High-Precision Permanent Magnet Localization Using an Improved Artificial Lemming Algorithm Integrated with Levenberg–Marquardt Optimization

Magnetic localization technology plays a significant role in medical device navigation and human–computer interaction. However, existing localization methods based on local optimization suffer from poor initial solutions and slow convergence. To address the aforementioned challenges, this paper presents a hybrid localization approach, referred to as the Improved Artificial Lemming Algorithm (IALA) Integrated with Levenberg–Marquardt (LM) Optimization. Building upon the Artificial Lemming Algorithm (ALA), the proposed method incorporates an adaptive Gaussian–Lévy hybrid mutation strategy designed to enhance search performance through improved exploration–exploitation dynamics, as quantitatively demonstrated by the diversity-based analysis where IALA maintains higher exploration percentages on multimodal functions while achieving superior optimization results on high-dimensional problems. By introducing a competitive foraging mechanism inspired by the aggressive behavior of the Tasmanian Devil Optimization (TDO) algorithm, it enhances population diversity and search initiative. Furthermore, a time-varying tracking and escape strategy is adopted to improve dynamic optimization performance in complex solution spaces. The proposed method leverages IALA to generate high-quality initial solutions, significantly accelerating the convergence speed and stability of the LM algorithm, thereby improving the overall performance of the permanent magnet localization system. The experimental results show that, using a horizontal test platform of 60 mm × 60 mm with 41 uniformly distributed test points, and acquiring data at vertical heights ranging from 15 mm to 65 mm in 5 mm increments for two distinct orientations of the permanent magnet, the IALA-LM algorithm achieves an average localization success rate of 96.9% over 902 trials, with a mean position error of 1.1 mm and a mean orientation error of 0.17°. Compared with the standard LM algorithm, the proposed IALA-LM algorithm reduces the position error by approximately 66.7% (from 3.3 mm to 1.1 mm) and the orientation error by approximately 94.3% (from 3.0° to 0.17°). Consequently, the proposed method enables high-precision, high-stability, and high-efficiency localization of permanent magnets. It can provide reliable spatial pose estimation support for demanding applications such as miniature implantable or ingestible medical devices (e.g., capsule endoscopy, intramedullary nail fixation, and tumor localization), human–computer interaction, and industrial inspection.