Correlation bias analysis - A novel method of sinus cardinal model for least squares estimation in cross-correlation

On the subject of discrete time delay estimation (TDE), especially in the domain of sonar signal processing, in order to determine the time delays between signals received by two separate sensors, TDE techniques involve in locating the peak of cross-correlation function (CCF) between these signals. In many widely used applications of TDE, bias errors of delay estimate can occur when we try to fit the correlation function with a curve that may have an irrelevant shape, for example a parabola or a cosine. This paper thus addresses an analysis of correlation bias in estimating the time delay between a reference signal and a delayed signal by their CCF. Furthermore, we will also introduce a novel bias reduced approach for discrete TDE based on a sinus cardinal model fitting on the CCF of these two sampled signals. The experimental results have shown that the proposed method can provide relevant detection on simulated signals.