Clock of GPS receiver

As I understand, GPS is supposed to work because :

• You have 4 (or more, but let's say 4) satellites whose clocks are extremely highly synchronized (through atomic onboard clocks)

• You have a receiver that receives 4 pings / messages from these satellites, each containing a timestamp of date of emission wrt to the "GPS time"

• Supposing the receiver time / clock only has a bias wrt to GPS time (ie, a fixed, constant error), you can from these 4 signals and the map of satellites position, deduce your 3 cartesian coordinates + the time bias error of your receiver clock wrt to GPS time.

That's all fine in theory, but in practice :

• The timing accuracy we are looking for is in nanoseconds (as there is c involved and the goal is to achieve metric-like accuracy on pseudo-ranges)

• So is it technologically "easy" to ensure that the actual "sending" of the signal by the GPS satellites is at the actual timestamp of the atomic clocks ? I mean, it's going through an electronic system, then a real-world, physical, analog antenna. I'm not talking about adding a known delay (which is not a problem as it can be accounted for as long as it is known), but what about unknown delay / jitter ? For example, is it "easy" to ensure that the analog antenna's emission date is within requirements / specs ?

• Same question with the antenna / circuitry of the receiver ?

• Additionally, on the receiving end, there is also problem of jitter / repeatability of the "time bias" wrt to the GPS clock. Since we're actually looking for nanoseconds, this seems not obvious. I get / guess the receiver has a well-known stable quartz (or similar) low frequency clock and a jittering VCO for nanoseconds granularities ? And the jitter of this VCO is low enough to allow ignoring it when solving the GPS equation system supposing a fixed biais ?

Of course, feel free to move the question elsewhere if Electrical Engineering is not the adequate community (in the end the question is I think more about pure circuitry than aeronautics, so I chose to ask it here, but I may be wrong).

So is it technologically "easy" to ensure that the actual "sending" of the signal by the GPS satellites is at the actual timestamp of the atomic clocks ?

Delays of onboard electronics are no concern, as long as they are constant. The clock offset of the space vehicles z-count against GPS-time is compensated as a whole. Variable delays, such as jitter, are a concern, but atomic clocks have excellent phase noise performance.

Phase center stability of the antenna is also a concern, the signal should (seem to) originate from a well defined point in the space-vehicle. This is by no way easy, f.e. the DoD got it wrong when they hooked a L5-demonstration-payload on SVN47. This equipment introduced an elevation dependant phase shift on the signal, rendering the whole space-vehicle unusable for navigation purpose. (read the story at InsideGNSS).

Same question with the antenna / circuitry of the receiver ?

The receiver uses one Antenna, one LNA, one VCO, one mixer, one filter and one ADC for all the signals. Dispersion (delay depending on frequency) is no concern, all signals occupy the same frequency. Any delay will affect all the signals the same way, the relative timing of the signals is not affected. Delays will only result in a local clock error, not in a position error.

Local oscillator phase noise will also result in local clock error and not affect positioning. It can seriously restrict the receivers ability to track the signal, but relatively cheap temperature compensated crystal are OK.

The receiver does not take timestamps, it rather evaluates the relative phase of the signals. In order to cope with such a high frequency, L1 (1575.42MHz) is downconverted to an IF of, lets say, 4.096 Mhz and sampled at 10MHz (equivalent to 100ns) clock. It is important to understand that this downconversion does not affect position accuracy, as one cycle phase shift of L1 translates into one cycle for IF.

This way, the receiver can easily detect a phase shift of one cycle, which corresponds to 19cm line of sight. (So why do receivers not have 19cm DOP? The answer does not fit here).

Direction dependant delay in the antenna is a concern for precision GPS, as is the reception of reflected signals (multipath). Precision receivers use choke-ring-antennas or even fractal element antenna to mitigate.

I get / guess the receiver has a well-known stable quartz (or similar) low frequency clock and a jittering VCO for nanoseconds granularities ?

Phase noise (power spectral density) of a TCXO is around -100dBc/Hz at 100Hz offest from nominal. The PLL/VCO will add a few dB. This phase noise affects the SNR in a complicated way. As long as you do not track extremely weak signals or need to track fast receiver dynamics (like a rocket guidance), this performance is OK.

More precise oscillators can be used to enhance performance in different ways, for example by using narrower (digital) filters.

And the jitter of this VCO is low enough to allow ignoring it when solving the GPS equation system supposing a fixed bias ?

See above, you need not consider jitter for position errors,as it affects all signals by the same amount.

