A Procedure for Accurate Calibration of the Orientation of the Three Sensors in a Vector Magnetometer

We present a procedure for simultaneously determining the orientations of the three sensors of a vector magnetometer and the three coils necessary for calibration. Cartesian coordinate systems in the sensor assembly and in geographic coordinates are established by an optical cube on the sensor and two theodolites on the earth. The relative orientations of these systems are measured by theodolite reflections from the faces of the optical cube. The sensor assembly is placed at the center of the coil assembly and known fields are applied along each coil axis. In each case the vector output is recorded providing three vector measurements. This procedure is repeated a total of four times with the sensor rotated 90° between each set of measurements. The 12 vector measurements are used in an iterative program to determine the 18 direction cosines of sensors and coils. The program assumes the axis orientations are known to roughly one-half degree by construction. With this assumption it is possible to formulate an approximate model which predicts the measurements made in each of the four sensor orientations. Differences between the predictions and measurements are used to calculate a correction to the initial model. This correction is added to the initial model and the calculation repeated. In a computer simulation convergence to 10⁻⁷ was obtained in three steps. An analysis of the probable errors suggests an accuracy of about 5 arcseconds should be obtainable. This corresponds to an error of 1 γ in the 50 000 γ earth's field.