Marcus Bever, ExoAnalytic Solutions, Inc.

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Abstract:

The present study on orbit determination leverages an optical measurement system based on the lunar south pole with the objective to track a satellite along a periodic, yet dynamically unstable, trajectory in the circular restricted three-body problem. Midway through each scenario, a modest spacecraft maneuver is performed to assess the algorithms’ ability to recover valid estimates. Given a motivation to test the robustness of several filtering schemes, in the first effort of this paper, exact observation sensor conditions and the initial state error are tuned to extreme values, such that few algorithms repeatably obtain a quality result. This process of refining suggests a hierarchy of the more robust approaches. Continuing, the second portion of the work, perhaps of greater interest, is an empirically driven analysis of estimator consistency over stochastically-chosen initial conditions. This Monte Carlo simulation uses a more modest noise configuration to avoid continual divergence for a family of estimators. Results suggest that the two most robust filters of the set investigated include the quadrature and cubature Kalman filters, although more accurate estimates were often achieved by the two nonlinear Gaussian mixtures. The credibilistic approach was prone to degeneracy when the information content was sufficiently diluted. In all, the following filtering algorithms are evaluated: credibilistic Gaussian mixture (using the unscented transform), probabilistic Gaussian sum (unscented transform), cubature Kalman, quadrature Kalman, and unscented Kalman.