GPS & Relativity: Position Error Lower Than 38000 Feet?

[Integral]

If the corrections made are unnecessary, why does the system work? Seems to me that if we made corrections to correct for a drift that was not happening then the system would be drifting. Are you saying that the corrections made actually sum to zero? Isn't it strange that no one has noticed?

 

[Brucep]

It is compounding. That's why the correction is needed.

86,400 seconds/day * 4.4453EE10 = 38,407 nanosecond/day

You're also trying to argue that the relativistic correction isn't needed because the
effect is small and GPS operations would balance out a 38,407 foot/day error.

There's a reason the correction is accounted for.

 

[George Jones]

But positioning could work nearly as well without the compensation. The paper doesn't state opposite.

The paper doesn't, but author does. From the same author, one of the world's leading experts on GPS,

How big will be the difference in rates of a clock on Earth and a clock in orbit? Big enough to cause a navigational error of 13 km in a day if it is not corrected for.

http://www.aapt.org/doorway/TGRUTalks/Ashby/AshbyTalk3of6.htm#13 km

 

[Suxxor]

It is compounding. That's why the correction is needed.

86,400 seconds/day * 4.4453EE10 = 38,407 nanosecond/day

You're also trying to argue that the relativistic correction isn't needed because the
effect is small and GPS operations would balance out a 38,407 foot/day error.

There's a reason the correction is accounted for.

Are you winding me up? Are you serious? I cannot believe it.

It doesn't matter how big the time drift between ground and satellite is as long as there is no time drift between satellites themselves, error would not accumulate.

ground time is not used for position calculation. Even your own Taylor and Wheeler paper confirms that. That's why they use 4 satellites instead of 3.

Do you see now what I mean? Ground time is not used. So for position calculation, time difference between ground and satellite does not matter. Because ground time is not used. Get it?

 

[Suxxor]

I don't think his argument is that an error exists due to SR/GR, I think he is implying that the error is static, not compounding. This appears to be more of an engineering/computing than a physics question.

That's correct.

Since the satellites constantly change position relative to the receiver (they are orbiting the earth), you must determine distance through timing, which will necessarily involve your planetside clock and the relativity corrections that go with it.

Not necessarily. Since 4 satellites are used, planetside clock is eliminated from the equations; chingel's post proves that.

A simple page I found talking about GPS:

http://www.kowoma.de/en/gps/positioning.htm

The clock on the receiver isn't accurate enough to measure the time it took to receive the signal with high accuracy anyway, it just uses relative times, hoping the clock is accurate enough that it doesn't change it's speed too much and the relative time proportions are relatively accurate. Then it calculates the position and also corrects the clock by making the spheres of the distances from the satellites intersect.

So it seems that the receiver isn't just synchronizing the clock from time to time, it is actually figuring out the correct time based on the relative times of the signals for each position calculation, otherwise it would have much less accuracy. This should mean that there would be no error build-up.

 

[sophiecentaur]

Please keep the discussion dispassionate and free from insult, either explicit or implicit.

I couldn't agree more.

 

[atyy]

Some quick thoughts, which may of course be wrong. It looks like the constant resetting of the ground clock is needed because the ground clock isn't a stable atomic clock. So the resetting using the 4th satellite essentially makes the cheap ground clock into an atomic clock. But we know that even if atomic clocks were used, the Schwarzschild metric (or an approximation of it) must be used somewhere in the calculation.

 

[Brucep]

Are you winding me up? Are you serious? I cannot believe it.

It doesn't matter how big the time drift between ground and satellite is as long as there is no time drift between satellites themselves, error would not accumulate.

Do the project instead of trying to 'mine stuff' that you think supports your erroneous position. GR predicts the error would accumulate, that's why the correction is included. It's okay since what we say here won't make any difference whatsoever.

 

[Suxxor]

The paper doesn't, but author does. From the same author, one of the world's leading experts on GPS,


http://www.aapt.org/doorway/TGRUTalks/Ashby/AshbyTalk3of6.htm#13 km

On the same slides, he has written "... reference clock is on Earth equator". But in GPS system, reference clock is on one of the satellites, not on Earth equator.

