What has become known as the “Incompleteness Theorem” asserts that no statement can prove its own truth. One of the well-known analogies is that no one can lift themselves up in the air by their own bootstraps, no matter how hard they pull.
Verification of the positional stability/drift, accuracy, and position resolution of a closed-loop positioning system requires an independent sensor (of higher accuracy). In the nanopositioning world, the most credible results come from a standards-traceable instrument, such as a laser interferometer because it measures distance directly using the wavelength of light. Good laser interferometers are expensive and the setup requires trained technicians and a stable, vibration and temperature controlled environment.