Thread: GPS clock correction

I know that , before launch, the atomic clocks are frequency corrected according to the formula:




In addition to the frequency correction, there needs to be a time delay correction. If the launch takes in the frame of the launcher (Earth), then the satellite will be behind when it reaches the intended position on its orbit, so needs to be added to the atomic clock. I cannot find any mention of how this delay time is calculated, actually, I cannot find any reference to this subject at all. Nor am I sure how to calculate the very complicated integral. One idea is to neglect the terms in since . You cannot do this for the frequency correction because you would lose the gravitational effects but you could (?) do this for the time delay calculation. Any suggestions?

For practical uses, complicated integrals are probably just computed numerically. For something like a satellite launch, spending a few computer-days crunching numbers would be worth it. (I have no idea how long it'd take, but AFAIK any integral can be integrated numerically to any precision you want, given enough time.)

Originally Posted by MagiMaster

For practical uses, complicated integrals are probably just computed numerically. For something like a satellite launch, spending a few computer-days crunching numbers would be worth it. (I have no idea how long it'd take, but AFAIK any integral can be integrated numerically to any precision you want, given enough time.)

Thank you,
I am aware of that, I am looking for references.

I am not sure I understand the issue at hand - when the satellite is in operation, it will be in position in a predetermined orbit of known radius above earth; the only quantities that then need to be corrected for a relativistic effects from relative velocity and differences in gravitational potential. I don't see the relevance of the satellite's launch into orbit, since the GPS relies only on differences in signal times, not on absolute clock readings...or am I missing something here ?

You might find something here.
N. Ashby and J. J. Spilker, in Global positioning system:
theory and applications, Vol. I, edited by B. W. Parkinson
and J. J. Spilker (American Institute of Aeronautics and
Astronautics, 1996), pp. 623-697.

I did find out that the prelaunch correction is not an exact correction and the satellite clocks have to transmit an offset so the ground stations can correct the time signal.

Originally Posted by Markus Hanke

I am not sure I understand the issue at hand - when the satellite is in operation, it will be in position in a predetermined orbit of known radius above earth; the only quantities that then need to be corrected for a relativistic effects from relative velocity and differences in gravitational potential. I don't see the relevance of the satellite's launch into orbit, since the GPS relies only on differences in signal times, not on absolute clock readings...or am I missing something here ?

The frequency is corrected (decreased) at launch in order to make the clocks (ground and satellite) tick at the same rate.
Therefore, once placed in orbit, the satellite clock will accumulate a certain proper time
The ground clock will accumulate

So,



But is unknown, unless we calculate it.

Originally Posted by dan hunter

You might find something here.
N. Ashby and J. J. Spilker, in Global positioning system:
theory and applications, Vol. I, edited by B. W. Parkinson
and J. J. Spilker (American Institute of Aeronautics and
Astronautics, 1996), pp. 623-697.

I did find out that the prelaunch correction is not an exact correction and the satellite clocks have to transmit an offset so the ground stations can correct the time signal.

Thank you,

This is what I was getting at. Do you have the book?

Originally Posted by xyzt

Do you have the book?

No, but if you search googlebooks with a few keywords it might take you to the relevant pages.

Global Positioning System: Theory and Applications - Google Books

Originally Posted by dan hunter

Originally Posted by xyzt

Do you have the book?

No, but if you search googlebooks with a few keywords it might take you to the relevant pages.

Global Positioning System: Theory and Applications - Google Books

thank you, I am very familiar with the Neil Ashby chapter. Couldn't find anything on the time delay offset, just the frequency.

Originally Posted by xyzt

Originally Posted by Markus Hanke

I am not sure I understand the issue at hand - when the satellite is in operation, it will be in position in a predetermined orbit of known radius above earth; the only quantities that then need to be corrected for a relativistic effects from relative velocity and differences in gravitational potential. I don't see the relevance of the satellite's launch into orbit, since the GPS relies only on differences in signal times, not on absolute clock readings...or am I missing something here ?

The frequency is corrected (decreased) at launch in order to make the clocks (ground and satellite) tick at the same rate.
Therefore, once placed in orbit, the satellite clock will accumulate a certain proper time
The ground clock will accumulate

So,



But is unknown, unless we calculate it.

OK,

I found it. What I call is known as "receiver bias" . The calculation is done brute force, through a least square method. See here. It is interesting to notice that the method considers that the "receiver bias" varies with receiver position. If we consider that the GPS receiver contains an inexpensive "clock" whose frequency is not that stable, we can easily understand why the calculations are repeated at each iteration.
On the positive side, no need to calculate the complicated integral I was mentioning earlier :-)