Closed-form, robust and accurate multi-frequency phase unwrapping: frequency design and algorithm

A closed-form algorithm, named “concerto”, is proposed for phase-based distance estimation in multi-frequency phase unwrapping (MFPU) system. The concerto method consists of three coherent estimation stages,i.e., initial modified BW estimation, residual error estimation and LS estimation , each of which has a closed-form expression and cooperates closely with each other like a concerto. Due to a specially designed frequency pattern, concerto is reliable, accurate, and computationally simple. Meanwhile, measurement frequency selection is an easier task. Performance comparisons with beat wavelength (BW), excess fractions (EF) and Chinese remainder theorem (CRT) method confirm that our method outperforms these methods both in accuracy and reliability and can asymptotically achieve the Cramér-Rao bound (CRB).