  When dealing with an orbit determination problem, uncertainties naturally
arise from intrinsic errors related to observation devices and approximation
models. Following the least squares method and applying approximation schemes
such as the differential correction, uncertainties can be geometrically
summarized in confidence regions and estimated by confidence ellipsoids. We
investigate the asymptotic behaviour of the confidence ellipsoids while the
number of observations and the time span over which they are performed
simultaneously increase. Numerical evidences suggest that, in the chaotic
scenario, the uncertainties decay at different rates whether the orbit
determination is set up to recover the initial conditions alone or along with a
dynamical or kinematical parameter, while in the regular case there is no
distinction. We show how to improve some of the results in \cite{maro.bonanno},
providing conditions that imply a non-faster-than-polynomial rate of decay in
the chaotic case with the parameter, in accordance with the numerical
experiments. We also apply these findings to well known examples of chaotic
maps, such as piecewise expanding maps of the unit interval or affine
hyperbolic toral transformations. We also discuss the applicability to
intermittent maps.
