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EFILN: The Electric Field Inversion-Localization Network for High-Precision Underwater Positioning

Yimian Ding, Jingzehua Xu, Guanwen Xie, Haoyu Wang, Weiyi Liu, Yi Li

TL;DR

The paper tackles precise underwater target localization using electric-field measurements by introducing EFILN, a deep neural network that inverts electric-field signals to 3D coordinates. It integrates physical principles through a Coulomb-law–based loss and employs a two-stage optimization strategy (Adam followed by L-BFGS) to achieve high-precision localization while demonstrating robustness to noise and strong small-sample learning. Key contributions include the first use of deep learning for Coulomb-law–driven electric-field inversion, robustness to environmental perturbations, and SSL capability, with open-source code to accelerate further research. The approach offers a practical, real-time solution for underwater positioning in complex environments and lays groundwork for validation with real-field data.

Abstract

Accurate underwater target localization is essential for underwater exploration. To improve accuracy and efficiency in complex underwater environments, we propose the Electric Field Inversion-Localization Network (EFILN), a deep feedforward neural network that reconstructs position coordinates from underwater electric field signals. By assessing whether the neural network's input-output values satisfy the Coulomb law, the error between the network's inversion solution and the equation's exact solution can be determined. The Adam optimizer was employed first, followed by the L-BFGS optimizer, to progressively improve the output precision of EFILN. A series of noise experiments demonstrated the robustness and practical utility of the proposed method, while small sample data experiments validated its strong small-sample learning (SSL) capabilities. To accelerate relevant research, we have made the codes available as open-source.

EFILN: The Electric Field Inversion-Localization Network for High-Precision Underwater Positioning

TL;DR

The paper tackles precise underwater target localization using electric-field measurements by introducing EFILN, a deep neural network that inverts electric-field signals to 3D coordinates. It integrates physical principles through a Coulomb-law–based loss and employs a two-stage optimization strategy (Adam followed by L-BFGS) to achieve high-precision localization while demonstrating robustness to noise and strong small-sample learning. Key contributions include the first use of deep learning for Coulomb-law–driven electric-field inversion, robustness to environmental perturbations, and SSL capability, with open-source code to accelerate further research. The approach offers a practical, real-time solution for underwater positioning in complex environments and lays groundwork for validation with real-field data.

Abstract

Accurate underwater target localization is essential for underwater exploration. To improve accuracy and efficiency in complex underwater environments, we propose the Electric Field Inversion-Localization Network (EFILN), a deep feedforward neural network that reconstructs position coordinates from underwater electric field signals. By assessing whether the neural network's input-output values satisfy the Coulomb law, the error between the network's inversion solution and the equation's exact solution can be determined. The Adam optimizer was employed first, followed by the L-BFGS optimizer, to progressively improve the output precision of EFILN. A series of noise experiments demonstrated the robustness and practical utility of the proposed method, while small sample data experiments validated its strong small-sample learning (SSL) capabilities. To accelerate relevant research, we have made the codes available as open-source.

Paper Structure

This paper contains 11 sections, 26 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. The Task Scenario of Underwater Localization
  4. Principles of Electric Field Localization
  5. Algorithm Design
  6. Loss Function Design
  7. The EFILN Algorithm
  8. Experiments and Results
  9. Experiment Settings
  10. Experiment Results
  11. Conclusion

Figures (4)

  • Figure 1: Illustration of the underwater target localization scenario.
  • Figure 2: The overall architecture of our proposed EFILN algorithm.
  • Figure 3: Comparison of three-directional training loss under different noise levels: (a) x-direction's training loss (b) y-direction's training loss (c) z-direction's training loss.
  • Figure 4: Comparison of real and predicted trajectories under three different simulation paths: (a) spiral trajectory (b) circular trajectory (c) randomly selected points.