Maximum Likelihood Estimation Based Robust Multidimensional Chinese Remainder Theorem and its Fast Algorithm

In this paper, we study the multidimensional Chinese remainder theorem (MD-CRT) for vectors in the presence of erroneous remainders, where the remainder errors are modeled by a $D$-dimensional wrapped normal distribution. We propose a fast maximum likelihood estimation (MLE) algorithm for this problem, termed MLE MD-CRT, which extends the existing robust MLE CRT framework to multiple dimensions. Our method achieves the optimal estimate of the common remainder with only $D{×} L$ searches, where $L$ denotes the number of moduli, enabling direct reconstruction of the real vector via the MD-CRT. Furthermore, we establish a necessary and sufficient condition to guarantee the robust estimation using the proposed algorithm. To demonstrate its practical value, we apply the proposed algorithm to multidimensional sinusoidal frequency estimation. Simulation results confirm that it consistently outperforms existing methods.