Uncertainty propagation of dynamical systems is a common need across many domains and disciplines. In nonlinear settings, the extended Kalman filter is the de facto standard propagation tool. Recently, a new class of propagation methods called sigma-point Kalman filters was introduced, which eliminated the need for explicit computation of tangent linear matrices. It has been shown in numerous cases that the actual uncertainty of a dynamical system cannot be accurately described by a Gaussian probability density function. This has motivated work in applying the Gaussian mixture model approach to better approximate the non-Gaussian probability density function. A limitation to existing approaches is that the number of Gaussian components of the Gaussian mixture model is fixed throughout the propagation of uncertainty. This limitation has made previous work ill-suited for nonstationary probability density functions either due to inaccurate representation of the probability density function or computational b...

The population of space objects (SOs) is tracked with sparse resources and thus tracking data are only collected on these objects for a relatively small fraction of their orbit revolution (i.e., a short arc). This contributes to commonly mistagged or uncorrelated SOs and their associated trajectory uncertainties (covariances) to be less physically meaningful. The case of simply updating a catalogued SO is not treated here, but rather, the problem of reducing a set of collected short-arc data on an arbitrary deep space object without a priori information, and from the observations alone, determining its orbit to an acceptable level of accuracy. Fundamentally, this is a problem of data association and track correlation. The work presented here takes the concept of admissible regions and attributable vectors along with a multiple hypothesis filtering approach to determine how well these SO orbits can be recovered for short-arc data in near realtime and autonomously. While the methods presented here are explored with synthetic data, the basis for the simulations resides in actual data that has yet to be reduced, but whose characteristics are replicated as well as possible to yield results that can be expected using actual data.