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

TL;DR

This paper enhances the Chinese Remainder Theorem for multiple numbers by integrating statistical methods and maximum likelihood estimation to improve robustness against arbitrary errors in ambiguity resolution tasks.

Contribution

It introduces an extended RCRTMN method that incorporates MLE, enabling the handling of unrestricted errors and improving robustness in CRT-based estimation.

Findings

Enhanced robustness to arbitrary errors in residue-based estimation.

Effective integration of statistical methods with RCRTMN.

Significant improvement in ambiguity resolution accuracy.

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.