Attitude-Independent Magnetometer Calibration for Spin-Stabilized Spacecraft

The paper describes a three-step estimator to calibrate a Three-Axis Magnetometer (TAM) using TAM and slit Sun or star sensor measurements. In the first step, the Calibration Utility forms a loss function from the residuals of the magnitude of the geomagnetic field. This loss function is minimized with respect to biases, scale factors, and nonorthogonality corrections. The second step minimizes residuals of the projection of the geomagnetic field onto the spin axis under the assumption that spacecraft nutation has been suppressed by a nutation damper. Minimization is done with respect to various directions of the body spin axis in the TAM frame. The direction of the spin axis in the inertial coordinate system required for the residual computation is assumed to be unchanged with time. It is either determined independently using other sensors or included in the estimation parameters. In both cases all estimation parameters can be found using simple analytical formulas derived in the paper. The last step is to minimize a third loss function formed by residuals of the dot product between the geomagnetic field and Sun or star vector with respect to the misalignment angle about the body spin axis. The method is illustrated by calibrating TAM for the Fast Auroral Snapshot Explorer (FAST) using in-flight TAM and Sun sensor data. The estimated parameters include magnetic biases, scale factors, and misalignment angles of the spin axis in the TAM frame. Estimation of the misalignment angle about the spin axis was inconclusive since (at least for the selected time interval) the Sun vector was about 15 degrees from the direction of the spin axis; as a result residuals of the dot product between the geomagnetic field and Sun vectors were to a large extent minimized as a by-product of the second step

A method of determining attitude from magnetometer data only

Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress