I heard that GPS is one of the few applications in daily life that needs to consider relativistic effects. So, the generated data must have already excluded these relativistic effects, right?
What generated data are you talking about and who was it generated by?
If you mean the output of commercial GPS units, then yes, all manner of error inducing effects have been compensated for in post aquisition processing that generates output.
This article is about raw GPS data .. which is a collection of raw data streamed from multiple satellites that then requires processing to generate an output, and quite often additional inputs from ground stations | naval corrections to improve accuracy.
There are many different GPS instrument providers who all do broadly similar things .. the devil is in the details.
> Moreover, the clocks on satellites don’t have to be explicitly slowed down to fix the cumulative relativistic speed-up of time. As part of their broadcasted message a satellite emits three coefficients that allow the receiver to correct for any offset or speed change of that satellite’s clock.
My understanding is that GPS satellites clocks are tuned to tick slow exactly to account for relativity.
> First, each GPS space vehicle (SV) clock is offset from its nominal rate by about -4.45x10^-10 (= -38 microseconds per day) to allow for the relativistic offsets between the differences between the SV and the ground. Of this -38 microseconds per day, about -45 are due to the gravitational potential difference between the SV at its mean distance and the earth's surface, and +7 to the mean SV speed, which is about 3.87 km/sec. To this mean correction, each receiver must add a term due to the eccentricity of the GPS orbit.
Time ticks at different rates depending on the strength of the gravity "force", or rather the rate at which objects fall into the space-time distortion caused by mass of the earth. Time also ticks slower for objects moving at higher speeds than the observer (satellites move pretty fast). Since GPS depends on time being in sync between the observer and satellites, the time tick is offset to account for the effects of special and general relativity.
The error budget in the pseudorange to the satellites has various factors due to relativity, but they are just lumped into the errors in the least squares problem that you solve to get the position estimate (as per the article).
So relativity is important, but you don't need to know much about it to solve for your position. Various flavours of long baseline/network RTK will need more sophisticated modelling though.
