[willis936]

Phase-locked loops[0] are not magic ;)

Also I imagine they are using a bog standard Kalman filter[1].

0. https://en.wikipedia.org/wiki/Phase-locked_loop

1. https://en.wikipedia.org/wiki/Kalman_filter

[Unklejoe]

I've implemented this (using GPS PPS to discipline a clock) using regular old PI control loops. I just make the loop damped enough to filter out the GPS PPS jitter and you're good.