Efficient methods for the linearization and solution of phase-invariant equations

This paper describes a linear least-squares procedure, whereby, through quadrupole relationships, the 2 pi integers that linearize sets of unique phase-invariant estimates can be determined. It is subsequently shown that the phase solutions for these linear equations can be obtained, even for basis sets of thousands of phases, without having to either build or invert the full least-squares matrix. The final r.m.s. phase errors achieved by this method can typically be less that 5 or 10 degrees.