Position Estimation Using Gravity, Sun, Planets, and Stars

Abstract

Before humanity can safely venture away from their terrestrial roots, robotic probes will be required to survey distant planets and moons. The current methodology for interfacing with rovers on the Moon and Mars is through teleoperated transmissions, whose reliability comes at the expense of inherent communication delays between the transmitter and the receiver. As distances between space assets increase, which implies more pronounced time delays, so too will the need for offloading requirements in a way that promotes navigational independence. This thesis presents a novel approach to autonomous vehicle localization using celestial observations (e.g., Sun, stars, and the visible planets) and a reference measurement of the unit gravity vector provided by a higher-fidelity planetary shape model than the traditional axial-symmetric ellipsoid, i.e., the exact direction provided by the geoid. Using the geoid, the reference ellipsoid description of gravity can be corrected by considering two angular deflections that describe the direction of the local vertical plumbline with respect to astronomical observations. In doing so, the mapping between local and body reference frames is improved and position errors are mitigated by two or three orders of magnitude. This work also includes a literature review on topics such as space vehicle localization, optimal attitude estimation, navigation filtering, and measurement data processing/fitting using two-dimensional orthogonal polynomials, as well as derivations for a multivariate nonlinear least-squares technique and inclinometer covariance matrix with extended Kalman filter. Finally, a full-system sensitivity analysis was conducted using two test data sets, namely, the Himalayan mountain range on Earth and the Olympus Mons volcano on Mars, whose markedly different topologies were used to characterize the algorithm's performance.