A Nonlinear Rotation Correction Method for Magnetic Gradient Tensor System

This article proposes a nonlinear correction method for the magnetic gradient tensor system, aiming to mitigate single-sensor errors and misalignment errors within the sensor array during measurement. Initially, this article establishes a sensor error model based on the mechanism of sensor error generation. Subsequently, the total least-squares (TLS) ellipsoid fitting method is employed to solve the sensor error compensation parameters. Following this, this article introduces the differential evolution (DE) algorithm for the nonlinear correction of misalignment errors within the sensor array. The DE algorithm, when utilized for correcting errors in the magnetic gradient tensor system, demonstrates the ability to adaptively adjust parameters, effectively addressing complex optimization problems to minimize errors. Experimental findings reveal that even under nonuniform magnetic fields, the sensor outputs exhibit significant improvements in overlap and coaxiality post-correction. Moreover, after undergoing ellipsoid fitting correction, the root-mean-square error (RMSE) of the total magnetic intensity (TMI) for each magnetic sensor is reduced to below 100 nT. In addition, the average RMSE of each component within the actual tensor system drops from 6079.15 to 55.11 nT/m, thereby confirming the effectiveness of the proposed method.