Comparative study of time delay estimators for steady-state and transient acoustic leak signals

The effectiveness of leak detection in water pipes using acoustic methods is partly determined by how accurately the time delay between the leak signals is estimated. This comparative study of correlation-, error-, and wavelet-based time delay estimators using simulated and real steady-state and transient leak signals shows that while these estimators perform well at high signal-to-noise ratio (SNR), their performance degrades at low SNR. They are more effective for estimating delays in steady-state signals, although wavelet-based methods also perform well for transient signals. The effectiveness of wavelet-based methods depends primarily on the scale or decomposition level, rather than on the type of wavelet used. The results of this study also shows that an accurate time delay estimate can be obtained directly in the frequency domain from the unwrapped cross-spectral phase; however, this method requires the exclusion of additional phase shifts caused by resonances and reflections in order to improve accuracy.