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

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