Time of arrival difference estimation for narrow band high frequency echolocation clicks

Algorithms are presented for the accurate time of arrival difference estimation of high frequency narrow band echolocation clicks from Harbor Porpoise. These clicks typically have a center frequency of around 130 kHz (wavelength ∼1.2 cm) and duration of <0.1 ms. When using hydrophones spaced centimeters apart, spatial aliasing can cause large errors on inter-hydrophone timing measurements due to the incorrect peak in the cross-correlation function of two signals being selected. It is shown that at sample rates of less than about 6 times the fundamental frequency, the incorrect correlation peak will be selected in 55% of measurements leading to large errors in time of arrival estimates. For clicks with a SNR > 10 dB these errors can be reduced by over two orders of magnitude through a combination of up-sampling the data and parabolic interpolation of peaks in the cross-correlation functions.