Improving the Coverage of Earth Targets by Maneuvering Satellite Constellations
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Satellite constellations around Earth can be used for observing and/or communicating with targets on the surface. This work addresses maneuvering existing satellite constellations in order to improve coverage of multiple targets over a timespan of 30 to 120 days. A direct relationship is established between a satellite's orbital geometry and the coverage provided by that satellite. This is accomplished by (1) identifying the view of the satellite orbit from an inertial sphere centered on the Earth, and (2) utilizing information from all the orbital views across the target's inertial latitude in order to arrive at lower and upper bounds on coverage. Altering a satellite orbit also alters the coverage that it provides. Gauss' variational equations are used to find maneuvering strategies that effect maximal changes in orbital geometry. These distinct maneuvering strategies are then compiled into a list that will be used in the subsequent optimization. The problem of reconfiguring existing satellite constellations in order to improve coverage is phrased as a multiobjective optimization problem. In it, each satellite in the satellite constellation can be assigned any one of the maneuvering strategies as well as an allotment of propellant that will be consumed during the maneuvering. These become the parameters in the optimization problem. An algorithm that is well suited for solving this optimization problem is a multiobjective evolutionary/genetic algorithm. Such an algorithm is capable of handling, without further transformations, the three difficulties with the stated problem: (1) continuous and discrete optimization parameters (e.g. propellant allotment, a distinct maneuvering strategy, etc.), (2) nonlinear optimization objectives (e.g. total coverage time, number of coverage windows, etc.), and (3) multiple optimization objectives (e.g. total coverage time over Target 1, total coverage over Target 2, etc.). This algorithm is implemented by adopting features from other similar algorithms. Finally, a set of examples is investigated in order to study the effectiveness of this approach.