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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 eld. Useful as a backup algorithm in cases of rate gyro malfunctionsor during the initial acquisitionphase, the estimatorconsists of an extended Kalman lter, based on the assumptionthat the inertial geomagnetic eld vector does not signi cantly 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 lter's propagation phase, allowing a signi cant 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 eld observations are not differentiated with respect to time as an external pre ltering procedure but are directly processed by the lter. 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 ltering theory. A simulation study employing a standard tenth-order International Geomagnetic Reference Field model is presented to demonstrate the performance of the algorithm.