High-order expansion of the solution of preliminary orbit determination problem |
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Authors: | Roberto Armellin Pierluigi Di Lizia Michele Lavagna |
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Institution: | 1.Dipartimento di Ingegneria Aerospaziale,Politecnico di Milano,Milan,Italy |
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Abstract: | A method for high-order treatment of uncertainties in preliminary orbit determination is presented. The observations consist
in three couples of topocentric right ascensions and declinations at three observation epochs. The goal of preliminary orbit
determination is to compute a trajectory that fits with the observations in two-body dynamics. The uncertainties of the observations
are usually mapped to the phase space only when additional observations are available and a least squares fitting problem
is set up. A method based on Taylor differential algebra for the analytical treatment of observation uncertainties is implemented.
Taylor differential algebra allows for the efficient computation of the arbitrary order Taylor expansion of a sufficiently
continuous multivariate function. This enables the mapping of the uncertainties from the observation space to the phase space
as high-order multivariate Taylor polynomials. These maps can then be propagated forward in time to predict the observable
set at successive epochs. This method can be suitably used to recover newly discovered objects when a scarce number of measurements
is available. Simulated topocentric observations of asteroids on realistic orbits are used to assess the performances of the
method. |
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