Originally developed as a method to assist in the assessment of optical components, the phase shifting technique has recently seen application to many other types of interferometers, including holographic, speckle, and moire systems for strain analysis. In these applications, close control of the phase shifts may be impossible due to the effect of mechanical vibrations, and this presents difficulties when extracting the phase, since the reference phase shifts are generally assumed to be known. Several approaches to the problem of determining the reference phase shifts in a perturbing environment are critically evaluated using computer simulations. The precision and accuracy of these methods are demonstrated through a practical solid mechanics example. It was found that the reference phase shifts can be determined with sufficient accuracy using all of the methods considered, and that the ultimate precision of the system was limited by additional factors -- particularly grating noise.