Subsample Time Delay Estimation by Quadratic Interpolation of Correlation Function of Digitized Ultrasonic Probing Signals

The article is considered to the study of one of the digital signal processing methods effectiveness during of transit-time ultrasonic flowmeters. Signal processing allows increasing the measuring accuracy of the propagation time difference (time-of-flight) in the ultrasonic signals or the time delay between the signals. This discussed method consists in calculating the direct cross-correlation function of two discretized probing signals. Finding a correlation function global maximum will correspond to the desired parameter. Typically, the signals time delays are not integer multiples of the sampling period, and the sampling rate of the received signals remains relatively low, so locating the largest sample of the discrete correlation function is an imprecise estimate. For this purpose, in ultrasonic flow metering, subsample interpolation techniques between signal samples and correlation function are used. Most often, it is customary to discuss three-point interpolation methods in the correlation function peak. The report proposes to study one of this interpolation methods for a correlation function - quadratic or using a parabola. A numerical simulation using the MatLab software for interpolation errors estimating of the correlation function peak showed that the achieved results, in contrast to those presented by other researchers, are worse than expected. This is due to possible limitations of the chosen interpolation method and is proved theoretically. Additional analytical equations are presented and verified to evaluate the interpolation errors. The obtained calculations of the time delay estimating accuracy were compared with the simulation results.