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A validation framework for orbit uncertainty propagation using real satellite data applied to orthogonal probability approximation

Sivasankar, Pugazhenthi, Lewis, Bennie G., Probe, Austin B., and Elgohary, Tarek A., 2025. A validation framework for orbit uncertainty propagation using real satellite data applied to orthogonal probability approximation. Acta Astronautica, 232:453–478, doi:10.1016/j.actaastro.2025.02.034.

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@ARTICLE{2025AcAau.232..453S,
       author = {{Sivasankar}, Pugazhenthi and {Lewis}, Bennie G. and {Probe}, Austin B. and {Elgohary}, Tarek A.},
        title = "{A validation framework for orbit uncertainty propagation using real satellite data applied to orthogonal probability approximation}",
      journal = {Acta Astronautica},
     keywords = {Space situational awareness, Uncertainty propagation, GRACE data, Chebyshev approximation, FireOPAL data},
         year = 2025,
        month = jul,
       volume = {232},
        pages = {453-478},
     abstract = "{This paper presents a validation framework using data for uncertainty
        propagation techniques for space situational awareness (SSA)
        applications. In particular, we validate a novel technique for
        uncertainty propagation, dubbed here as Orthogonal Probability
        Approximation (OPA) This technique describes the evolution of
        state/parameter uncertainties, e.g. initial condition and/or
        drag coefficient, of nonlinear dynamical systems at a future
        time. This new uncertainty quantification method employs
        Liouville's theorem and Chebyshev polynomial approximation to
        create a functional representation of the probability density
        function (PDF) at the future time of interest at a fraction of
        the computational cost of classical high-fidelity uncertainty
        propagation methods. OPA is first compared against Polynomial
        Chaos Expansions and Monte-Carlo simulations to numerically
        demonstrate the accuracy of the method. For the real data
        validation, two sources of satellite data are used: GRACE
        navigation data from the Jet Propulsion Laboratory (JPL)
        database, and FireOPAL ground-based observer provided by
        Lockheed Martin. In the presented validation framework, the
        state/parameter uncertainties of resident space objects (RSOs)
        are propagated by OPA without using any measurements. The
        maximum likelihood estimate and the uncertainty bounds of the
        RSO state from OPA are compared with documented estimates and
        uncertainty bounds obtained from real satellite/object tracking
        data as well as other uncertainty propagation methods Results
        indicate successful validation using GRACE navigation data
        (precise orbit determination in LEO), and FireOPAL sensor
        tracking data for Yamal 202 (GEO case) and a rocket body of
        Block-DM satellite with highly elliptical orbit (HEO). The
        results show the capability of OPA to accurately estimate the
        states of RSOs in the absence of continuous measurements, and,
        in addition, the presented framework can be used to validate any
        uncertainty propagation technique.}",
          doi = {10.1016/j.actaastro.2025.02.034},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2025AcAau.232..453S},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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