Ph.D Thesis

Ph.D StudentShtark Tomer
SubjectRegional Positioning Using a Low Earth Orbit Satellite
DepartmentDepartment of Aerospace Engineering
Supervisor PROF. Pinchas Gurfil
Full Thesis textFull thesis text - English Version


Navigation satellite constellations orbit the Earth in medium and geosynchronous orbits. These high altitudes raise the operational and launching costs, but provide wide coverage, which may be redundant if only regional coverage is needed. Low Earth orbit satellites, on the other hand, suffer from reduced coverage capabilities, among other issues.

This research develops methods for designing low Earth orbit satellite constellations, which provide discontinuous coverage, aimed at positioning determination at a predefined geodetic region. This problem is solved by two strategies: spreading the satellites in a time-varying latitude strip, or spreading them over few orbital planes. The former strategy produces a relatively high revisit frequency, but requires a relatively high number of orbital planes, and produces relatively low coverage durations. The latter strategy produces long coverage durations, requires significantly fewer orbital planes, but produces a lower revisit frequency. In all constellations developed in this research, the satellites reside in circular orbits, and share the same mean semi-major axis and mean inclination.

The spreading strategy is synthesized using two methods: a numerical method, and a simplified method. The numerical method optimizes the constellations based on their geometries in a single epoch, whereas the simplified method derives its basic geometry from the numerical method results. While the numerical method produces more planes and requires considerably more computational effort than the simplified method, it usually produces better performance. The other strategy is implemented using a constellation, whose satellites inhabit 3 orbital planes, with a constant differential node. The satellite relative geometry is optimized so that the positioning error over time in the region of interest is minimized. Subsequently, the produced design is modeled using a mathematical function and a few design guidelines. Consequently, the design benefits from having a well-founded numerical background and a simplified mathematical expression.

The final chapter of this research thoroughly investigates the performance of one constellation. The unknown position and velocity of a moving aerial target is explicitly solved, and refined using an Extended Kalman Filter (EKF). Later, we analyze the navigation errors when coverage is available and when it is absent, and when the EKF’s dynamical model matches the real receiver dynamics, and when they mismatch.