On time delay estimation by evaluation of three time domain functions

Time delay estimation (TDE) is an important problem in many fields of the engineering. The work is looking from the sonar based applications point of view, where the time difference between transmitted pulse and received echo is important for target and object detection and recognition. From many available well know methods, only three time domain methods were considered and investigated: Direct Correlation Function (DCF), Average Square Difference Function (ASDF), and Average Magnitude Difference Function (AMDF). Results obtained for TDE are compared by simulation. We investigate the resolutions of the methods depending on SNR. All investigate methods are valid down to 0 dB Signal to Noise Ratio (SNR). DCF algorithms seems to have the best behavior, in the sense that they have the constant estimations over a wide range of SNR. The ASDF and AMDF based methods needs an estimation of the range where the delay could be. All estimations are biased and slightly depend on the value of the time delay.