Study on the Equivalence Between Nonlinear Least Squares Method and Correlation Method in Period Extraction of Torsion Pendulum

Abstract

Abstract. In the measurement of G using time-of-swing method, the accurate determination of G depends on the period extraction of torsion balance with high precision. There are a great many methods of extracting period, and the nonlinear least squares fitting method and the correlation method are most frequently applied to extract the torsion balance period accurately. Though some papers have claimed the two methods are equivalent, lacking in complete theoretical derivation. In this paper, the influence of Gaussian white noise on the period extraction accuracy by the two methods is theoretically derived detailedly and simulated in MATLAB. Both results show that although there exists some differences between two methods in process of data analysis, the accuracy of period extraction is still the same.