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

TL;DR

The paper introduces 'concerto', a closed-form, robust, and accurate multi-frequency phase unwrapping algorithm that outperforms existing methods in accuracy and reliability, with simpler frequency selection.

Contribution

It presents a novel closed-form algorithm with a specially designed frequency pattern for reliable and accurate phase unwrapping, simplifying frequency selection.

Findings

Outperforms BW, EF, and CRT methods in accuracy and reliability.

Achieves asymptotic CRB performance.

Features a computationally simple and reliable frequency pattern.

Abstract

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 Cramer-Rao bound (CRB).