• Since the relative timing of the satellite signals is not changed through the antenna cable, the receiver actually reports the position of the antenna, not of the receiver itself. Feb 12, 2017 at 22:03
• @PeterBennett True. Did I tell otherwise? Feb 12, 2017 at 22:06
• no, but I wanted to make it clear for less-technical readers. No criticism intended. Feb 12, 2017 at 22:09
• @PeterBennett Hmm yes, "relative timing" describes it better, I will add it to my answer. Thanks. Feb 12, 2017 at 22:15
• Also, I'm not sure what you're trying to say in your answer to the second question. One cycle of the L1 carrier corresponds to about 19 cm. One cycle of a 10 MHz clock would correspond to about 30 meters. Feb 12, 2017 at 22:28

A few additional bits to Andreas's answer:

So is it technologically "easy" to ensure that the actual "sending" of the signal by the GPS satellites is at the actual timestamp of the atomic clocks?

GPS is one of those things were the basic concept is simple enough to understand, the implementation is a nightmare. If anyone ever tells you that they know everything about how GPS works or that anything to do with it is easy then they are either a) A lair, b) To stupid to realize how much they don't know or c) have at least 7 PhDs in various branches of maths and physics.
So not "easy". But they cheat a bit. There is a network of monitoring stations that are constantly sending correction information to the SVs, mostly they are correcting the orbital information that is broadcast but they also monitor and send corrections for the clocks. As long as the delays within the electronics remain constant and low jitter they can be corrected for.

I get / guess the receiver has a well-known stable quartz (or similar) low frequency clock and a jittering VCO for nanoseconds granularities? And the jitter of this VCO is low enough to allow ignoring it when solving the GPS equation system supposing a fixed bias?

A good GPS commercial will have a TCXO selected not necessarily for it's accuracy (that can be corrected for, you have to correct for it anyway since it's never going to be atomic clock accurate) but for a very low phase noise which is the measure of jitter in the clock output.

The receivers work by creating a local copy of the signal they expect to see and then trying to line that up against the incoming signal. They aren't ever looking at a single sample, the signal is too weak for that, they are looking at a large collection of samples taken over a reasonable time period. Clock jitter in the receiver will decrease how well these two copies match and so will reduce the SNR of the signal however the time period being compared is long enough that local jitter will tend to average out and so have a relatively small impact on the accuracy of the measurements.

• Let's not deter people from starting DIY GPS projects. Building and maintaining a a space- or control-segment is hard, but you can receive the signal with a homebrew baseband. Not easy, but can be very rewarding. Feb 13, 2017 at 10:03
• True. But then complete understanding is never required to make use of anything. I wasn't trying to discourage anyone, the point I was trying to get across is that just about any explanation you get is going to be a simplified version, don't assume it's complete. That doesn't mean it's not good enough for your use. The Newtonian laws of motion are a simplification but they are perfectly good for most applications. Feb 13, 2017 at 12:41
• I agree. I'm fully aware my answer is a simplification. Still hope it helped the OP understand that it does not take a delicate lab setup to receive GPS. It seems to be his misconception, that the receiver has to measure time intervals with high precision. Feb 13, 2017 at 12:57
• Thanks @Andrew for your answer too. It was a bit too early for me a couple days ago (still had to digest Andreas' answers first), but now your addition makes a lot of sense and explains some of the new questions I've been having, especially your last paragraph. Feb 15, 2017 at 12:12

The reason why it needs four satellites can be simplified as follows:

• the first supplies the accurate time reference;
• the second supplies the radial distance giving a sphere;
• the third supplies an intersecting radial distance and we are left with an arc;
• the fourth intersects the arc giving two points, one in space and the other close to the surface of the earth.

The algorithm in the GPS receiver uses a statistical model to obtain the best fit and remove outliers, calculating the position and absolute time.

Each satellite must have a very accurate clock and broadcast its own accurate position.

Yes, with long antenna cables compensation in the receiver is required to reproduce very accurate time signals.

• Your mental model is overly simplistic. You get a radial distance from the first satellite, too. So, once you have measurements from four satellites, you have enough information to solve for four unknowns without any ambiguity: the receiver's X, Y and Z location, plus its clock bias. Feb 12, 2017 at 21:39
• @Dave you need accurate time to get distance, or accurate distance to get time. You need two satellites to get distance and time. The clock bias you mention is accurate time. (I think we are saying the same thing here...) Feb 12, 2017 at 21:59