# Applied Math question: Is there a way to use the set of GPS satellite positions as a lattice?

Okay,

I am wondering if it is possible to take a satellite constellation, say the gps satellites, and use the satellites' positions (at time $t$) as points (shown below) and use them as a lattice.

Some facts about the constellation:

• GPS Satellites lie in 6 planes.
• Each plane is inclined 55 degree.
• There are between 4 and 6 satellites in each plane. (they are not evenly spaced)
• Their orbital paths are circular (i.e. $\text{eccentricity} \approx 0$). If it helps, let's assume that that their orbits are circular.

I suppose what I am looking for is this: Given a set of points at time $t$, $GPS_t$ with specifications stated above, is there a mapping, $f$, that derives a lattice, $L_{GPS_t}$?

# EDIT

what i mean by lattice is a convex polytope from $GPS_t$.

references

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I edited your question to include the image. – Alex Becker Jul 15 '12 at 2:52
Certainly there is a way to derive the position of each satellite at a given time. They broadcast their ephemeiris, which gives the position. From there you can get the distance between any pair. Is that what you mean by "derive a lattice"? – Ross Millikan Jul 15 '12 at 3:05
What do you mean by 'a lattice'? – copper.hat Jul 15 '12 at 3:17
you might get better answers at mathematica.stackexchange.com – magma Aug 14 '12 at 9:29