Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approaches to relativistic positioning around Earth and error
  estimations   In the context of relativistic positioning, the coordinates of a given user
may be calculated by using suitable information broadcast by a 4-tuple of
satellites. Our 4-tuples belong to the Galileo constellation. Recently, we
estimated the positioning errors due to uncertainties in the satellite world
lines (U-errors). A distribution of U-errors was obtained, at various times, in
a set of points covering a large region surrounding Earth. Here, the
positioning errors associated to the simplifying assumption that photons move
in Minkowski space-time (S-errors) are estimated and compared with the
U-errors. Both errors have been calculated for the same points and times to
make comparisons possible. For a certain realistic modeling of the world line
uncertainties, the estimated S-errors have proved to be smaller than the
U-errors, which shows that the approach based on the assumption that the
Earth's gravitational field produces negligible effects on photons may be used
in a large region surrounding Earth. The applicability of this approach -which
simplifies numerical calculations- to positioning problems, and the usefulness
of our S-error maps, are pointed out. A better approach, based on the
assumption that photons move in the Schwarzschild space-time governed by an
idealized Earth, is also analyzed. More accurate descriptions of photon
propagation involving non symmetric space-time structures are not necessary for
ordinary positioning and spacecraft navigation around Earth.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat