Scalar Calibration of Total Instrument Errors of Tri-Axial Magnetometer Using Constrained Optimization Independent of Magnetic Field Intensity

A tri-axial magnetometer (TAM) needs to calibrate its instrument parameters, including nonorthogonality, scale factor among three axis, and bias, to improve measurement precision. In general, most scalar calibrations require a scalar magnetometer to measure magnetic field intensity as a reference field for calibration, which will increase the cost of the calibration facilities. In this article, a scalar calibration method of total instrument errors of TAM, independent of magnetic field intensity, is proposed based on the constrained optimization using the sequential quadratic programming (SQP) algorithm. The relationship between the residual error of calibration and the attitude amount for different standard deviations (STDs) of noise is numerically demonstrated, and the effect of noise on calibration accuracy is also theoretically and numerically analyzed. A tri-axial fluxgate magnetometer is used to experimentally test the scalar calibration algorithm independent of magnetic field intensity. The result shows that the measurement error of geomagnetic field intensity is reduced to 15.52 and 14.99 nT by applying the scalar calibration using SQP and the differential evolution (DE) algorithms, respectively.