A simple multiple cross-correlations phase delay estimator

A simple multiple cross-correlations phase delay method (MCC) for unbiased estimation of the phase-shift between two real sinusoidal signals in white noise is proposed. The estimator removes the bias of the correlation methods and enhances the signal-to-noise ratio (SNR) by utilizing multiple cross-correlations of the real signals. The results obtained by MCC in simulations and on real samples are given. A comparison between the phase delay results estimated by MCC, general cross correlation (GCC) method, quadrature delay estimator (QDE), unbiased QDE (UQDE), Sliding Goertzel algorithm (SGA), and discrete-time Fourier transform (DTFT) algorithm is presented. Computer simulations and field test results validate the effectiveness of the proposed method (MCC).