Range estimation based on Chinese remainder theorem with optimal common remainder

Pulse Doppler (PD) radar combines the advantages of the range resolution of pulse system radar with the velocity resolution of continuous-wave radar. Therefore, it exhibits strong ground and moving clutter suppression capabilities. However, due to the high pulse repetition frequency of PD radar, range ambiguity exists in the detection of long-distance targets. This paper proposes an algorithm for range estimation of two targets based on the Chinese remainder theorem (CRT) with optimal common remainders. Firstly, the multi-pulse repetition frequency of PD radar and the apparent distance of two targets are utilized to construct the congruence equations in the case of apparent distance errors. By partitioning the set of common remainders into two subsets, the average dispersion between the two subsets is calculated to obtain the two optimal subsets. Besides, the closed-form solution of two optimal common remainder is obtained by adopting the property that the sum of the circular distances between the optimal common remainders and each element in the optimal subset is minimized. Finally, the true ranges of the two targets are reconstructed with the optimal common remainder and the ambiguous integers which need to be solved similarly. Consequently, the algorithm does not require the process of searching for an optimal solution and prior auxiliary information. Theoretical analysis and simulation demonstrate that the method proposed in this paper can effectively estimate the ranges of two targets while maintaining low computational complexity in the presence of errors in apparent ranges.