Least square procedures to improve the results of the three-parameter sine fitting algorithm

Abstract

The paper presents two approaches to improve the three parameter sine fitting algorithm and attain accurate estimates of the parameters of a sinusoidal signal corrupted by noise. As the four parameter sine fitting algorithm, which is usually adopted to improve the estimates of the three parameter algorithm, in theory, the proposed ones can be inserted into iterative schemes and repeated until a target precision is gained. Anyway, the use of the proposed algorithms is particularly suggested for those applications in which the results must be gained in very short times, which are in contrast to long iterative procedures. In these cases, when a single run of the algorithms has to offer the required improvement, the proposed ones are valid alternatives with respect to the four parameter algorithm, sharing with it almost comparable accuracy.

Influences on amplitude estimation using three-parameter sine fitting algorithm in the velocity mode of the Planck-Balance

“…In the linear sine-fitting algorithm, the oscillation frequency fsig is assumed to be known, and it is taken as an input parameter to the fitting model. If there is an error fsig in the input frequency, an additional contribution will be included in the fitting model, which is described by a linearly damped oscillation [16].…”

“…According to (14) and (16), the influences of the time jitter will be stronger for a sampled signal with a higher oscillation frequency and a lower number of samples. In the current measurement of the PB, the number of the sample points is not below 5000, and the oscillation frequency is lower than 15 Hz.…”