Decreasing of Bias of Modified Cross-Correlation Method for Phase Shift Measurement

This paper discusses an approach for the removal of bias of the modified cross-correlation method for phase shift measurement. Unlike the traditional cross-correlation method, which implies the calculation of the cross-correlation function between the signals with the same frequencies, the modified method is based on preliminary calculation of several inner products of the analyzed signals with the auxiliary sine functions with different frequencies. The removal of bias is attained by the specific selection of frequencies of the auxiliary sine functions. Paper also presents the results of the comparative analysis of noise stability of the conventional and the modified cross-correlation methods under the affect of the additive and normally distributed noise contamination. The results of simulations have shown a higher level of noise stability of the modified method for the case of low values of phase shift between the analyzed signals. For the case of values of phase shift close to $90^{\mathrm{o}}$ the conventional cross-correlation method has shown a higher level of noise stability and its applying still remains preferable.