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Tech2025
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Why do GPS need a cesium clock accurate to 10ns? Is this strictly for time keeping or is there some synchronization between satellites?
Simplistically, the signal from a particular satellite gives you your current distance from that satellite. This is determined by subtracting the time when the signal was sent from the time it was received. The accuracy of those times determines the accuracy of the position fix.Tech2025 said:Why do GPS need a cesium clock accurate to 10ns? Is this strictly for time keeping or is there some synchronization between satellites?
If you have an accurate clock, and a satellite with a known position broadcasts a time signal, then you can compare the time on your accurate clock with the time signal from the satellite and you know the distance to the satellite. That tells you that your position is somewhere on a sphere of a known radius centered around that satellite.Tech2025 said:Why do GPS need a cesium clock accurate to 10ns? Is this strictly for time keeping or is there some synchronization between satellites?
Because GPS *is* a collection of clocks. Comparing the timing of the signals from the satellites is how the system works!Tech2025 said:Why do GPS need a cesium clock accurate to 10ns? Is this strictly for time keeping or is there some synchronization between satellites?
You'd still need clocks if they were stationary because GPS essentially uses ranging via signal delay.Janus said:The satellites are not in geostationary orbits, which means they are over different points of the Earth at different times . To know where a particular one is when using it to get a position fix, you have to know when it is.
Sorry to piggyback on this thread but this is something I have been wondering about for a while and I still have not found a satisfactory answer.jbriggs444 said:Simplistically, the signal from a particular satellite gives you your current distance from that satellite. This is determined by subtracting the time when the signal was sent from the time it was received. The accuracy of those times determines the accuracy of the position fix.
Of course, that simple strategy would require your own GPS unit to carry a well-synchronized atomic clock. So the truth is a bit more complex. With four satellites in view, one can receive signals from all four and solve a set of four simultaneous equations to determine your 3 dimensional position plus current time.
I imagine that it's easier to have the times running as near correctly as possible so that the drift is easier to compensate for. The satellites are constantly being updated, afaiia by referencing known positions and times on Earth stations.Nick89 said:Can anyone enlighten me? :)
We are talking about a control loop here. When you design a system that involves control loops you have to consider stability, loop delay and the acceptable error. Dragging a very stable oscillator back to an agreed frequency value (and the ones in all the other satellites too) can introduce problems so, even if they could get away with a lower stability 'on a good day', why make life difficult?Nick89 said:First of all, I don't see how having the times "as near correctly as possible" simplifies the daily drift corrections. Does it matter if you have to correct 2 nanoseconds or 2 milliseconds or even 2 years drift? It seems just as easy to me regardless of how much drift you are correcting for.
But alright, I can see that it would be preferrable to have the clocks stay roughly in sync with Earth just because it "would be nice". But I think you both agree that it is not strictly necessary? That means that in fact all of these articles (I'm not going to bother finding sources but look at any random article about GPS) claiming "GPS would not work without SR/GR corrections" are wrong? In fact GPS would work just fine without the corrections.
No. The relativistic corrections are needed to account for the relative motions between satellites and receivers, and for gravitational effects on signals between satellites and receivers.Nick89 said:That means that in fact all of these articles (I'm not going to bother finding sources but look at any random article about GPS) claiming "GPS would not work without SR/GR corrections" are wrong? In fact GPS would work just fine without the corrections.
One answer is that the role of GPS is to determine our location in 4D space (including time), not just 3D.Nick89 said:In fact GPS would work just fine without the correction
https://en.wikipedia.org/wiki/Global_Positioning_System#More_detailed_description said:Each GPS satellite continually broadcasts a signal (carrier wave with modulation) that includes:
Conceptually, the receiver measures the TOAs (according to its own clock) of four satellite signals. From the TOAs and the TOTs, the receiver forms four time of flight(TOF) values, which are (given the speed of light) approximately equivalent to receiver-satellite ranges. The receiver then computes its three-dimensional position and clock deviation from the four TOFs.