 

[chingel]

If the corrections made are unnecessary, why does the system work? Seems to me that if we made corrections to correct for a drift that was not happening then the system would be drifting. Are you saying that the corrections made actually sum to zero? Isn't it strange that no one has noticed?

What is it that needs to be corrected to make the system work considering the effect of relativity? Is it the clock on the satellite or the clock on the receiver? If all the clocks on the satellites would go 38000 ns ahead every day, why wouldn't a standard GPS receiver not work or start drifting? Consider that a whole years worth of time delay due to relativity is less than the daily clock error on the receiver.

 

[Suxxor]

Do the project instead of trying to 'mine stuff' that you think supports your erroneous position. GR predicts the error would accumulate, that's why the correction is included. It's okay since what we say here won't make any difference whatsoever.

I went through the project, pointed out a contradiction (post #21), which you discarded as nonsense. Your posts in this thread do not lead anywhere. We all saw your point, but sadly you are not able to see ours.

I did not try to 'mine stuff', just make you understand our argument. If you could unerstand it, then you could give a counter-argument. I can see yours. You are saying that since ground time and satellite time drifts because of relativistic effects, the difference would result in GPS position error.

I'm saying that GPS does not use ground time (based on multiple sources, including your own ) in position calculations, so why do you use ground time at all in your position error calculations?

 

[George Jones]

I think that the error accumulates because position determination involves time differences between clocks on different satellites. I'll try to elaborate on this possibly cryptic statement later today or tomorrow, because, right now, my five-year-old daughter is not letting me concentrate sufficiently to think or type.

 

[sophiecentaur]

Do the project instead of trying to 'mine stuff' that you think supports your erroneous position. GR predicts the error would accumulate, that's why the correction is included. It's okay since what we say here won't make any difference whatsoever.

What "error?
The word "error" is not the right one. A much more appropriate word would be "offset". If you were to invent a system for measuring the length of a railway station platform from the moving train, then you would automatically build in the speed of the train into your measurement system. No one would call the effect of the train's motion an "error"; it would just part of the measurement arrangement.

I cannot believe why you are all going over this same ground again and again. From what I can read, we all are aware of the effects involved. Some are calling the relativistic effect on the timing of the signals an error whilst some are just building it into the model of the GPS system.
The only totally wrong statement that I have read is that the "error" is of the order of the speed of light (1ft per ns). That's clearly nonsense; it's only the difference in apparent elapsed time that counts. The rest is just arguing about nothing really.
Let it lie - as they say.

 

[atyy]

On the same slides, he has written "... reference clock is on Earth equator". But in GPS system, reference clock is on one of the satellites, not on Earth equator.

Absolute ground time may not be used, but it seems ground time difference is still used, since the ground receiver must carry a lousy clock? If all timing were external, it would surely be cheaper to omit even the lousy clock?

 

[Brucep]

What "error?
The word "error" is not the right one. A much more appropriate word would be "offset". If you were to invent a system for measuring the length of a railway station platform from the moving train, then you would automatically build in the speed of the train into your measurement system. No one would call the effect of the train's motion an "error"; it would just part of the measurement arrangement.

I cannot believe why you are all going over this same ground again and again. From what I can read, we all are aware of the effects involved. Some are calling the relativistic effect on the timing of the signals an error whilst some are just building it into the model of the GPS system.
The only totally wrong statement that I have read is that the "error" is of the order of the speed of light (1ft per ns). That's clearly nonsense; it's only the difference in apparent elapsed time that counts. The rest is just arguing about nothing really.
Let it lie - as they say.

I'm not going over the same stuff unless I have to. Error is the wrong word but who's nitpicking? You need to do the project because time dilation effects are not apparent. IE relative time and distance intervals are real natural phenomena. Since you intend to introduce that 'nonsense' catch you later. What's been said is light travels 1 foot/nanosecond. Figure it out from there.

 

[sophiecentaur]

I'm not going over the same stuff unless I have to. Error is the wrong word but who's nitpicking? You need to do the project because time dilation effects are not apparent. IE relative time and distance intervals are real natural phenomena. Since you intend to introduce that 'nonsense' catch you later.

