How does GPS correct for time dilation?

[pervect]

I am surprised that this thread has gone on for 3 pages. I'm afraid I haven't had the time to go through each and every response. I still have a remark that I hope will be helpful.

My $.02. It would indeed be possible, in theory, to not adjust the rate of the GPS clocks. For a reference, see "Precis of General Relativity" by Misner, http://arxiv.org/abs/gr-qc/9508043 (or http://arxiv.org/pdf/gr-qc/9508043v1.pdf for the pdf).

For GPS the measuring instruments can be taken to be either ideal SI atomic clocks in trajectories determined by known forces, or else electromagnetic signals describing the state of the clock that radiate the signal. Each clock maintains its own proper time (but may convert this via software into other information when it transmits).

I believe Misner's paper was written in response to Ashby's.

However, it at least appears CONVENIENT, though not NECESSARY, to have the clocks transmit a coordinate time rather than proper time, specifically the coordinate time called atomic time, also known as TAI time. I was curious, personally, as to which approach the European Union's "Galileo" positioning system used, but I wasn't able to find anything definite in the amount of time I had to dedicate to find what sort of time the Galileo satellites transmitted.

Having the clocks transmit their coordinate time, rather than their proper time, makes analysis via coordinates easier (as long as you've settled on a consistent coordinate choice), and hopefully easy to understand as well. But either approach will do.

It is of course not absolutely NECESSARY to use any particular coordinate system. Usually the position coordinates are desired in an ECEF coordinate system (Earth centered, Earth fixed) - because in this coordinate system, points on the rotating Earth have constant coordinates, which is what's generally meant by a "position" on the rotating Earth. Light rays do not follow straight lines in the ECEF coordinates, however, so the usual choice is use a different coordinate system, ECI (Earth Centered Inertal) coordinates for the bulk of the analysis, which makes analysis of the trajectories of the radio signals easy because the radio signals can be presumed to travel in straight lines in this coordinate system (with the possible exception of some minor atmospheric effects). Then one converts the results from ECI back to ECEF at the end of the analysis. The usual choice for the time coordinate system is known as atomic time aka TAI time, thus the time coordinate used by TAI are hopefully familiar to the reader (though all of the technical details may not be familiar). Note that civil time, UCT, aka Coordinated universal time, is derived from TAI time by the addition of leap seconds to keep UCT in synch with the sun / solar time. TAI time is equal to proper time for objects at rest on the surface of the Earth only at sea level (more technically, on the geoid), as several other posters have already noted.

I also rather strongly suspect that some of the non-science-advisor posters in this thread are clinging to the notion of absolute time, most likely without realizing it, and that this is the ultimate source of their confusion with regards to the issue of time dilation. Unfortunately, I'm not aware of any good strategy to clear up this sort of confusion :(.

If there is interest, and I have the time, I might try to write something up about the relationship between the relativity of simultaneity and time dilation, but experience has shown me that it seems a hard point to get across.

 

[PeterDonis]

objects at rest on the ground have constant ECI coordinates

Is this correct? I thought the ECI frame was a non-rotating frame centered on the Earth, so in this frame an object at rest on the rotating Earth is moving (unless it's at one of the poles). I believe the term for a frame that is fixed to the Earth is ECEF (Earth-centered Earth-fixed). Evidently this frame would be a non-inertial frame.

 

[doaaron]

I'm not sure that's possible with the current satellite design; AFAIK the clock rate correction is fixed when the satellite is built. However, I don't see any reason in principle why you couldn't design a satellite clock whose rate was adjustable.

Just a disclaimer, I don't know whether the satellite's clock rate is adjustable or not.

That said, I think its very likely. Almost all electronics circuits which require precise timing consist of a not-so-stable, but controllable clock which is phase-locked to a stable reference clock rate (such as a quartz crystal oscillator, but I guess in the case of GPS it is the atomic clock). Using this method (its called a phase-locked-loop), you can get more or less any clock rate you want (that's an exaggeration so don't quote me), and its controllable.

If you already knew all that then pls ignore...regards,
Aaron

 

[pervect]

Is this correct? I thought the ECI frame was a non-rotating frame centered on the Earth, so in this frame an object at rest on the rotating Earth is moving (unless it's at one of the poles). I believe the term for a frame that is fixed to the Earth is ECEF (Earth-centered Earth-fixed). Evidently this frame would be a non-inertial frame.

Good catch - bad post - with luck I can fix it still.

 

[Fantasist]

I also rather strongly suspect that some of the non-science-advisor posters in this thread are clinging to the notion of absolute time, most likely without realizing it, and that this is the ultimate source of their confusion with regards to the issue of time dilation. Unfortunately, I'm not aware of any good strategy to clear up this sort of confusion :(.

If there is interest, and I have the time, I might try to write something up about the relationship between the relativity of simultaneity and time dilation, but experience has shown me that it seems a hard point to get across.

The issues addressed in this thread have as such little to do with Relativity. It is merely about how drifts of the satellite clocks (due to whatever causes) affect the GPS operations and what can and is being done to correct for these drifts. It is just a technical question, not a scientific one.

 

[doaaron]

The issues addressed in this thread have as such little to do with Relativity. It is merely about how drifts of the satellite clocks (due to whatever causes) affect the GPS operations and what can and is being done to correct for these drifts. It is just a technical question, not a scientific one.

That is what it has turned into. It wasn't my original question.Aaron

 

[Fantasist]

That is what it has turned into. It wasn't my original question.Aaron

You were asking how the clock corrections are working in practice, weren't you?
Well, the answer is simple: as mentioned in Chapt. 4-6 of the technical GPS documentation ( http://www.publications.usace.army.mil/Portals/76/Publications/EngineerManuals/EM_1110-1-1003.pdf ) , the satellite clocks are reset from the ground as often as required to a) keep all satellite clocks against each other within 20 ns, and the satellite clocks as a whole against the ground clock within 1 ms. This guarantees that GPS results are correct to within a few meters.

 

[pervect]

The issues addressed in this thread have as such little to do with Relativity. It is merely about how drifts of the satellite clocks (due to whatever causes) affect the GPS operations and what can and is being done to correct for these drifts. It is just a technical question, not a scientific one.

If it was a simple technical question, I don't think the thread would have gone on as long as it did (4 pages worth). Additionally, I think that Ashby's paper covers the technical aspects quite nicely, but it didn't seem to put the thread to rest.

Now, I can sympathize that not everyone necessarily has the necessary background to read Ashby's paper. But at that point the issue shifts from a merely technical question, to an educational one - how to understand the answers that are in the literature.

 

[doaaron]

You were asking how the clock corrections are working in practice, weren't you?

nope...but I did get that pdf you sent and its a good reference, so thanks.

The original question was basically: a person at the north pole would view a GPS satellite's time as running at rate f1, but a person at the north pole would view a GPS satellite's time as running at rate f2. So would there be any position inaccuracy? The conclusion was of course no...


regards,
Aaron

 

[A.T.]

Once again: only if you have no other prior knowledge about your position. But suppose the two surface points are 1000 km apart, and you know your approximate position to within 100 km.

Right, positions determined recently when one more satellite was received, allow you to pick among two sufficiently distant solutions, and thus get by with one satellite less, so you have:

#satelites = #varibables

But the above is not a general rule. At some point you needed:

#satelites = #varibables + 1