Automated celestial navigation is actually surprisingly old technology, first being pioneered in the 1950s on the snark missile. Of course at first it was extremely unreliable, with the snark flying off target so often the part of the ocean the missiles were being tested in was humorously dubbed "snark infested waters" due to all the off target missiles that sunk there. But eventually people got better and did amazing things with relatively primitive tools, and by the '60s decently successful guidance systems using the stars were common place on ICBMS.

As to technical details, here is a write up of the NAS26 astro-inertial guidance system from the '70s:

http://www.dtic.mil/dtic/tr/fulltext/u2/a090649.pdf

The navy and the air force get all the coolest toys, I tell you what.