A generalized Chinese remainder theorem for residue sets with errors and its application in frequency determination from multiple sensors with low sampling rates

The Chinese remainder theorem (CRT) has been recently generalized from determining a single integer from its remainders to determining multiple integers from their sets (residue sets) of remainders. In this letter, we consider the generalized CRT when the residue sets have errors. We first obtain a sufficient condition on the number of erroneous residue sets so that multiple integers still can be uniquely determined from their residue sets. We then propose a determination algorithm of multiple integers from their residue sets with errors. Finally, we apply the newly proposed algorithm to multiple frequency determination from multiple sensors with low sampling rates and show the effectiveness of the proposed algorithm with considering residue set errors over the one without considering residue set errors.