Calibration Optimization Study for Tilt-Compensated Compasses

This paper extends prior work on magnetic and inertial sensor frame calibration with an optimization study for the calibration of tilt-compensated electronic compasses. The novelty of this paper consists in formally demonstrating the optimal calibration orientations that maximize the observability of the various calibration coefficients. The optimal orientations are determined by analyzing the partial derivatives of the cost functions with respect to the calibration coefficients, and finding those orientations that produce their maximum slopes. This approach leads to the preservation of the information needed to determine the calibration coefficients by avoiding geometric dilution. Calibration schemes including optimal orientations for the accelerometers and magnetometers are determined not only for the alignment of the magnetometers and accelerometers sensor reference frames but also for the prerequisite calibrations in the sensor reference frames and partial body frames, respectively. This paper also shows that the optimal accelerometer orientations are different from the optimal magnetometer orientations, however, leaves the analysis of a possible compromise to future work. While confirming some intuitions about possible optimal orientations, this paper also offers an insight into those cases not supported by empirical wisdom, such as the misalignments, eliminating therefore the guesswork from the selection of the calibration profiles.