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

TL;DR

This paper introduces a real-time parameter estimation method for the truncated KdV water wave model using a direct filter approach, enabling effective detection of abrupt water depth changes from surface measurements.

Contribution

It presents a novel direct filter-based inverse method for real-time water bottom topography detection using the truncated KdV model.

Findings

Effective detection of abrupt water depth changes

Real-time parameter estimation capability

Validated through numerical experiments

Abstract

In this work, we develop a computational method that to provide realtime 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 water surface is the truncated KdV 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.