Bayesian approaches to low-thrust maneuvering spacecraft tracking



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The growth in number of space objects with low-thrust maneuvering capabilities has accelerated in recent years. The maintenance of a catalog of space objects ultimately requires the solution to a multi-target tracking problem. Theoretical guarantees are provided as long as each single target is tracked with a Bayesian approach. Bayesian methods to track maneuvering targets are challenging because one generally lacks a prior for the maneuvers. Super-Gaussian priors are robust to large deviations, and are therefore a natural choice for the maneuver prior distribution. A difficulty arises from the resulting large and nonlinear transitional prior. This thesis proposes two approaches to track maneuvering spacecraft using super-Gaussian distributions for the maneuvers. Both approaches work well when the observations are sparse, and when there is a large mismatch between expected maneuver and the true target's maneuver. One approach leverages principles from rare event simulation and a utilizes a novel k-nearest neighbor based ensemble Gaussian mixture filter. The other approach is an instance of a novel class of filters, the Gaussian integral filter, introduced in this dissertation. The Gaussian integral filter makes use of interpolation and quadrature to obtain a Gaussian sum filter with an infinite number of components. Additionally, the auxiliary Hamiltonian Monte Carlo for dynamic parameter estimation is introduced and tested in conditions of sparse observations. The approach is inspired by the auxiliary particle filter, but samples directly from the posterior, like Hamiltonian Monte Carlo methods. The auxiliary Hamiltonian Monte Carlo method combines time and measurement updates in a single step, avoiding the need to have an explicit transitional prior. However, prior data association is required, and, for the time being, the developed approach does not include maneuvers with nonlinear effects on the posterior. The majority of the methodologies explored in this thesis exploit multi-fidelity methods for fast propagation, and a major contribution of this dissertation is the advancement of these techniques in the context of astrodynamics.


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