Autonomous rendezvous and proximity operations are becoming increasingly important in modern space missions, such as formation flying, satellite servicing and active debris removal. These missions often deal with uncooperative targets and must estimate relative motion using only measurements collected by the observer. To lower mission costs and simplify navigation hardware, angles-only (AO) navigation is a promising solution since it relies on cheap, compact, power-efficient and widely available vision-based sensors. However, AO estimation is particularly challenging due to weak observability of the inter-satellite range, requiring more advanced estimation techniques. Batch methods typically yield the most accurate and robust estimates, as they exploit long measurement histories for relative orbit determination (ROD). Traditionally confined to the ground segment due to their high computational cost, recent studies propose the development of lightweight space-borne implementations to complement sequential methods. These filters would use analytical propagation to reduce computation, operate with limited measurements to minimise memory demands, and run as low-priority tasks. Their role is to back up sequential filters in case of divergence and to periodically reinitialise them, preventing stagnation. This paper proposes a novel batch filter based on the unscented transform (UT) for performing ROD within the AO framework. The batch unscented filter (BUF) is an extensively modified version of the non-recursive unscented filter, originally developed to estimate absolute orbits from ground-based range, azimuth, and elevation measurements. Key improvements include an augmented state incorporating both the relative orbital elements and the observer semi-major axis, Monte Carlo-based tuning of the UT, employment of physically meaningful convergence test and a covariance computation procedure inspired by the unscented Kalman filter. The BUF is evaluated in low Earth orbit scenarios inspired by the AVANTI and ARGON experiments, including cases with significant differential drag. Results show that the BUF is capable of estimating the augmented state with accuracy and robustness to noise. The filter remains effective even when using a minimal number of measurements (four) collected over a single orbital period. When combined with analytical propagation, this demonstrates potential for onboard implementation with limited memory and computational resources.