A Lossless Scalar Calibration Algorithm Used for Tri-Axial Magnetometer Cross Array and Its Effectiveness Validation

The accuracy of a magnetic gradient tensor (MGT) measured by tri-axial magnetometer cross arrays (TAMCAs) is compromised by inherent errors in individual tri-axial magnetometers (TAMs) and inter-sensor misalignment angles (MAs), both of which degrade the resultant MGT data quality. This paper proposes a novel lossless scalar calibration algorithm that eliminates mathematical approximations while tracking the fluctuation of the reference magnetic intensity (MI). The calibration algorithm is developed to improve TAMCAs' measurement precision; however it is difficult to provide a completely accurate MGT by experiments. Therefore, we have designed a kind of validation experiment based on a constrained Euler localization to demonstrate the effectiveness of the calibration algorithm. The fundamental principles of the proposed lossless scalar calibration methodology are systematically presented, accompanied by a numerical analysis of relative errors calibrating TAMCA parameters. Key influencing factors are carefully investigated, including the TAM noise level quantified by standard deviation (STD), calibration dataset size, and STD of reference MI fluctuations. In the experiments, to validate the effectiveness of calibrating TAMCAs composed of four fluxgate TAMs (FTAMs), we measured the true geo-MI using a proton magnetometer and regarded an energized circular coil as the alternating current (AC) magnetic source of the constrained Euler localization, respectively. The results indicated that the lossless scalar calibration algorithm significantly improves the measurement accuracy of the geo-MI of the calibration site and MGT of the energized coil.