Delay estimation using sinusoidal signals

The problem of estimating the difference in arrival times of a noisy sinusoid received at two spatially separated sensors is considered. Given the sinusoidal frequency, a simple delay estimator using the phase difference of the discrete time Fourier transforms (DTFTs) of the received signals is devised. With the use of a periodogram, the algorithm is extended to estimate the delay when the frequency is unknown. The minimum achievable delay variances for the cases of known/unknown frequencies and constant/rectangular envelopes are also given. The effectiveness of the method is demonstrated by comparing with the performance bounds for different frequencies, envelopes and noise conditions