There are plenty of real errors in a system like this but the main effect of orbital speed and the presence of the Earth's mass is surely not an error but a main feature of the whole system - and would have been included in the very first, idealised 'back of a fag packet' system concept.

I used the word 'nonsense' because I can see no reason how a measured position could possibly be regarded as drifting off at the rate of c. Can you?

 

[rorix_bw]

There is an atomic clock in each GPS sat. Because of their speed and the different gravity at their alititude, the clocks run 38 microseconds fast compared to Earth. Putting the numbers in the formula gives an error of about 300 meters per microsecond. That would be 11 kilometers per day, give or take. Sounds right to me.

Someone said if the clocks were ALL up in the satellites (they are, most GPS receivers do not contain atomic clocks) it wouldn't matter as they would all be fast by the same amount, and no Earth clock was used. That is not true.

The problem is distance = speed X time. The speed is of light is constant. So you need to know the time in order to measure how long the signal takes to reach you. You're relying on the GPS clock then to give you a 'start' and 'end' time for the signal, and if that clock is fast, how can your position be correct?

edit: forgot speed, writing too fast

edit: start/end might not be how it works but the key thing is the receiver uses the GPS clock to do all the timings, and you need at least two values to time something.

 

[Suxxor]

Someone said if the clocks were ALL up in the satellites (they are, most GPS receivers do not contain atomic clocks) it wouldn't matter as they would all be fast by the same amount, and no Earth clock was used. That is not true.

The problem is distance = speed X time. The speed is of light is constant. So you need to know the time in order to measure how long the signal takes to reach you. You're relying on the GPS clock then to give you a 'start' and 'end' time for the signal, and if that clock is fast, how can your position be correct?

The 'distance = speed X time issue' has been considered before in this thread: https://www.physicsforums.com/showthread.php?t=543848#13

The systematic error would be in a region of 1 cm. So GPS would still work as well.

Do you agree that, given that Earth-time is not used in position calculations, there would be no 11 km/day GPS position error build up? That is what the whole argument is about.

 

[sophiecentaur]

You do not need to know the absolute time of the signal arrival. Just knowing the difference in arrival time puts you somewhere on a possible hyperboloid with relation to a pair of satellites. The original land based 'hyperbolic' navigation systems (Decca Navigator) used simple LC oscillators in the receivers to get a phase difference between received signals and even they gave an accuracy of a few tens of m. (enough to find lobster pots in the fog, it was said).
That system was simpler because the ship's location was static relative to the (static) transmitters and it was essentially a two dimensional model. Three transmitters would give you your position at the intersection of three hyperbolae. The oldest systems involved reading numbers off a receiver and referring to charts with sets of hyperbolae actually drawn on them. The GPS is more complicated because of the fact that everything is on the move but all that is taken into account. The Earth is rotating at a constant rate relative to the frame of the satellite network and the receiver is taking all this into account whilst it is 'chasing' the relative phases of the signals it's looking at.

The GPS system could, in fact, be looked upon as telling you either your rapidly changing position in 3D or your fixed position on a spinning globe.

Very cleverly implemented but not too hard to grasp the fundamentals what's going on if you relate the problem to the older land-based system ideas. More available satellite signals gives you better accuracy because they each represent a time reference for the others.

 

[atyy]

Do you agree that, given that Earth-time is not used in position calculations, there would be no 11 km/day GPS position error build up? That is what the whole argument is about.

This guy gets something similar to what you are thinking?

http://osg.informatik.tu-chemnitz.de/lehre/old/ws0809/sem/online/GPS_presentation.pdf
http://osg.informatik.tu-chemnitz.de/lehre/old/ws0809/sem/online/GPS.pdf

"When using three satellites for position determination (equation (4)) this corresponds to an error up to 12km per day. For measurements based on four satellites, only the term Δ of equation (5) is affected by clock drifts. To correct this error, the time base of the GPS satellites is modified ... 39 μs.d^-1.

