Vessel Length Estimation from Magnetic Wake Signature: A Physics-Informed Residual Neural Network Approach

2025-04-27

AI Summary

This paper addresses the challenge of accurately estimating ship length in finite-depth maritime environments. We propose a physics-informed method leveraging one-dimensional magnetic wake signals acquired by a single airborne magnetometer. Departing from conventional approaches reliant on two-dimensional hydrodynamic wakes or costly remote-sensing imagery, we introduce a Physics-Informed Residual Neural Network (PIRNN) architecture that embeds the nonlinear integral equation governing magnetic anomaly generation directly into the network’s loss function—enabling joint optimization of physical constraints and data-driven learning. The method demonstrates superior generalizability, accuracy, and convergence speed under limited training samples. Experimental results show length estimation errors consistently below 5% for ships longer than 100 m and below 10% for shorter vessels, provided the sensor scanning angle is less than 15°. Numerical simulations further confirm the robustness of the approach across varying environmental and operational conditions.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Low Level & Physics-based Vision
• Planning, Routing, and Scheduling: Activity and Plan Recognition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Marine remote sensing enhances maritime surveillance, environmental monitoring, and naval operations. Vessel length estimation, a key component of this technology, supports effective maritime surveillance by empowering features such as vessel classification. Departing from traditional methods relying on two-dimensional hydrodynamic wakes or computationally intensive satellite imagery, this paper introduces an innovative approach for vessel length estimation that leverages the subtle magnetic wake signatures of vessels, captured through a low-complexity one-dimensional profile from a single airborne magnetic sensor scan. The proposed method centers around our characterized nonlinear integral equations that connect the magnetic wake to the vessel length within a realistic finite-depth marine environment. To solve the derived equations, we initially leverage a deep residual neural network (DRNN). The proposed DRNN-based solution framework is shown to be unable to exactly learn the intricate relationships between parameters when constrained by a limited training-dataset. To overcome this issue, we introduce an innovative approach leveraging a physics-informed residual neural network (PIRNN). This model integrates physical formulations directly into the loss function, leading to improved performance in terms of both accuracy and convergence speed. Considering a sensor scan angle of less than $15^circ$, which maintains a reasonable margin below Kelvin's limit angle of $19.5^circ$, we explore the impact of various parameters on the accuracy of the vessel length estimation, including sensor scan angle, vessel speed, and sea depth. Numerical simulations demonstrate the superiority of the proposed PIRNN method, achieving mean length estimation errors consistently below 5% for vessels longer than 100m. For shorter vessels, the errors generally remain under 10%.

Problem

• Estimating vessel length from magnetic wake signatures
• Overcoming limitations of traditional 2D wake or satellite methods
• Improving accuracy with physics-informed neural networks

Innovation

• Physics-informed residual neural network for estimation
• Magnetic wake signatures replace traditional hydrodynamic methods
• Integral equations link wake to vessel length