Statistical Robust Chinese Remainder Theorem for Multiple Numbers: Wrapped Gaussian Mixture Model
This addresses ambiguity resolution in signal processing or coding theory, offering improved robustness for applications like radar or communications, but appears incremental as it builds on existing CRT frameworks.
The paper tackles the problem of robust reconstruction in Chinese Remainder Theorem-based multiple parameter estimation, where deterministic methods degrade exponentially with more estimands, and shows that their statistical scheme achieves stronger robustness, especially in low to median SNR scenarios.
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.