This paper presents a new algorithm for autonomous multitarget tracking of resident space objects using optical angles-only measurements from a spaceborne observer. To enable autonomous angles-only navigation of spacecraft swarms, an observer must be able to identify and track multiple known or unknown target space objects in view, without reliance on a-priori relative orbit knowledge. Extremely high assignment precision is necessary with low measurement frequencies and limited computational resources. The new "Spacecraft Angles-only MUltitarget tracking System" (SAMUS) algorithm has been developed to meet these objectives and constraints. It combines domain-specific modeling of target kinematics with multi-hypothesis techniques to autonomously track multiple unknown targets using only sequential camera images. A measurement transform ensures that target motion in the observer reference frame follows consistent parametric models; curve fitting is used to predict track behavior; and kinematically-derived track gating and scoring criteria are applied to improve the efficiency and accuracy of the multi-hypothesis approach. Monte-Carlo testing with high-fidelity simulations demonstrates close to 100% measurement assignment precision and strong recall across a range of multi-spacecraft formations, in both near-circular and eccentric orbits. Tracking is maintained in the presence of eclipse periods, significant measurement noise, and partially known swarm maneuvers. A comparison to other tracking algorithms reveals strong advantages in precision, robustness and computation time, crucial for spaceborne angles-only navigation.