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 t...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.展开更多
Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the th...Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11575160)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160 and 11275075)the Natural Science Foundation of Key Projects of Hubei Province,China(Grant No.2013CFA045)
文摘Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.
