Asymptotic behaviour of orbit determination for hyperbolic maps

Abstract

We deal with the orbit determination problem for hyperbolic maps. The problem consists in determining the initial conditions of an orbit and, eventually, other parameters of the model from some observations. We study the behaviour of the confidence region in the case of simultaneous increase of the number of observations and the time span over which they are performed. More precisely, we describe the geometry of the confidence region for the solution, distinguishing whether a parameter is added to the estimate of the initial conditions or not. We prove that the inclusion of a dynamical parameter causes a change in the rate of decay of the uncertainties, as suggested by some known numerical evidences.

arXiv commentAdded new section on comparisons with existing numerical results. Some inaccuracies corrected

References in corpus (5)

• Chaos in navigation satellite orbits caused by the perturbed motion of the Moon
• Orbit Determination with the two-body Integrals. III
• Shadowing Lemma and Chaotic Orbit Determination
• Preliminary orbits with line-of-sight correction for LEO satellites observed with radar
• Orbit determination for standard-like maps: asymptotic expansion of the confidence region in regular zones