Optimal Satellite Formation Determination for Distributed Target State Estimation

This research addresses optimal orbit determination for a cluster of satellites such that the cluster optimally observes and tracks a target in an orbital trajectory segment. We have focussed on synthesizing stationary Keplerian orbits from which the cluster of satellites can optimally observe and track the target, and thus no orbit changes and associated thrust firing solutions are considered. We present a two-step approach to synthesizing the optimal target viewing orbits for a cluster of N satellites. The first step abstracts the cluster into a centroidal Formation Center orbit and solves a nonlinear, nonconvex search problem for this central orbit. The next step "explodes" the formation center to obtain N distinct orbits in some bounded regime about the formation center. This second step is a high-dimensional search (parameterized by number of satellites, N) posed in a linear perturbational form about the formation center. The overall search is rapid and converges within several seconds. We present simulation results from the target estimator, obtained from running the experiment along the orbital trajectories computed by this algorithm on our multi-satellite simulation testbed.