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 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.