A spatio-temporal noise robust filtering method for separation of 2D incident and reflected irregular waves

A spatio-temporal noise robust filtering method is proposed to separate 2D linear wave fields into incident and reflected irregular waves using water surface elevation gauges. The method is based on phased array methodologies, using delay-and-sum beamforming techniques with optimal noise attenuation. The method is developed for an arbitrary number of gauges and can be applied in real-time to surface elevation signals corrupted with measurement noise. The impact of the number of gauges and the distance between them on the performance achievable with the method is thoroughly analysed and a methodology to choose their optimum values is proposed. The robustness of the proposed method with respect to measurement noise is compared with the real-time method proposed by Frigaard and Brorsen and is shown to be adequate for noise levels higher than 1%. Separation errors smaller than 3% and 7% are obtained for simulated signals without noise and with 10% added noise, respectively.