I can't understand why GPS reciever clock is very good (stratum 0). I know it's very accurate and pure within itself; but when it passes through a long distance wireless channel, then it has low power and much noise and jitter, so how it can be better than other clocks?
A GPS receiver creates a local replica of something called "GPS system time", which is a virtual timebase created from all of the clocks on the satellites and ground stations. This replica is integral to the process of coming up with a navigation solution, which is based on measuring the signal delay from each satellite to an accuracy on the order of nanoseconds.
The algorithm that keeps this replica synchronized guarantees that there is no long-term drift with respect to GPS system time. Furthermore, it is specifically designed to deal with the errors introduced by the radio channels, so there is minimal jitter as well.
It is relatively easy to provide outputs based on this replica timebase, typically in the form of 1 pps or 10 MHz logic-level signals. Usually, the biggest source of jitter in these outputs is due to the fact that the replica timebase is asynchronous with respect to the receiver's own physical clock.
Therefore, the peak-to-peak jitter of these outputs is usually equal to the local clock period1, the short-term stability is equal to the stability of the local oscillator2 and the long-term stability is equal to GPS system time, which is based on atomic clocks. A PLL can easily filter out the jitter if the application requires it.
1 Many receivers have 10.23-MHz local clocks, which is why you frequently see a specification of ±50 ns on the 1 pps output.
2 Quartz oscillators generally have very good short-term stability. In fact, the best laboratory-grade quartz oscillators have better short-term stability specs than cesium time standards.
Simply because the system is more than good enough to do what's asked of it.
The power is low, but it's enough for a sensitive receiver with a clear view of the sky to reconstruct with high reliability. In fact, it's not just good enough that a receiver can decode and synchronize to the bit pattern, as the original design intended; it's good enough that a clever receiver can oversample it and measure the phase within a fraction of a bit time under good conditions.
The ionosphere causes path-dependent signal delays, but there are several effective ways of mitigating that, including multi-frequency reception (which allows inferring the ionospheric density — and thus the total delay — from the differential delay at two different frequencies), and augmentation systems (ground-based, satellite-based, and internet-based), which measure ionospheric and other slow-moving residual errors on the ground, build geometric models, and then disseminate them to receivers so that those errors can be canceled out.
Further, there are usually many satellites in view at any one time — generally 8 or more GPS satellites at once for a receiver with a clear sky view, and potentially many more for a multi-system receiver (GPS, GLONASS, Galileo and/or BeiDou). Many satellites means a wealth of information that a receiver can filter and combine, using consensus algorithms, to produce better results than any satellite alone can provide.
Lastly, really accurate GPS clocks derive good time by understanding where GPS's strengths lie. Even given everything I've said above, GPS timing is subject to jitter and other sources of short-term error. However, its long-term accuracy (as long as the system continues to be maintained from the ground by the US) is ultimate. Decent oscillators (from TCXO on up) are capable of better short-term accuracy than GPS, but every oscillator is inevitably subject to aging and drift over the course of hours, weeks, and years. A good clock has these sources of error characterized, and then its control system designed so that its short-term accuracy represents that of the oscillator, and its long-term accuracy represents that of the GPS system, again, creating something better than both. The better the oscillator is, the less the short-term errors of GPS need to be allowed to steer the system, and the better the clock can be overall.
In short, I would say, the system works because it was engineered to work in the 1970s, and our technological capabilities have generally increased in the past 4-5 decades, so now it works even beyond expectations.
There are 16 Stratum levels which degrade the phase noise and phase error and thus position accuracy . Not all levels are used in a network but there can only be one Level 0. Special ruggedized SC cut crystals that are a million times more stable than an AT cut crystal have an optimum flat temperature sensitivity in an Ovenized can.
The clocks in GPS Rx may have the phase noise and tuning range of down to a Stratum 4 clock with NTP digital correction on latency from >4 satellites if done well. Although the 10MHz is adequate for some but are inadequate for applications that need differential GPS RF synthesis due to phase noise unless local OCXO Stratum 2 capable clocks are used.
PC clocks are not Stratum Level clocks since they only correct seconds and not frequency so continual time corrections are done unless a local NTP network is needed.
I have read the 200+ page book on Time & Frequency Standards , so if you need to learn more , there is much more to learn. I have also designed Doppler Nav Systems since 1975 before you and GPS were “born”. However they were in the design stage with only 1 GOES sat.