Utilizing the L-curve criterion for the inverse magnetostatic problem of Hall drift current estimation

Abstract

Aiming at achieving the in-orbit diagnostic of Hall drift current, this study focuses on estimation through the indirect measurement methodology using a magnetic sensor array. It elaborates on the application of a pseudo-seminorm defined for the Hall drift current solution to address the inverse magnetostatic problems, which are formulated with a two-dimensional Tikhonov regularization constraint, and thereby offering a systematic approach to select regularization parameters. Our investigation discusses factors influencing the formation of the L-curve and the accuracy of the resultant solution obtained via the L-curve criterion. The results reveal that the formation of the defined pseudo-seminorm of the Hall drift current solution in the semi-logarithmic coordinate system is independent of the number of calibrating current elements or the number of magnetic sensors. This effectively resolves the issue of failing to generate an L-curve during regularization parameter selection. Furthermore, the study indicates that expanding the number of calibrating current elements—essentially increasing the unknown variables in the inverse magnetostatic equations—contributes to a significant enhancement in the accuracy of Hall drift current solutions. It also has extensibility to be applied to other areas where the contactless current measuring is required.