Future space missions require that spacecraft have onboard capability to autonomously navigate non-cooperative environments for rendezvous and proximity operations (RPO). Current relative navigation filters can have difficulty in these situations when optical sensors are used, diverging due to complications with data association, high measurement uncertainty, and clutter, particularly when detailed a priori maps of the target object or spacecraft do not exist. This thesis demonstrates the feasibility of random finite set (RFS) filters for spacecraft relative navigation and pose estimation. A generalized RPO scenario is formulated as a simultaneous localization and mapping (SLAM) problem, in which an observer spacecraft seeks to simultaneously estimate the location of features on a target object or spacecraft as well as its relative position, velocity and attitude. An RFS-based filter called the Gaussian Mixture Probability Hypothesis Density (GMPHD) is used. Simulated flash LIDAR measurements are tested, using a GMPHD filter embedded in a particle filter to obtain a feature map of a target and a relative pose estimate between the target and observer over time. Results show that an RFS-based filter such as the one used can successfully perform SLAM in a spacecraft relative navigation scenario with no a priori map of the target, and that the formulation behind RFS-based filtering is potentially well suited to spacecraft relative navigation.