Lunar Surface Navigation Using Gravity and Star Tracker Measurements

Abstract

This thesis develops and analyzes a method that uses measured gravity and starlight vectors to provide position and attitude estimates, given a predefined high-fidelity lunar gravity field. The gravity field uses provided values for the surface gravity magnitude and the East-West (EW) and North-South (NS) deflections of the gravity vector across the lunar surface. These gravity measurements are location-specific and are shown to be influenced by nearby craters and other topographic features. Gravity is more concentrated in these regions, causing the gravity vector to deflect in their direction. The gravity field used in this study (Lunar Gravity Model 2011 (LGM2011)) was developed specifically for surface use, resulting in more accurate gravity measurements compared to other models calculated using spherical harmonic expansions. Future lunar missions prompt the need for new surface navigation techniques. Current position and orientation (POSE) methods employ star trackers (ST) and accelerometers but do not incorporate the use of an external gravity field. The Multiplicative Extended Kalman Filter (MEKF) developed in this study uses these sensors and their data to define a state consisting of the attitude error vector, a, between the estimated quaternion—found using Shuster's Quaternion Estimator (QUEST) algorithm—and the reference quaternion, the longitude (λ) and latitude (ϕ) positions, and the dynamic accelerometer bias. The MEKF assumes constant state propagation between time steps and a covariance update influenced solely by the Moon's rotation. It also assumes that the reference gravity field is perfectly accurate. However, this assumption introduces inaccuracies in the position estimates due to discrepancies between the true measured gravity and the gravity predicted by the model. These biased position estimates, along with a known accurate reference position, are then used to solve for the correlated gravity bias in the lunar gravity field at various waypoints during a surface mission. As a test case, the reference position is determined using two-way ranging measurements between the ground system and the Lunar Pathfinder satellite. These measurements are processed through a combined weighted batch-to-EKF filter to produce the reference position. A least-squares cost function is then formulated using the MEKF outputs and reference positions to estimate biases in the gravity field. The gravity bias algorithms presented are demonstrated to enable successful surface navigation for a roving mission on the lunar surface.