxiii 1. Introduction..................................................................................................................................... 1 1.1 GPS based Orbit Determination for LEO Spacecrafts................................................................ 1 1.1.1 Main Attractions of Spaceborne GPS................................................................................. 1 1.1.2 Ground-based Precise Orbit Determination ....................................................................... 3 1.1.3 Onboard Orbit Determination............................................................................................. 6 1.2 The Objectives and Main Contributions of the Study ................................................................. 7 1.2.1 Major Research Objectives ................................................................................................ 7 1.2.2 Benefits of the Research..................................................................................................... 9 1.2.3 Scope of the Research ...................................................................................................... 10 1.3 Organization of the Thesis ........................................................................................................ 10 2. A Review of Onboard Orbit Determination Using GPS ............................................................ 13 2.1 Overview of GPS-based LEO mission and Onboard Orbit Determination Systems………….13 2.1.1 Mission Overview ............................................................................................................ 13 2.1.2 Onboard OD Software System ......................................................................................... 14 2.1.3 LEO Missions Used in the Simulation Experiments ........................................................ 17 2.2 Onboard GPS Navigation Solution........................................................................................... 19 2.3 Extended Kalman Filter............................................................................................................ 21 2.3.1 The Observation Models .................................................................................................. 22 2.3.2 The Extended Kalman Filter ............................................................................................ 23 2.3.3 Process Noise and Measurement Noise............................................................................ 24 2.3.4 Discussion ........................................................................................................................ 26 2.4 Phase-connected Kinematic Filter ............................................................................................ 26 2.4.1 Phase-connected Point Positioning Filter......................................................................... 26 2.4.2 Filter Models and Solution............................................................................................... 27 2.4.3 Discussion ........................................................................................................................ 28 2.5 Onboard Simplified General Perturbations – SGP4 Filter........................................................ 29 2.5.1 SGP4 Model Overview .................................................................................................... 29 iii 2.5.2 Osculating to Mean Elements Conversion........................................................................30 2.5.3 SGP4 Elements Estimation from GPS Measurements Using Kalman Filter ....................30 2.5.4 Discussion.........................................................................................................................31 2.6 Proposed Onboard Orbit Determination Methods.....................................................................32 2.6.1 Motivations.......................................................................................................................32 2.6.2 Summary of the Proposed Methods..................................................................................33 3 Simplifications of Dynamic Models for Low Earth Orbiters......................................................35 3.1 Orbit Dynamical Models for LEO.............................................................................................35