Improving Magnetic Dipole Localization Accuracy by Modeling Individual Sensing Axis Spatial Separation in a Tri-Axis Magnetometer

Accurate magnetic dipole localization using single tri-axis magnetometers is crucial for high-precision applications. While efficient for initial estimates, the conventional Single-Point Sensor Assumption (SPSA) introduces significant errors in steep magnetic field gradients due to its failure to account for the inherent spatial separation of its individual sensing axes. This paper systematically investigates this sensor-internal spatial separation and proposes the Multi-Point Sensor Assumption (MPSA) model. Crucially, the MPSA incorporates this physical separation into the dipole field equation, whilst using only a single tri-axis magnetometer, which offers a cost-effective solution compared to multi-sensor systems. Through extensive simulations and experiments under varying permanent magnet speeds and altitudes, the MPSA model is rigorously compared against the SPSA and another advanced model, the Modified Curl Dipole Modeling (MCDM) approach. The MPSA model consistently achieved sub-millimeter-level localization accuracy—demonstrating superior performance and a substantial reduction in both localization and magnetic field error. Thus, this paper presents a novel, robust, and highly accurate methodology for magnetic dipole tracking, enabling enhanced performance in high-precision, high-gradient field applications.