A Generalized Robust Chinese Remainder Theorem of Dual-Band Integers for Phase Unwrapping

The traditional CRT based algorithms have been proposed to solve the problem of range estimation with multi-frequency phase unwrapping, where the wavelengths of the multi-frequency signals should to be pair-wisely co-prime after they are divided by their greatest common divisor (GCD). To get a robust reconstruction result, the upper bound of the remainder errors should be smaller than a quarter of the GCD of all the moduli. In this paper, the generalized dual-band robust CRT is presented to reconstruct the distance from dual-band wrapped phases, where the pair-wisely co-prime condition is relaxed, and the error levels of the two groups of remainders are different. It is shown that when signals can be robustly retrieved in each band, the reconstruction across the two bands by the proposed algorithm is robust too. The theoretical analysis and simulation results show that the proposed method can achieve better performance than the previous works.