Questions concerning GPS Navigation

[edraganov]

Hello everyone,

Although I am not a physicist, I have been trying to understand the relativity effects on GPS clocks.

It's seems pretty logic, however I've stumbled upon on a specific issue:

Given a atomic clock without any kind of relativistic adjustment, if the GPS clock is running ahead of the Earth clock, the time when the signal was received is probably going to be behind the time the signal was sent. If the distance is measured by C(T1-T0), this will lead to a negative distance.

In my mind, the GPS system wouldn't be imprecise, it simply would not work at all! Am I right?

Thanks in advance,
Erik

 

[mfb]

Common GPS receivers do not have an atomic clock inside - they cannot do absolute distance measurements, just relative measurements. The calculated position of the satellites would drift away from the real position if their clocks are "wrong", so you would get some errors after a while if the error does not get corrected.

A GPS receiver with an atomic clock would get wrong distances, indeed - but it would take a long time for them to become negative.

 

[edraganov]

Common GPS receivers do not have an atomic clock inside - they cannot do absolute distance measurements, just relative measurements. The calculated position of the satellites would drift away from the real position if their clocks are "wrong", so you would get some errors after a while if the error does not get corrected.

A GPS receiver with an atomic clock would get wrong distances, indeed - but it would take a long time for them to become negative.

Mfb, would you mind explaining (briefly) how GPS receivers without atomic clocks actually make those calculations, just for me to understand how a clock running ahead can affect the calculated position?

 

[mfb]

GPS satellites send their position and their current timestamp.

A receiver gets data which looks a bit like that:

Satellite 1: [Position in space 1], 9.6.13 1:25:03.454625364
Satellite 2: [Position in space 2], 9.6.13 1:25:03.452124145
Satellite 3: [Position in space 3], 9.6.13 1:25:03.455839951
Satellite 4: [Position in space 4], 9.6.13 1:25:03.453602913

The is a difference of 0.002501219 seconds between satellite 1 and 2, indicating that satellite 1 is 750km closer to the receiver than satellite 2. Satellites 3 and 4 give two additional differences, so we have three parameters to determine the position in space (and the time can be determined, too).

If all clocks run too quick by 2 parts in a billion, this shifts all times by 250ms in 20 years - it will break any direct comparison with atomic clocks on earth, but it does not influence the usual method to determine the position. The differences are shifted by the same amount, of course, but 2 parts in a billion just correspond to a few millimeters - not an issue.
Within 250ms, the satellites move about 1km. If you do not correct that, the position will be wrong.

 

[edraganov]

GPS satellites send their position and their current timestamp.

A receiver gets data which looks a bit like that:

Satellite 1: [Position in space 1], 9.6.13 1:25:03.454625364
Satellite 2: [Position in space 2], 9.6.13 1:25:03.452124145
Satellite 3: [Position in space 3], 9.6.13 1:25:03.455839951
Satellite 4: [Position in space 4], 9.6.13 1:25:03.453602913

The is a difference of 0.002501219 seconds between satellite 1 and 2, indicating that satellite 1 is 750km closer to the receiver than satellite 2. Satellites 3 and 4 give two additional differences, so we have three parameters to determine the position in space (and the time can be determined, too).

If all clocks run too quick by 2 parts in a billion, this shifts all times by 250ms in 20 years - it will break any direct comparison with atomic clocks on earth, but it does not influence the usual method to determine the position. The differences are shifted by the same amount, of course, but 2 parts in a billion just correspond to a few millimeters - not an issue.
Within 250ms, the satellites move about 1km. If you do not correct that, the position will be wrong.

Thank you very much, MFB! Everything is much more clear to me now!

Just to make sure I'm really in the same page: since the receiver does not rely on an internal atomic clock and thereby calculates relative distances based on satellites timestamps, relativistic effects are not much of a problem, since the differences between satellites are going to shift accordingly. However, after many years, when satellite clocks are running well ahead, given that the satellite is orbiting Earth on a certain speed, the receiver will get consecutive timestamps from all satellites with a greater variance in time in comparison with the last ones received from the same satellites. This will lead to wrong calculations since it will look like all satellites are in a position far ahead than their current one. Am I correct?

 

[mfb]

Well, the calculated position in space for the satellites gets wrong, if the satellites do not adjust their own position from time to time. They have to do this anyway, it is not possible to determine the orbit for 20 years in advance with a precision of centimeters.

 

[edraganov]

Well, the calculated position in space for the satellites gets wrong, if the satellites do not adjust their own position from time to time. They have to do this anyway, it is not possible to determine the orbit for 20 years in advance with a precision of centimeters.

Got it! Thank you very much, once again!

 

[Naty1]

lots of good information here:

http://en.wikipedia.org/wiki/GPS_system#Navigation_equations

and in the related links at the bottom of the article.

 

[pervect]

Hello everyone,

Although I am not a physicist, I have been trying to understand the relativity effects on GPS clocks.

It's seems pretty logic, however I've stumbled upon on a specific issue:

Given a atomic clock without any kind of relativistic adjustment, if the GPS clock is running ahead of the Earth clock, the time when the signal was received is probably going to be behind the time the signal was sent. If the distance is measured by C(T1-T0), this will lead to a negative distance.

In my mind, the GPS system wouldn't be imprecise, it simply would not work at all! Am I right?

Thanks in advance,
Erik

Did you know that the GPS atomic clocks (which are in the satellites, and not the recievers) had to have their frequency adjusted to account for relativistic time dilation effects?

In the early days, people weren't sure about GR yet, so they "turned off" the clock frequency adjustment (they built the clocks so the adjustment could be turned on and off), saw that it was needed, and of the correct value, and turned it back on again.

Also, the atomic satillite clocks are updated occasoinally, to insure they remain synchronized with the ground statitons.