A robust Chinese remainder theorem with its applications in moving target Doppler estimation

Abstract

The Chinese remainder theorem (CRT) is an ancient result about simultaneous congruences in number theory, which reconstructs a large integer from its remainders modulo several moduli. It is well known that the CRT has tremendous applications in many fields, such as computing and cryptography, an important one of which could be radar signal processing and radar imaging. However, it is also well-known that CRT is not robust in the sense that a small error in any remainders may cause a larger error in the reconstruction result, which will lead to a non-robust estimation. In this paper, we introduce a robust reconstruction algorithm called robust CRT. We show that, using this robust CRT algorithm, the reconstruction error is upper bounded by the maximal remainder error range named remainder error bound, if the remainder error bound is less than one quarter of the greatest common divisor (gcd) of all the moduli. Although CRT has existed for about 2500 years, this robustness is the first time in the literature. Then, we show how this robust CRT can be used into the field of radar detection and Doppler ambiguity resolution, especially for fast moving targets, and later, simulations are given to illustrate the effectiveness and validness of this robust CRT algorithm.