Noniterative method for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference

Abstract

We discuss how we can obtain noniteratively an exact solution for the modified normal equation in least-squares phase estimation from the measured phase difference. To achieve this, we introduce the idea of equivalent transformation of the measured phase difference into a periodic one. We perform this tranformation by using a geometric procedure based on mirror reflection. Computer simulation results indicate that the proposed noniterative algorithm works well, as was expected, and can overcome the difficulties caused by such singularities as isolated zero points.