Sensor fusion algorithms are proposed that enable proximity navigation and mapping of an unknown space object, such as an asteroid. The sensors envisioned are a range sensor (Flash LIDAR), and a synchronized and co-registered HD video camera, and an IMU. The transition from intermediate to close proximity is considered wherein the observability early-on allows only the 3DOF range vector to be determined, and in close proximity where the full 6DOF relative pose is observable and the object geometry can be recursively learned/estimated. Our algorithms are novel because of (i) unique utilization of sensor field overlap-induced information redundancy to eliminate poor features and retain the most consistent features on the object based on statistical hypothesis-testing and (ii) utilization of a recently discovered way to rigorously linearize the least square fusion of two overlapping point clouds, without approximation. End-to-end experiments in our laboratory http://lasr.tamu.edu/ are proposed to accelerate maturation and evaluation of the technology.