Spacecraft Angular Rate Estimation from Magnetometer Data Only Using an Analytic Predictor

A method is presented for fast estimation of the angular rate of a tumbling spacecraft in a low-Earth orbit from sequential readings of Earth’s magnetic field. Useful as a back up algorithm in cases of rate gyro malfunctions or during the initial acquisition phase, the estimator consists of an extended Kalman filter, based on the assumption that the inertial geomagnetic field vector does not significantly change during the short sampling time. As the external disturbance torque is neglected, an analytic solution of Euler’s equations can be used in the filter’s propagation phase, allowing a significant savings of computation time compared to numerical integration of Euler’s equations. Contrary to most existing angular rate estimators, the spacecraft’s attitude is neither used nor estimated within the proposed algorithm. Moreover, the body-referenced geomagnetic field observations are not differentiated with respect to time as an external prefiltering procedure but are directly processed by the filter. This processing gives rise to a colored effective measurement noise,which is properly handled via approximate Markov modeling and application of Bryson and Henrikson’s reduced-order filtering theory. A simulation study employing a standard tenth-order International Geomagnetic Reference Field model is presented to demonstrate the performance of the algorithm.