The problem of wide-angle astrometry via interferometry is to recover the two coordinates for each star from the observed delays. In the absence of atmospheric turbulence, the geometrical delay can be defined as: dG, ij(t) ≡ dj(t) ‒ di(t) = Bij(t)·ŝ0 ‒ Cij. Here the geometrical delay is the difference between the delay line lengths di and dj that is required to equalize the effective optical paths from the star to the point of beam combination via each of two apertures i and j. Bij(t) is the baseline between the apertures, ŝ0 is the star position, and Cij is the difference between the ‘fixed’ internal optical path lengths Ci and Cj within the instrument. In principle, sufficient delay measurements would allow solution for the baseline vectors and the delay constants, as well as the positions of the stars. However, the actual situation is greatly complicated by the presence of the atmosphere and the fact that neither the delay ‘constants’ Cij nor the baseline vectors are stable over time. The design of, and the analysis of the data from, any ground-based optical interferometer must overcome all three of these effects. The design, operation, and the analysis of data from the Navy Prototype Optical Interferometer (NPOI) are presented here as examples of how to overcome the effects of the atmosphere and the instrumental instabilities in order to achieve accurate wide-angle astrometry. The status of the implementation of these techniques at the NPOI is presented.