Parameter Estimation for the Truncated KdV Model through a Direct Filter Method

In this work, we develop a computational method to provide real-time detection for water bottom topography based on observations on surface measurements, and we design an inverse problem to achieve this task. The forward model that we use to describe the feature of the water surface is the truncated Korteweg–de Vries equation, and we formulate the inversion mechanism as an online parameter estimation problem, which is solved by a direct filter method. Numerical experiments are carried out to show that our method can effectively detect abrupt changes of water depth.