But you are relying on a third party / network. Your rubidium clock is only good for accurately measuring the length of a second. It has no idea when a UTC second begins. You are relying on GPS time in order to know when the UTC begins.
You need time and frequency for "proper time."
You can measure the angle of the sun to sync with UTC. I believe you can get within seconds using commodity equipment.
edit: A paper from 1989 on the subject: http://tycho.usno.navy.mil/ptti/1989/Vol%2021_14.pdf