A generalized robust Chinese remainder theorem for multiple numbers and its application in multiple frequency estimation with low sampling rates

Generalized robust Chinese remainder theorem has been proposed to reconstruct one positive real number when all the moduli have a common factor and the remainders have errors. In this paper, we consider the generalized robust Chinese remainder theorem to reconstruct multiple numbers when all the moduli have a common factor and all residue sets have errors. We apply the newly proposed theorem to multiple frequency estimation with low sampling rates and show the accuracy and effectiveness of the proposed theorem.