Time-delay estimation for sinusoidal signals

Abstract

The problem of estimating the difference in arrival times of a complex 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 of the received signals is devised. Using the 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 derived. Extension to time-delay estimation using real sinusoids is also investigated. The effectiveness of the method is demonstrated by comparing it with the performance bounds for different frequencies, envelopes and noise conditions.