A Sensitivity Analysis of Satellite Navigation Using Landmarks

This work evaluates the sensitivity of satellite orbit determination using known landmarks to orbital altitude and imaging geometry. Known landmark-based orbit determination is an autonomous navigation technique that uses a satellite's optical observatory to image known landmarks. Measurements for orbit determination are generated by using image processing algorithms to find the location of known landmarks in each image. Previous work stretching back to the Apollo Program has shown landmark navigation to be feasible and evaluated its sensitivity to lighting, inclination, pointing accuracy, image resolution, and number of images collected. Evaluating sensitivity to altitude and imaging geometry is useful for selecting an orbit for the satellite and for tasking the satellite in order to maximize the information gained from each collected image. First, a kinematic solution is studied to understand sensitivity when only a minimum amount of data are available, for example in an initial orbit determination. Separate solutions are found for small and large Field of View (FoV) observatories. For the small FoV case results show images near nadir are ideal. For the large FoV case results show that geometrical diversity is important when data are limited. Specifically there is a trade-off between minimizing the ground resolved distance and maximizing the angle between images from the satellite's perspective. Second, a batch weighted least squares covariance analysis is performed over a day with hundreds of measurements. Results show that when data are abundant imaging landmarks closer to nadir and from lower altitude produces more accurate orbit solutions for a given observatory. These conditions minimize the ground resolved distance and provide the most information about the in-track position of the satellite, typically the most uncertain coordinate. This work is a step towards fully autonomous satellite navigation and provides useful information for those designing image processing algorithms as well as satellite missions.