Estimating Phase Difference and Lead of Discrete Cosine Ultrasonic Wave Signals Based on Hilbert Transform and Lissajous Figure Features

It is required to measure the phase difference and lead of two trains of cosine ultrasonic wave (CSUW) in underwater positioning with a super short base line (SSBL) based on a sound beacon. This paper presents an improved method to estimate the phase difference based on Hilbert transform, and does an effective one to identify their phase lead based on Lissajous figure features. According to the proposed methods, simulation is performed with cosine waves superposing a Gaussian noise, and the results of it indicated that error of phase difference is less than 0.001 degrees degree when a SNR is bigger 45 and that identification of phase lead is valid and correct in a tiny phase difference. Furthermore, an experiment set-up has been developed to verify the effectiveness of the proposed method.