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

TL;DR

This paper tackles estimating vessel length from magnetic wake measurements using a 1D airborne scan in finite-depth water. It derives nonlinear integral equations linking the magnetic wake to hull geometry and proposes a physics-informed residual neural network (PIRNN) that embeds these physical laws into the learning objective, improving accuracy and convergence over a DRNN baseline. Numerical results show PIRNN achieving mean length errors below $5\%$ for vessels longer than $100$ m (and typically below $10\%$ for shorter vessels) across varying sensor angles, speeds, and sea depths, with performance boosted by Monte Carlo integration in the loss. The work demonstrates a practical, passive remote sensing approach for vessel characterization that remains robust under realistic environmental conditions and finite-depth effects.

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\%.

Figures (9)

• Figure 1: Airborne magnetic wake measurement.
• Figure 2: Residual block.
• Figure 3: Overall structure of the proposed PIRNN.
• Figure 4: Illustration of the typical vessel magnetic wake in an area of $800\times1000m^2$.
• Figure 5: Mean error resulting from different training scenario.

Theorems & Definitions (1)

• Remark 1