Optimal estimation of the amplitude of signal with known frequency in the presence of thermal noise *Project supported by the National Natural Science Foundation of China (Grant No. 11575160). (September 2019) - Luo 罗, Jie 杰; Ke 柯, Jun 俊; Liu 柳, Yi-Chuan 一川; Zhang 张, Xiang-Li 祥莉; Yin 殷, Wei-Ming 蔚明; Shao 邵, Cheng-Gang 成刚
Abstract : In the torsion pendulum experiments, the thermal noise sets the most fundamental limit to the accurate estimation of the amplitude of the signal with known frequency. The variance of the conventional method can meet the limit only when the measurement time is much longer than the relaxation time of the pendulum. By using the maximum likelihood estimation and the equation-of-motion filter operator, we propose an optimal (minimum variance, unbiased) amplitude estimation method without limitation of the measurement time, where thermal fluctuation is the leading noise. While processing the experimental data tests of the Newtonian gravitational inverse square law, the variance of our method has been improved than before and the measurement time of determining the amplitude with this method has been reduced about half than before for the same uncertainty. These results are significant for the torsion experiment when the measurement time is limited.