This paper demonstrates the use of polynomial chaos expansions (PCEs) for the nonlinear, non-Gaussian propagation of orbit state uncertainty. Using linear expansions in tensor-products of univariate orthogonal polynomial bases, PCEs approximate the stochastic solution of the ordinary differential equation describing the propagated orbit, and include information on covariance, higher moments, and the spatial density of possible solutions. Results presented in this paper use non-intrusive, i.e., sampling-based, methods in combination with either least-squares regression or pseudo-spectral collocation to estimate the PCE coefficients at any future point in time. Such methods allow for the utilization of existing orbit propagators. Samples based on Sun-synchronous and Molniya orbit scenarios are propagated for up to ten days using two-body and higher-fidelity force models. Tests demonstrate that the presented methods require the propagation of orders of magnitude fewer samples than Monte Carlo techniques, and provide an approximation of the a posteriori probability density function that achieves the desired accuracy. Results also show that Poincaré-based PCEs require fewer samples to achieve a given accuracy than Cartesian-based solutions. In terms of pdf accuracy, the PCE-based solutions represent an improvement over the linear propagation and unscented transformation techniques.

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Previous labeled random finite set filter developments use a motion model that only accounts for survival and birth. While such a model provides the means for a multi-object tracking filter such as the Generalized Labeled Multi-Bernoulli (GLMB) filter to capture object births and deaths in a wide variety of applications, it lacks the capability to capture spawned tracks and their lineages. In this paper, we propose a new GLMB based filter that formally incorporates spawning, in addition to birth. This formulation enables the joint estimation of a spawned object's state and information regarding its lineage. Simulations results demonstrate the efficacy of the proposed formulation.

The cubed-sphere gravitational model is a modification of a base model, e.g., the spherical harmonic model, to allow for the fast evaluation of acceleration. The model consists of concentric spheres, each mapped to the surface of a cube and combined with an appropriate interpolation scheme. The paper presents a brief description of the cubedsphere model and a comparison of it with the spherical harmonic model. The model was configured to achieve a desired accuracy so that dynamical tests, e.g., evaluation of the integration constant, closely approximate that of the spherical harmonic model. The new model closely approximates the spherical harmonic model, with propagated orbits deviating by a fraction of a millimeter at or above feasible Earth-centered altitudes.