Three-axis magnetometer calibration using total least squares

In this paper attitude-independent three-axis magnetometer (TAM) sensor calibration algorithms are presented from a total least squares approach. One algorithm estimates biases only, whereas the other performs full calibration, which includes biases, scale factors, and nonorthogonality corrections. All calibration parameters are assumed to be constant. It is shown that the TAM calibration problem using a standard least squares point of view is statistically inconsistent because the effective measurement variance is a function of the calibration parameters. This inconsistency is overcome by using the total least squares formulation. The error covariance of the calibration parameters is also derived, which is shown to be equivalent to the standard least squares formation to within first-order terms. Also, the covariance of the measurement-to-estimate residual vector is derived, which cannot be accomplished using a standard least squares approach. This covariance is useful to quantify the effects of the measurement covariance for attitude determination in real-world situations. Both simulated and experimental results are shown to assess the performance of the TAM calibration algorithms, as well as the derived covariance expressions.