Electric field positioning method of constant current elements in layered conductive media

The primary objective of this research is to address the challenges associated with localizing constant current sources within layered conductive media, particularly in marine environments. Given the significant potential for utilizing the electrical signatures of maritime targets such as ships and underwater vehicles for positioning, the study focuses on developing an efficient and robust method for electric field localization. Current elements serve as fundamental models for simulating underwater electric fields, and thus, the research aims to overcome limitations such as complex instrumentation, limited range, and reliance on initial estimates in existing passive localization techniques. By proposing an improved Differential Evolution (DE) algorithm, our aim is to achieve precise and reliable localization of constant current sources in layered conductive media, thereby improving the effectiveness of marine surveillance and navigation systems.

To achieve the research purpose, we devised a novel positioning method based on a modified DE algorithm. This method involves employing a non-uniform sensor array with randomly distributed electrodes within a designated region to measure the target potential. The core of the approach lies in the introduction of parameter adaptive strategies and boundary mutation mechanisms into the DE algorithm. These enhancements address issues such as initial value dependence, entrapment in local optima, and noise sensitivity, significantly improving the optimization process and localization accuracy. The proposed method was validated through simulations targeting the localization of constant current sources in a shallow sea environment (modeled as a three-layered conductive medium consisting of air, seawater, and seabed). Additionally, laboratory experiments using a scaled-down underwater vehicle model in a simulated shallow sea environment further demonstrated the practical feasibility of the approach.

The key innovation of this research is the successful development and validation of an improved DE algorithm tailored for electric field localization in layered conductive media. This method not only mitigates the limitations of existing techniques but also demonstrates several notable improvements. First, it achieves localization with high precision (within 7% error) and fast convergence (within 40 iterations), significantly enhancing operational efficiency. Second, the integration of parameter adaptivity and boundary mutation mechanisms enhances the algorithm’s robustness against noise and its ability to escape local optima, ensuring reliable performance under varying conditions. Third, through comprehensive simulations and experiments, we systematically analyze the impact of factors such as electrode layout, noise intensity, and target orientation on localization performance, providing valuable insights for practical applications.

The results of both the simulation and experimental validations confirm the efficacy of the proposed localization method within stratified conductive media environments, particularly shallow seas. The method’s ability to operate independently of initial values, coupled with its quick convergence speed and resilience to local optima, underscoring its suitability for real-world applications. The extensive analysis of influencing parameters not only supports the theoretical foundation of the technique but also provides actionable recommendations for optimizing the setup of electrodes and enhancing the overall reliability of the localization process. This research lays a solid theoretical foundation for applications ranging from maritime security measures such as early warning systems, tracking, and navigation to non-military uses like geological surveys and obstacle avoidance. The successful experimental implementation using a miniature submarine model further demonstrates the method’s readiness for practical deployment, marking a significant step forward in the field of passive electric field localization for underwater targets.