Abstract
A method to deal with uncertainties in initial orbit determination (IOD) is presented. This is based on the use of Taylor differential algebra (DA) to nonlinearly map uncertainties from the observation space to the state space. When a minimum set of observations is available, DA is used to expand the solution of the IOD problem in Taylor series with respect to measurement errors. When more observations are available, high order inversion tools are exploited to obtain full state pseudo-observations at a common epoch. The mean and covariance of these pseudo-observations are nonlinearly computed by evaluating the expectation of high order Taylor polynomials. Finally, a linear scheme is employed to update the current knowledge of the orbit. Angles-only observations are considered and simplified Keplerian dynamics adopted to ease the explanation. Three test cases of orbit determination of artificial satellites in different orbital regimes are presented to discuss the feature and performances of the proposed methodology.
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Acknowledgments
R. Armellin acknowledges the support received by the Sklodowska-Curie Grant 627111 (HOPT -Merging Lie perturbation theory and Taylor Differential algebra to address space debris challenges). The authors are grateful to Monica Valli, who implemented a preliminary version of the DA-based IOD update. R. Armellin is thankful to Cristina Parigini for her help in the visualization of the results.
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Armellin, R., Di Lizia, P. & Zanetti, R. Dealing with uncertainties in angles-only initial orbit determination. Celest Mech Dyn Astr 125, 435–450 (2016). https://doi.org/10.1007/s10569-016-9694-z
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DOI: https://doi.org/10.1007/s10569-016-9694-z