 

[Suxxor]

This guy gets something similar to what you are thinking?

http://osg.informatik.tu-chemnitz.de/lehre/old/ws0809/sem/online/GPS_presentation.pdf
http://osg.informatik.tu-chemnitz.de/lehre/old/ws0809/sem/online/GPS.pdf

"When using three satellites for position determination (equation (4)) this corresponds to an error up to 12km per day. For measurements based on four satellites, only the term Δ of equation (5) is affected by clock drifts. To correct this error, the time base of the GPS satellites is modified ... 39 μs.d^-1.

Thanks. This is proof that a normal GPS receiver would determine the position accurately even if clock frequency on satellites wasn't corrected, because a normal receiver uses at least 4 satellite signals so equation 5 in the paper applies (the term Δ in equation 5 is calculated independently of coordinates r, which remain unaffected as the author states).

So the fact that without relativistic time drift compensation, GPS positioning would result in position error of 38000 feet per day and GPS would not be usable is a widespread misconseption, because no device without an atomic clock can afford to use just 3 satellites.

 

[atyy]

Thanks. This is proof that a normal GPS receiver would determine the position accurately even if clock frequency on satellites wasn't corrected, because a normal receiver uses at least 4 satellite signals so equation 5 in the paper applies (the term Δ in equation 5 is calculated independently of coordinates r, which remain unaffected as the author states).

So the fact that without relativistic time drift compensation, GPS positioning would result in position error of 38000 feet per day and GPS would not be usable is a widespread misconseption, because no device without an atomic clock can afford to use just 3 satellites.

That seems correct, very interesting indeed. I certainly had the 38000 ft.d^-1 number in my head, but didn't know it had to be qualified by "if 3 satellites are used, whereas in reality at least 4 satellites and a lousy clock are used"

Do knowledgeable folks like sophiecentaur agree?

 

[rorix_bw]

I have looked into how a gps receiver works and it seems as you say to get a time signal from the satellite and then compare the satellite's signal to one that it generates itself, comparing the two to determine the distance.

If the satellite clock is fast, so time is running faster for the satellite? Would not it therefore produce a compressed signal? And the compression of this signal would continue to increase as time difference continued to build up? So the receiver would get increasingly less accurate? So the GPS error would indeed accumulate? In the same way as the guy who flies close to light speed ages much more slowly than the guys he left behind on his planet?

How does the 4th satellite prevent this? What exactly is the local clock in the Mario Haustein paper?

edit: Oh i get it now, It seems that it doesn't accumulate with >3 satellites.

edit again: No, I don't get it. I'll read it some more. Unless anyone can explain?

 

[rorix_bw]

I'd read it some more and knocked up a quick bit of Lego that can determine its position from observing two beacons.

I don't want to comment on my own post but I can't edit it. Basically before I accept the assertion that error would not accumulate I need that formula (4) and (5) from the Haustein paper explained to me - because from where I sit it seems to violating basic engineering principles, so I'm really not sure the guy is correct.

 

[phinds]

I think that the error accumulates because position determination involves time differences between clocks on different satellites. I'll try to elaborate on this possibly cryptic statement later today or tomorrow, because, right now, my five-year-old daughter is not letting me concentrate sufficiently to think or type.

George, I look forward to your feedback on this concept.

Suxxor has made some points that I'm not competent to refute and he is convinced that the correction is NOT necessary. This "feels" wrong to me, but I well know how little the universe cares about how I "feel" about things.

Here's the thing: Since engineers hate to complicate things for no reason, why would the designers of the system have added in an unneeded correction?

 

[mrspeedybob]

Even atomic clocks are not perfect. If they were then I think the OP would have been right. For everything to stay synchronized the clocks on each satellite must re-synchronize from time to time with a master clock. The master clock is ground based so if relativistic effects were not compensated for then a satellite that just had its clock synchronized would be out of sync with a satellite that had been synchronized less recently. having satellites out of sync would certainly cause error, though I don't know how much.

http://tycho.usno.navy.mil/gpsinfo.html

Also, the GPS system is designed to provide 4 co-ordinates, not 3. The 4'th being time. If the master clock were space based and time dilation were not accounted for the time co-ordinate would drift. A cheap receiver with a fallible clock would not know how much drift to account for.