On the subsample time delay estimation of narrowband ultrasonic echoes

Correlation based time delay estimators, optimal under certain conditions, exhibit the well-known threshold effect of poor performance at low signal-to-noise ratio (SNR). This sudden reduction in performance of the correlation based time delay estimators at low SNR arises from the misidentification of one unique "extremum" in very noisy conditions and from the peak fitting procedure in the case of the subsample time delay estimation. In this paper, two new estimators-the MSX and MXS-for the estimation of subsample time delays in narrow-band signals are proposed. In these estimators, cross-correlations and autocorrelations are matched at a number of different lags to yield a number of time delay estimates which are subsequently combined to obtain one robust time delay estimate. They seem to perform adequately over the SNR range used in simulations of -5 to 20 dB. Their performances are compared to those of two cross-correlation based estimators. Using simulated data, it is demonstrated that all four estimators perform well at high SNR, but at low SNR the proposed MSX and MXS estimators offer significant improvements in the bias and variance of the estimates. Additionally, these findings are verified using ultrasonic experimental data at three different SNR.