Recently i tested a dual band GNSS receiver (NEO F10N) with a helical antenna outside yet close to the window - roughly half sky view. Height determinations once a second exhibited a rms of about 1 m, which corresponds to 3 nsec. Of course, in order to get there, one will need a fairly complex correction scheme.
I just executed a similar exercise synchronizing a local clock (STM32 RTC) using LwIP with SNTP, with a time comparison every 120 seconds. Averaging 30 of those time comparisons i got 0.14 msec RMS during a week. This is with the RTC clock inside a thermal chamber. The systematic error yet unknown might amount to some msec.
In the case of GPS there will be systematic errors, too: antenna cable and other communication delays, maybe 50 nsec.
I hope to do the triple comparison soon: RTC, SNTP and GPS. And the GPS antenna should move above the roof to get the full sky view.
Precision time isn't something easy. For example there is a difference of 18 seconds between our local time as reported by the SNTP and GPS as GPS ignores leap seconds. Don't know yet what happens when using GNSS. Looks like Galileo implements UTC and takes leap seconds into account.
If the OP question isn't about time but about frequency: Assuming a jitter of 3 nsec, in order to reach a nominal 10E-13 accuracy one needs about one day of second pulses. After an hour one reaches about 10E-12, good enough to calibrate a Rubidium oscillator. The NEO F10N receiver has a configurable reference frequency output and a TXCO. Doing the comparison at 10 MHz instead of 1 Hz should be somewhat faster.
Regards, Dieter