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Dynamic Data-Driven Uncertainty Quantification via Polynomial Chaos for Space Situational Awareness

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Handbook of Dynamic Data Driven Applications Systems

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Abstract

Knowledge of all space objects in orbit and the space environment is collected and maintained by the Space Surveillance Network (SSN). This task is becoming more difficult as the number of objects currently tracked increases due to breakup events and improvements in sensor detection capabilities. The SSN is tasked with maintaining information on over 22,000 objects, 1,100 of which are active. In particular, low-Earth orbiting satellites are heavily influenced by atmospheric drag which is difficult to model due to fluctuations in the upper atmospheric density. These fluctuations are caused by variations in the Solar energy flux which heats Earth’s atmosphere causing it to expand. This research uses probabilistic models to characterize and account for the fluctuations in the Earth’s atmosphere. By correctly estimating the fluctuations, our work contributes to improving the ability to determine the likelihood of satellite collisions in space.

The main focus of this chapter is the application of a new Polynomial Chaos based Uncertainty Quantification (UQ) approach for Space Situational Awareness (SSA). The challenge of applying UQ to SSA is the long-term integration problem, where simulations are used to forecast physics over long temporal and/or spatial extrapolation intervals. This chapter applies a Polynomial Chaos (PC) expansion and Gaussian Mixture Models (GMMs) in a hybrid fashion for UQ applied to satellite tracking. This chapter uses the GMM-PC approach for orbital UQ and the PC approach for atmospheric density UQ. Two different application examples are shown. The first example demonstrates the GMM-PC approach for orbital UQ for a low Earth orbit satellite under the influence of atmospheric perturbations. The second example demonstrates the PC approach for atmospheric density UQ, where a physics-based model is used to capture the uncertainty of the atmospheric density under uncertain Solar conditions. These two examples are not combined under this work but the tools developed provide a framework for an unified understanding of UQ for low Earth orbiting satellites.

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Notes

  1. 1.

    This number is problem dependent.

  2. 2.

    Multidimensional quadratures.

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Acknowledgements

The first author wish to acknowledge support of this work by the Air Force’s Office of Scientic Research under Contract Number FA9550-18-1-0149 issued by Erik P. Blasch.

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Authors and Affiliations

  1. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Richard Linares

  2. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX, USA

    Vivek Vittaldev

  3. Applied Mathematics Group, Los Alamos National Laboratory, Los Alamos, NM, USA

    Humberto C. Godinez

Authors
  1. Richard Linares
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  2. Vivek Vittaldev
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  3. Humberto C. Godinez
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Corresponding author

Correspondence to Richard Linares .

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Editors and Affiliations

  1. Air Force Office of Scientific Research, Arlington, VA, USA

    Erik P. Blasch

  2. InfoSymbiotics Systems Society, Boston, MA, USA

    Frederica Darema

  3. Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

    Sai Ravela

  4. Air Force Research Lab, Rome, NY, USA

    Alex J. Aved

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Linares, R., Vittaldev, V., Godinez, H.C. (2022). Dynamic Data-Driven Uncertainty Quantification via Polynomial Chaos for Space Situational Awareness. In: Blasch, E.P., Darema, F., Ravela, S., Aved, A.J. (eds) Handbook of Dynamic Data Driven Applications Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-74568-4_4

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  • DOI: https://doi.org/10.1007/978-3-030-74568-4_4

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