Optimal estimates of common remainder for the robust Chinese Remainder Theorem

• We give two optimal estimates of common remainder for the robust Chinese Remainder Theorem.
• Two different optimal estimates are obtained based on the different definitions of circular distance.
• Simulation results show that the two optimal estimates have nearly the same performance.
• The second optimal estimate has less computational complexity than the first one.
• These optimal estimates can improve the efficiency of estimating the common remainder.

Common remainder is significant to the estimation of the robust Chinese Remainder Theorem (CRT). This paper presents two optimal estimates of common remainder for the robust CRT. The two different optimal estimates are obtained based on different definitions of circular distance. Both of the two estimations are more effective with lower computational complexity than the existing searching method. Simulation results show that the two estimations have nearly the same performance, however, the second optimal estimation has less computation than the first one. These optimal estimates can improve the performance of the estimation of the robust CRT.