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This paper demonstrates the use of polynomial chaos expansions (PCEs) for the non-linear, 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(More)
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 cubed sphere model,(More)
We describe a new method for numerical integration, dubbed bandlimited collo-cation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer(More)
This paper presents the application of polynomial chaos (PC) to estimating the probability of collision between two spacecraft. Common methods of quantifying this probability for conjunction assessment use either Monte Carlo analyses or include simplifying assumptions to improve tractability. A PC expansion, or PCE, provides a means for approximating the(More)
The tracking of space objects poses unique challenges when compared to traditional applications. Direct application of standard multi-target tracking models fails to yield accurate results for the case of space objects. For example, dynamic models for traditional applications require simple, often linear, discrete-time models. This is not the case for space(More)
Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the(More)
The cubed-sphere model provides rapid evaluation of the gravity field for more efficient orbit propagation. This paper characterizes the improved computational efficiency of sequential orbit determination, specifically the extended and unscented Kalman filters, when using this new model instead of the common spherical harmonic model. To use the new gravity(More)
In its classical form, the cardinalized probability hypothesis density (CPHD) filter does not model the appearance of new targets through spawning, yet there are applications for which spawning models more appropriately account for newborn objects when compared to spontaneous birth models. In this paper, we propose a principled derivation of the CPHD filter(More)
This paper presents a measurement-based birth model with the Cardinalized Probabilistic Hypothesis Density (CPHD) filter using the probabilistic admissible region (PAR) for tracking space objects. Insufficient information content in a short-duration time series of observations makes track instantiation for space objects difficult. Models based on the(More)