- A pseudorandom code (sequence of ones and zeros) that is known to the receiver. By time-aligning a receiver-generated version and the receiver-measured version of the code, the time of arrival (TOA) of a defined point in the code sequence, called an epoch, can be found in the receiver clock time scale
- A message that includes the time of transmission (TOT) of the code epoch (in GPS time scale) and the satellite position at that time
In practice the receiver position (in three dimensional Cartesian coordinates with origin at the Earth's center) and the offset of the receiver clock relative to the GPS time are computed simultaneously, using the navigation equations to process the TOFs.
...
It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is only the case if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are significant performance benefits to the user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If this were an essential part of the GPS concept so that all users needed to carry a synchronized clock, then a smaller number of satellites could be deployed. However, the cost and complexity of the user equipment would increase significantly.
I would start here:Nick89 said:Can anyone enlighten me? :)
You missed the point/the daily correction issue is pulling you off in a different direction. The problem started is that every receiver would need an additional, real-time correction built into the position calculation. Otherwise by the end of the day they'd be way off. in short: 1-2ns isn't a big deal, but 38ns is. This is a continuous problem, separate from/on top of the daily calibrations.Nick89 said:First of all, I don't see how having the times "as near correctly as possible" simplifies the daily drift corrections. Does it matter if you have to correct 2 nanoseconds or 2 milliseconds or even 2 years drift? It seems just as easy to me regardless of how much drift you are correcting for.
It's a bit of a nitpick: the way they are designed, the correction at the satellite clock level is a [zero effort] feature, so it must work properly for the system to work properly. But the system could have been designed differently - to include an additional calculation in the every receiver's workload as a workaround - and function almost as well.But alright, I can see that it would be preferrable to have the clocks stay roughly in sync with Earth just because it "would be nice". But I think you both agree that it is not strictly necessary? That means that in fact all of these articles (I'm not going to bother finding sources but look at any random article about GPS) claiming "GPS would not work without SR/GR corrections" are wrong? In fact GPS would work just fine without the corrections.
No, it is not just nice, it is necessary in order for GPS to meet its accuracy targets. However, it would be possible to move the correction to a different segment.Nick89 said:I can see that it would be preferrable to have the clocks stay roughly in sync with Earth just because it "would be nice". But I think you both agree that it is not strictly necessary?
Remember that there is a continuous error. You have to know the altitude of the satellite and unfortunately their orbits are continuously degrading and so that accuracy is limited.Dale said:If you have an accurate clock, and a satellite with a known position broadcasts a time signal, then you can compare the time on your accurate clock with the time signal from the satellite and you know the distance to the satellite. That tells you that your position is somewhere on a sphere of a known radius centered around that satellite.
Two such signals puts your position somewhere on the circle where the two spheres intersect. Three such signals narrows your position down to one of two points where all three spheres intersect. And four or more such signals only intersect in a single point. But you need an accurate clock for determining each radius.
There are some tricks you can do to use more satellites and a cheaper clock.
My understanding is the terrestrial clocks tick at one second per second, but the satellite clocks do not tick at one second per second with respect to their rest frame.jbriggs444 said:It presumably simplifies things a bit to have them tick at the same rate as the terrestrial master clock(s) they are synchronized against.
Right. They count off one notional second per second in the conventional GPS frame.David Lewis said:My understanding is the terrestrial clocks tick at one second per second, but the satellite clocks do not tick at one second per second with respect to their rest frame.
jbriggs444 said:Right. They count off one notional second per second in the conventional GPS frame.
An accurate clock is necessary for GPS because the system relies on precise timing to calculate the distance between the receiver and multiple satellites. This timing is used to triangulate the receiver's position on Earth.
If the clock used in GPS is not accurate, it can result in errors in the timing measurements. This can lead to incorrect calculations of the receiver's position, leading to decreased accuracy in GPS location.
The clock used in GPS is an atomic clock, specifically a cesium clock. This type of clock is extremely accurate and is used in many scientific and technological applications that require precise timing.
No, GPS cannot work without an accurate clock. The entire system is based on the concept of precise timing, and any errors in the clock will result in errors in the calculated position of the receiver.
The clock in GPS satellites is synchronized with ground control stations multiple times a day to ensure accuracy. This is necessary due to the effects of relativity and other factors that can cause the clock to drift slightly over time.