Time delay estimation using continuous wavelet transform coefficients

Accurate time delay estimation between two turbulent signals is challenging due to the non-stationary behaviour of these signals. Existing method for delay estimation, such as, using cross correlation algorithm is limited to stationary signals. In this paper, a method based on continuous wavelet transform, is proposed for turbulent signal delay estimation. Three steps are required for the proposed method, transforming the signal into wavelet domain using continuous wavelet transform, calculating the time delay between wavelet coefficients using time domain cross correlation, and finally estimating the final delay. In the final delay estimation, three approaches were proposed based either on the mean value, the maximum value, or the most frequent estimated delay. The accuracy of the proposed method was evaluated by simulating two modes of signals, fractal and intermitted periodic signals with different levels of signal-to-noise ranged from 1 to 50. In order to find the final delay, three statistical methods were applied, mean, maximum, and mode of delays that estimated for each wavelet scales. The using of delays mode has been more accurate than the other, and estimated the final delay with maximum error of 0 for fractal signal, and 50 for periodic signal. The percentage of correct estimated time delay between continuous wavelet transform scales for noisy fractal and periodic signals is 26.56 and 7.81 respectively. However, for both signals, the increasing of noise level resulted in increasing of error in delay estimation, and decreasing the number of correct delays estimated between the wavelet coefficients. © 2017 American Scientific Publishers All rights reserved.