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 in 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.
Highlights
This paper is concerned with the behaviour of the confidence region coming from an orbit determination process as the number of observation increases.We recall that orbit determination consists of recovering information on some parameters of a model given some observations and goes back to Gauss (1809)
We study the behaviour of the confidence region in the case of simultaneous increase in the number of observations and the time span over which they are performed
We have considered the problem of orbit determination under the assumption that the number of observations grows simultaneously with the time span over which they are performed
Summary
This paper is concerned with the behaviour of the confidence region coming from an orbit determination process as the number of observation increases. We recall that orbit determination consists of recovering information on some parameters (initial conditions or dynamical parameters) of a model given some observations and goes back to Gauss (1809). The solution, called nominal solution, relies on the least squares algorithm, and the confidence region summarises the uncertainties coming from the intrinsic errors in the observational process. This research is part the authors’ activity within the UMI-DinAmicI community (www.dinamici.org) and the GNFM-INdAM, Italy
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