Estimating a target's 6-DoF motion in underwater proximity operations is difficult because the chaser lacks target-side proprioception and the available relative observations are sparse, noisy, and often partial (e.g., Ultra-Short Baseline (USBL) positions). Without a motion prior, factor-graph maximum a posteriori estimation is underconstrained: consecutive target states are weakly linked and orientation can drift. We propose a generalized constant-twist motion prior defined on the tangent space of Lie groups that enforces temporally consistent trajectories across all degrees of freedom; in SE(3) it couples translation and rotation in the body frame. We present a ternary factor and derive its closed-form Jacobians based on standard Lie group operations, enabling drop-in use for trajectories on arbitrary Lie groups. We evaluate two deployment modes: (A) an SE(3)-only representation that regularizes orientation even when only position is measured, and (B) a mode with boundary factors that switches the target representation between SE(3) and 3D position while applying the same generalized constant-twist prior across representation changes. Validation on a real-world dynamic docking scenario dataset shows consistent ego-target trajectory estimation through USBL-only and optical relative measurement segments with an improved relative tracking accuracy compared to the noisy measurements to the target. Because the construction relies on standard Lie group primitives, it is portable across state manifolds and sensing modalities.

A Markov decision process-based state switching is devised, implemented, and analyzed for proximity operations of various autonomous vehicles. The framework contains a pose estimator along with a multi-state guidance algorithm. The unified pose estimator leverages the extended Kalman filter for the fusion of measurements from rate gyroscopes, monocular vision, and ultra-wideband radar sensors. It is also equipped with Mahalonobis distance-based outlier rejection and under-weighting of measurements for robust performance. The use of probabilistic Markov models to transition between various guidance modes is proposed to enable robust and efficient proximity operations. Finally, the framework is validated through an experimental analysis of the docking of two small satellites and the precision landing of an aerial vehicle.

This work presents an Online Supervised Training (OST) method to enable robust vision-based navigation about a non-cooperative spacecraft. Spaceborne Neural Networks (NN) are susceptible to domain gap as they are primarily trained with synthetic images due to the inaccessibility of space. OST aims to close this gap by training a pose estimation NN online using incoming flight images during Rendezvous and Proximity Operations (RPO). The pseudo-labels are provided by adaptive unscented Kalman filter where the NN is used in the loop as a measurement module. Specifically, the filter tracks the target's relative orbital and attitude motion, and its accuracy is ensured by robust on-ground training of the NN using only synthetic data. The experiments on real hardware-in-the-loop trajectory images show that OST can improve the NN performance on the target image domain given that OST is performed on images of the target viewed from a diverse set of directions during RPO.