  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, it is the first rigorous analysis on the underlying statistical
model of CRT-based multiple parameter estimation. To address the problem, two
novel approaches are established. One is to directly calculate a conditional
maximum a posteriori probability (MAP) estimation of the residue clustering,
and the other is based on a generalized wrapped Gaussian mixture model to
iteratively search for MAP of both estimands and clustering. Residue error
correcting codes are introduced to improve the robustness further. Experimental
results show that the statistical schemes achieve much stronger robustness
compared to state-of-the-art deterministic schemes, especially in heavy-noise
scenarios.
