An improved correlation method for amplitude estimation of gravitational background signal with time-varying frequency.

In the measurement of the gravitational constant G with angular acceleration method, the accurate estimation of the amplitude of the useful angular acceleration generated by source masses depends on the effective subtraction of the spurious gravitational signal caused by room fixed background masses. The gravitational background signal is of time-varying frequency, and mainly consists of the prominent fundamental frequency and second harmonic components. We propose an improved correlation method to estimate the amplitudes of the prominent components of the gravitational background signal with high precision. The improved correlation method converts a sinusoidal signal with time-varying frequency into a standard sinusoidal signal by means of the stretch processing of time. Based on Gaussian white noise model, the theoretical result shows the uncertainty of the estimated amplitude is proportional to σNT, where σ and N are the standard deviation of noise and the number of the useful signal period T, respectively.