Attitude independent estimation of spacecraft angular rate using geomagnetic field observations

A method is presented for fast estimation of the angular rate of a tumbling spacecraft in a low-Earth orbit, fiom sequential readings of Earth's magnetic field. Useful as a backup algorithm in cases of rate gyro malfunctions, or during the initial acquisition phase, the estimator consists of an extended Kalman filter, based on the underlying assumption that the geomagnetic field vector does not significantly change (relative to an inertial fiame of reference) during the short sampling time. Neglecting the external disturbance torque, the analytical solution of the rigid body motion in terms of the Jacobian elliptic functions can be used in the propagation phase of the filter. This strategy allows a significant saving in terms of computation time, compared to numerical integration of the Euler's equations between two sampling times. Contrary to previously introduced angular rate estimators, the spacecraft's attitude is not assumed to be known (nor is it estimated as part of the proposed procedure). Moreover, the body-referenced geomagnetic field observations are not differentiated with respect to time as a prefiltering procedure, but are directly processed by the filter. A simulation study employing a standard 10th order IGRF geomagnetic field model is presented to demonstrate thc performance of the algorithm. © 2003 IEEE