Differential optimization measurement technique for magnetic gradient tensors in magnet positioning

The magnetic gradient tensor provides more information about the magnetic source in anomaly detection. However, approximation errors inevitably arise from the differential measurement method. Therefore, a differential optimization measurement method based on sensor positions fine-tuning is proposed in this study. This method introduces offset coefficients to establish a theory-measurement discrepancy model. Also, a minimum-overall-discrepancy optimization strategy is used to guide the hybrid PSO-Dogleg algorithm in parameter searching. Thus, the differential approximation closely estimates the gradient. The numerical simulation shows the proposed method is applicable across various detection regions, magnetic moments, and noise levels. Furthermore, the correlation between tensor measurement errors and positioning performance was analyzed, and positioning experiments were conducted. As a result, the root mean square error of the tensor component is reduced by 7.1 %, while the average positioning error is reduced from 0.244 m to 0.136 m, which effectively improves the positioning accuracy of the magnetic gradient tensor.