Accuracy comparison of time delay estimation of random signals using the single-point cross-spectrum phase and direct cross-correlation

Abstract

Time delay estimation (TDE) is a common issue in signal processing. For random signals, various statistical methods of analysis are used. In this work, standard uncertainties (standard deviations) of the TDE were analytically analysed and compared for two methods: direct cross-correlation function (CCF) and phase of the cross-spectral density function (CSDF). In the frequency domain, the CSDF-phase single-point method was considered, consisting of determining the time delay for one selected frequency. The metrological properties of the CCF and the single-point phase method are presented for three models of stochastic signals contaminated with white noise interferences. For these models, the standard uncertainties of the TDE have been compared taking advantage phase CSDF and CCF for the signal-to-noise ratio (SNR) in the range 0.1 ≤ SNR ≤ 100. It was found that for small SNR values (SNR < 1) the CCF method is more accurate. On the other hand, for larger SNR values (especially above one), lower values of the standard uncertainty of the time delay are obtained for the phase method. Specific SNR values for which the single-point phase method is more accurate depend on the adopted models and parameters of the signals and on the parameters of the analysis.