I have done some work in farm irrigation systems where 2cm precision is required.
The main system I have used is RTK GPS which has a cost upwards of $30,000 for the GPS gear alone. It is reliable and accurate easy to implement but I'm glad that I'm not paying the bill. Not for you, but just letting you know that GPS can be very accurate.
The second best system that they use is a buried wire which transmits a signal which is in turn picked up by a couple of sensors like a radio version of the "white line" robot. This may be your best bet.
The third system that they use is furrow guidance where a dolly wheel tracks a furrow in the ground. No good for you.