Enabling Onboard Analytical Batch Filtering for Angles-Only Navigation to Non-Cooperative Space Targets

Angles-only relative navigation enables autonomous operations with non-cooperative targets such as defunct satellites and orbital debris, which lack the means of communicating with other satellites or ground stations. In fact, this navigation paradigm relies on gathering information about the target only by means of passive cameras mounted on the chaser satellite. The camera provides a pair of bearing angles which are used by the navigation filter to estimate the relative orbit. As of today, sequential filters are typically employed for on-board applications due to their computational efficiency, whereas batch filters are mostly confined to ground-based operations, where their higher computational cost poses no limitation. In this work we revisit the semi-analytic batch least-squares (LSQ) filtering framework with the aim of bringing its on-board implementation closer to practical feasibility. The proposed LSQ filter preserves the analytical propagation required for real-time use while improving accuracy and observability through three key upgrades: (i) a closed-form propagation model including first-order J2, J4, J6 and second-order Keplerian and J2 effects; (ii) an exact measurement model with improved mean-to-osculating transformation; (iii) an efficient circular-buffer configuration. The proposed filter is tested in a high-fidelity 750 km sun-synchronous orbit simulation with realistic perturbations and is shown to achieve accurate relative state estimation without manoeuvre-induced observability.