Small Body SLAM With Silhouette-Based Gaussian Process Batch Filtering

Recent small body missions have successfully utilized Stereo-Photoclinometry (SPC) to model the shape of small bodies for landmark-relative navigation. To simplify estimation for onboard, autonomous implementation, the small body's shape is modeled using a Gaussian Process (GP), where multiple basis nodes and basis radii are used to predict the entire shape. The GP methodology was previously implemented into an Iterative Extended Kalman Filter (IEKF) for Simultaneous Localization and Mapping (SLAM) of the small body Eros. The IEKF was proven to be successful, yet sensitive to initial state estimates and errors. Thus a maximum-likelihood, GP batch least-squares algorithm is developed where conservative initial conditions are utilized. Simulated images of Eros are processed to extract the visible horizon and associated to a truth and estimated GP shape model. Through multiple batch iterations with a declining measurement under-weighting scheme, the GP batch algorithm estimates the body's shape to within meters of error, while also estimating the body's orientation, the body's spin rate, and the satellite's position and velocity. The GP batch algorithm is tested on a circular orbit and a hyperbolic approach trajectory for various small bodies. The GP batch implementation itself is a powerful tool for small body mapping and navigation, but subsequent work will focus on using the final state estimate and covariance from the batch filter as initial conditions for perturbing the truth states within a Monte Carlo study of the IEKF.