As described above the issue would be continuous observation, not how to follow it assuming you never lose sight of it.
You certainly can't do continuous observation but even just with commercial satellite offerings you can get pretty close.
For example nowadays Planet Labs [1] offers 30-50cm resolution imaging at a rate of one image or 120sec video stream every 90 minutes over a given 500 km^2 region. There is no situation where an aircraft carrier is going to be capable of evading a commercial satellite offering with that frequency and resolution. Once you know approximately where it is or even where it was in the semi-recent past, it's fairly trivial to narrow in and build a track off the location and course.
Commercial operations like Planet Labs currently cover most of the Earth multiple times a day.