Unrolling the Plug-and-Play Primal–Dual Hybrid Gradient algorithm for magnetic compensation

In precision magnetic measurement systems utilizing magnetometers for perception, navigation, and detection, carrier magnetic interference compensation techniques are critical for enhancing measurement accuracy and reliability. This paper proposes an Unrolled Plug-and-Play Primal–Dual Hybrid Gradient (UPnP-PDHG) algorithm for magnetic compensation. Specifically, the compensation task is formulated as a weighted elastic net regression problem based on the Tolles-Lawson model, which is subsequently transformed into a saddle point optimization (SPO) problem for solution. By employing the deep algorithm unrolling methodology, the traditional iterative Primal–Dual Hybrid Gradient (PDHG) steps for solving the SPO problem are unrolled into cascaded neural network layers with learnable parameters replacing fixed ones. Additionally, a Plug-and-Play (PnP) denoiser is introduced to effectively handle the proximal operator by learning complex patterns in data distributions. Through this unrolled architecture integrated with the PnP module, the UPnP-PDHG network allows end-to-end learning of all algorithmic parameters. This hybrid model-data-driven architecture demonstrates superior compensation performance on both synthetic and real measurement data. Experimental results show that the UPnP-PDHG algorithm achieves the lowest residual magnetic interference intensity and the highest improvement ratio across different experimental conditions. The proposed method exhibits enhanced effectiveness and robustness in magnetic compensation tasks compared to conventional approaches.