Three-Dimensional Pendulum Red-Billed Blue Magpie Optimizer Hybrid Algorithm for Triaxial Magnetometer Calibration

Triaxial magnetometers are susceptible to various non-ideal factors, resulting in the distortion of their output data points from an ideal spherical distribution to an ellipsoidal distribution, which seriously compromises the measurement accuracy. To address the error compensation problem of triaxial magnetometers, this paper proposes a calibration scheme based on an improved ellipsoid fitting methodology. Traditional algebraic methods suffer from ambiguous physical interpretations of parameters and uncontrollable accuracy. To overcome these limitations, a Three-dimensional Pendulum Algorithm based on geometric principles is proposed and integrated with the Red-billed Blue Magpie Optimizer (RBMO), resulting in the Pendulum Red-billed Blue Magpie Optimizer (P-RBMO) hybrid algorithm. This algorithm utilizes the Three-dimensional Pendulum Algorithm to calculate the shortest distance that satisfies the accuracy requirement from each sampling point to the fitted ellipsoid, and then used as the fitness function for RBMO, which optimizes the ellipsoid’s geometric parameters. Experimental results indicate that the P-RBMO hybrid algorithm achieves high-accuracy ellipsoid fitting, consequently providing effective calibration for triaxial magnetometers. The calibrated magnetic field magnitudes closely approximate the theoretical value with significantly reduced fluctuations, which validates the effectiveness and robustness of the proposed method.