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High-order expansion of the solution of preliminary orbit determination problem

Armellin, R, Di Lizia, P and Lavagna, M (2012) High-order expansion of the solution of preliminary orbit determination problem Celestial Mechanics and Dynamical Astronomy, 112 (3). pp. 331-352.

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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.

Item Type: Article
Subjects : Electronic Engineering
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
AuthorsEmailORCID
Armellin, RUNSPECIFIEDUNSPECIFIED
Di Lizia, PUNSPECIFIEDUNSPECIFIED
Lavagna, MUNSPECIFIEDUNSPECIFIED
Date : 1 March 2012
Identification Number : https://doi.org/10.1007/s10569-012-9400-8
Copyright Disclaimer : © 2012 Springer Science+Business Media B.V.
Uncontrolled Keywords : Preliminary orbit determination, Differential algebra, Uncertainty mapping, High-order methods
Depositing User : Symplectic Elements
Date Deposited : 30 Nov 2016 10:14
Last Modified : 30 Nov 2016 10:14
URI: http://epubs.surrey.ac.uk/id/eprint/812997

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