They need recalibration after every 1-2 sorties for best results but they don't require input from GPS or other sensors. GPS synchronization largely eliminates the need for support staff to recalibrate. INS is incredibly accurate on its own, assuming pre-flight calibration.

Source: Worked on said GPS/INS systems in the military.

And what do you use to tell it where exactly it is during pre-flight calibration?

They "require" GPS input in the sense that if I handed you an INS that was initialized/calibrated with some precision (Oministar/RTK/P-code GPS/ whatever) reference but had been running in the trunk of my car (or dangling from the collar of a feral cat) for N hours/days, there's no way you'd fly a plane with it without initializing it with some sort of position referene.

(If you came up with "sit it on some previously surveyed datum, and you don't need GPS" on your own, you get an A)