Delay estimation using sinusoidal signals

The problem of estimating the di erence 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 di erence of the discrete time Fourier transforms (DTFTs) of the received signals is devised. With the use of 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 e ectiveness of the method is demonstrated by comparing with the performance bounds for di erent frequencies, envelopes and noise conditions.