High Accuracy Time Delay Measurements for Band-Pass Signals

A commonly used technique for the estimation of the time delay between signals received at two spatially separated sensors makes use of real or complex sinusoidal signals with constant amplitude. However, when the test signal is band-pass or band-limited, the methods developed for constant amplitude sinusoidal signals are inadequate, since the characteristics of the band-pass signals are not fully utilized. In this paper, the given central frequency and bandwidth of the transmitted band-pass signals, two simple delay estimators are proposed, which use the phase differences accumulated in the frequency domain of the two received signals. The theoretical standard deviations (STD) of the proposed estimators are derived and also compared with the Cramer-Rao lower bound. Simulations are conducted to verify the derived theoretical STDs, and show the simplicity and the effectiveness of the proposed methods.