Ocean wave directional spectrum estimation using spatio-temporal array of acoustic ranging and current measurement

An approach to estimate ocean wave directional spectrum using spatio-temporal array of acoustic ranging and current measurement is proposed, and the five-beam acoustic Doppler current profiler (ADCP) constructs a spatio-temporal array of acoustic ocean surface elevation tracking and acoustic Doppler current velocity measuring for directional wave observation. Based on the linear wave theory and the space-time equivalence principle, the time-space transfer function applicable to the spatio-temporal array is proposed, and then the time delay term is compensated in the calculation of the covariance matrix. This method can reduce the error of the directional spectrum estimation. Simulation results show that for the low signal-to-noise ratio from 0 dB to 5 dB, compared with the four-beam synchronous array method, this method has a smaller root-mean-square error of the peak estimation of the directional spectrum. The field test shows that, compared with the four-beam synchronous array method, the five-beam spatio-temporal array method improves the kurtosis index of the directional spectrum from 2.31 to 2.80, and the correlation coefficient between the peak wave direction results of the ADCP and the buoy is increased from 0.80 to 0.83 in mild wave condition. Furthermore, the spatio-temporal array method can increase the degree of freedom of wave measurement, reduce the minimum aperture of the array, and increase the upper cut-off frequency of the estimable directional spectrum.