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Old 11th Jun 2013, 14:27
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Luc Lion
 
Join Date: Mar 2006
Location: Vance, Belgium
Age: 58
Posts: 181
The calculation is also compounded by the fact that the time reference of the satellite is different from the time reference of the GPS receiver.
Not only is the "starting point" of time measurement different but also is the rate at which the time flows. That's relativity.

Special relativity states that the satellite clock (tsv in the document) beats slowlier than the GPS receiver clock when evaluated in the GPS receiver reference frame (when evaluated in the satellite reference, it is the opposite ; the GPS receiver clock beats slowlier). (drifting rate ~= -7000 ns per day)
On top of that, general relativity states that clocks at the satellite altitude beat quicker than clocks at the level of the ground. (drifting rate ~= +45000 ns per day)
In total, the satellite clock is quicker.

The exact correction depends on the relative speed of the satellite and GPS receiver, thus on the position of the GPS receiver relative to the satellite trajectory.
This is what is computed in equation (2) of page 102.
Coefficients af0, af1 and af2 express the dependency to the satellite trajectory and, thus, the 3 first items contain the special relativity correction.
The fourth item Δtr contain the general relativity correction.

Last edited by Luc Lion; 11th Jun 2013 at 14:28.
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