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Generalized Chinese Remainder Theorem (CRT) has been shown to be a powerful approach to solve the ambiguity resolution problem. However, with its close relationship to number theory, study in this area is mainly from a coding theory perspective under deterministic conditions. Nevertheless, it can be proved that even with the best deterministic condition known, the probability of success in robust reconstruction degrades exponentially as the number of estimand increases. In this paper, we present the first rigorous analysis on the underlying statistical model of CRT-based multiple parameter estimation, where a generalized Gaussian mixture with background knowledge on samplings is proposed. To address the problem, two novel approaches are introduced. One is to directly calculate the conditional maximal a posteriori probability (MAP) estimation of residue clustering, and the other is to iteratively search for MAP of both common residues and clustering. Moreover, remainder error-correcting codes are introduced to improve the robustness further. It is shown that this statistically based scheme achieves much stronger robustness compared to state-of-the-art deterministic schemes, especially in low and median Signal Noise Ratio (SNR) scenarios.
Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our knowledge, i
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
Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to noises, t
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number of outliers
We prove the equidistribution of subsets of $(Rr/Zz)^n$ defined by fractional parts of subsets of~$(Zz/qZz)^n$ that are constructed using the Chinese Remainder Theorem.