Estimation of velocity potential of water waves using a Luenberger-like observer

Abstract

We propose a Luenberger-like observer for a water wave system. The water wave dynamics are assumed to be governed by the linearized water wave equation (LWWE). Our proposed observer estimates the velocity potential of water waves by measuring only the surface wave elevation. The information of the water-wave velocity field is then extracted from the gradient of the velocity potential. It is shown that the estimation error of the observer converges exponentially to zero as time tends to infinity. Furthermore, we numerically solve the LWWE and observer equation by the finite difference method. The efficiency of our proposed numerical scheme and the performance of the observer are validated by numerical simulation results.