Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relativistic positioning: errors due to uncertainties in the satellite
  world lines   Global navigation satellite systems use appropriate satellite constellations
to get the coordinates of an user -close to Earth- in an almost inertial
reference system. We have simulated both GPS and GALILEO constellations.
Uncertainties in the satellite world lines lead to dominant positioning errors.
In this paper, a detailed analysis of these errors is developed inside a great
region surrounding Earth. This analysis is performed in the framework of the
so-called relativistic positioning systems. Our study is based on the Jacobian,
J, of the transformation giving the emission coordinates in terms of the
inertial ones. Around points of vanishing J, positioning errors are too large.
We show that, for any 4-tuple of satellites, the points with J=0 are located at
distances, D, from the Earth centre greater than about 2R/3, where R is the
radius of the satellite orbits which are assumed to be circumferences. Our
results strongly suggest that, for D-distances greater than 2R/3 and smaller
than 100000 km, a rather good positioning may be achieved by using appropriate
satellite 4-tuples without J=0 points located in the user vicinity. The way to
find these 4-tuples is discussed for arbitrary users with D<100000 km and,
then, preliminary considerations about satellite navigation at D<100000 km are
presented. Future work on the subject of space navigation -based on appropriate
simulations- is in progress.

2
The categories of this paper are: math
18
The categories of this paper are: econ
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat