GPS satellite and satnav receiver clock synchronisation

[quitequick]

As far as I understand it...

Each satellite transmits a signal that the receiver receives. This signal consists of (at least) a satellite identification together with a time-stamp of when the signal was sent and its position at that time. The receiver calculates the distance from the satellite by comparison of the time-stamp to its own internal clock (distance = speed-of-light x time-difference). With three different satellite signals the intersection of three spheres can be found and therefore the position of the receiver.

So, the accuracy of the receiver's clock against the satellite's clocks would seem to be critical - in fact fundamental to the accuracy of the distance measurement. But if the receiver does not know exactly how far away the satellite is, how could it accurately compensate for the delay in receiving a time synchronisation signal? Assuming that the receiver does not have an on-board atomic clock, any clock it does have will have to be sync'ed probably very regularly.

So the question is, how is the receiver's clock sync'ed to the GPS satellite's clocks, given that the receiver does not know far away the satellite is, so it can correct for the time-delay?

Sounds like a chicken and egg problem to me!

 

[chingel]

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

It seems that it is just assumed the clock is wrong by some amount, but wrong by the same amount during the time interval in which the signals from the different satellites arrive, which is probably a good estimate considering the small time interval. Then they just fit the time error of the clock such that the four spheres intersect in a single spot, or try to minimize the variation of the intersection point considering all the spheres or some other method.

 

[quitequick]

Thanks, chingel. The Wikipedia page lead me to...

http://web.archive.org/web/20110719232148/http://www.macalester.edu/~halverson/math36/GPS.pdf

which explains it thoroughly.

 

[davenn]

Thanks, chingel. The Wikipedia page lead me to...

http://web.archive.org/web/20110719232148/http://www.macalester.edu/~halverson/math36/GPS.pdf

which explains it thoroughly.

interesting paper, thanks for the link

I'm the tech working for a company that's sells GPS gear into the survey and heavy machine industry ... road construction, mining etc
I have to admit that, even working with precision GPS equip all day every day, there's still lots I don't know about the GPS basics. ( mainly because it isn't essential to repairing the equip)

I had to giggle with that 80metre accuracy comment in the opening lines.
we are now easily down to less than 10mm ( 1cm) 5mm is quite achieveable using 2 linked receivers

Dave

 

[pmacias]

I can explain the process of GPS satellite and satnav receiver clock synchronization. The accuracy of the receiver's clock is indeed crucial for the accuracy of distance measurements in the GPS system. However, the receiver does not need to know the exact distance to the satellite in order to synchronize its clock with the satellite's clock. This is because the GPS system uses a technique called "pseudorange" to estimate the distance to the satellite.

Pseudorange is calculated by multiplying the speed of light by the time difference between when the satellite's signal was transmitted and when it was received by the receiver. This time difference is measured using the receiver's own clock. So, even though the receiver's clock may not be perfectly synchronized with the satellite's clock, it can still accurately calculate the pseudorange.

The GPS system also uses a process called "differential correction" to further improve the accuracy of the receiver's clock. This involves comparing the time signals from multiple satellites and using the differences to adjust the receiver's clock. This is why GPS receivers often require an initial period of time to acquire signals from multiple satellites before providing accurate location information.

Additionally, many modern GPS receivers do have on-board atomic clocks, which are extremely accurate and do not require frequent synchronization. However, even if the receiver does not have an atomic clock, the regular synchronization with multiple satellites allows for accurate timekeeping.

In summary, the GPS system uses pseudorange and differential correction techniques to synchronize the receiver's clock with the satellite's clock, ensuring accurate distance measurements and location information. This eliminates the chicken and egg problem and allows for precise navigation using GPS technology.