On Solving Ambiguity Resolution with Robust Chinese Remainder Theorem for Multiple Numbers

2018/06/29 by Hanshen Xiao, Xiao, Hanshen, Guoqiang Xiao +1 · 1 citation
Earth and Planetary Sciences · Engineering · #FOS: Computer and information sciences #Geophysical Methods and Applications #Information Theory (cs.IT) #Seismic Imaging and Inversion Techniques #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1807.00022

openalex publication_date 2018/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Chinese Remainder Theorem (CRT) is a powerful approach to solve ambiguity resolution related problems such as undersampling frequency estimation and phase unwrapping which are widely applied in localization. Recently, the deterministic robust CRT for multiple numbers (RCRTMN) was proposed, which can reconstruct multiple integers with unknown relationship of residue correspondence via generalized CRT and achieves robustness to bounded errors simultaneously. Naturally, RCRTMN sheds light on CRT-based estimation for multiple objectives. In this paper, two open problems arising that how to introduce statistical methods into RCRTMN and deal with arbitrary errors introduced in residues are solved. We propose the extended version of RCRTMN assisted with Maximum Likelihood Estimation (MLE), which can tolerate unrestricted errors and bring considerable improvement in robustness.

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