A time delay estimator based on the signal integral: theoretical performance and testing on ECG signals

We present a theoretical and experimental performance study of a method for time delay estimation (TDE), based on the signal integral (TDE-SI). The TDE-SI method considers the delay between two transient signals as the difference between the center of mass of these signals. The method has three special cases: In the first, time is the mass coordinate and the signal sit) is the mass distribution (estimate Dˆ_s); in the second case, the squared signal s² (t) is the mass distribution (estimate Dˆ(s²)); and the last is a variant of the second. The bias and the standard deviation to) of the estimate have been evaluated when the signal is contaminated by Gaussian white noise. Dˆ_s is not biased but the σ of the TDE is higher than that obtained when working with Dˆ(s²). Moreover, the Dˆ(s²) estimate is biased. The special case of a bias-corrected estimate (Dˆ´(s²)) is presented; this Dˆ´(s²) yields a σ of its TDE lower than the estimate Dˆ_s. Hence, Dˆ´(s²) is the most suitable of the three TDE-SI options for TDE. Theoretical estimations are validated by simulation results with artificially generated signals and by real so-called QRS complex waves (ventricular activity) from an electrocardiographic (ECG) signal