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, while the other performs full calibration, which includes biases, scale factors and nonorthog-onality corrections. 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.