Physics-Based Calibration with Neural Network Residual Correction and Uncertainty Quantification for Temperature-Aware AMR Magnetometers

Accurate calibration of anisotropic magnetoresistive (AMR) sensors under varying environmental conditions is crucial for reliable magnetic field measurements in geophysics, navigation, and space applications. Traditional physics-based calibration models offer interpretability but are limited in modeling complex nonlinear effects and typically lack trustworthy uncertainty estimation, whereas purely data-driven approaches often suffer from poor physical consistency and uncalibrated uncertainty estimates. This study proposes a hybrid calibration approach that integrates a physics-based analytical model for primary calibration with a neural network used exclusively for residual error correction, together with explicit uncertainty quantification. A temperature-compensated analytical calibration model is first estimated using nonlinear multivariate regression, with physics-based aleatoric uncertainty quantified via Quasi-Monte Carlo sampling and epistemic uncertainty propagated through a combination of parameter sampling and a Jacobian-based covariance approach. Residual errors not captured by the analytical model are learned using heteroscedastic neural networks, while Monte Carlo DropConnect is employed to quantify neural network epistemic uncertainty. The final calibrated output is computed by integrating physics-based predictions with data-driven error corrections and their associated uncertainties. Experimental results and simulation studies exhibit improved calibration accuracy and statistically consistent confidence interval coverage.