Non-Convex Elastic Net for Adaptive Magnetic Compensation via the Dual Proximal Gradient Technique

Magnetic compensation is essential for reducing the impact of magnetic interference generated by the motion of carrier platforms during magnetic surveys, such as geomagnetic navigation, anomaly detection, and geological mapping. Existing compensation methods are often hindered by performance degradation due to the time-varying characteristics of magnetic interference and the ill-conditioning of the Tolles-Lawson (TL) magnetic interference compensation model. Moreover, traditional ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub>-norm-based feature selection and model sparsity methods tend to over-penalize large coefficients. To address these challenges, this paper introduces an adaptive magnetic compensation approach based on the non-convex elastic net regression (NCENR) model. Instead of the standard ℓ1 penalty, the minimax-concave (MC) penalty is employed to identify the most relevant features of the TL model, enhancing the model’s generalization capability. To solve the problem efficiently while maintaining computational simplicity, the dual proximal gradient technique, combined with the recursive least squares algorithm, is employed to iteratively update the compensation coefficients. The proposed NCENR model with the MC penalty, solved via dual proximal gradient, is validated through a comprehensive comparison using both synthetic data and real measurement data from vehicle and aircraft platforms. Experimental results show that across different experimental platforms and conditions, the NCENR model consistently achieves the lowest residual magnetic interference intensity and the highest improvement ratio, demonstrating its effectiveness and robustness in adaptive magnetic compensation.