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

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<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>Codes are available at https://github.com/Xiboxtg/EFILN.