This paper develops methods for estimating the rotation rate of a spacecraft using only measured magnetic field data. The goal is to provide rate information for use in applications such as de-tumbling, nutation damping, and momentum management without using gyroscopes. Two algorithms are developed, a deterministic algorithm and an extended Kalman filter. Both algorithms employ the magnetic field direction kinematics equation and Euler's equation for attitude motion of a rigid body with

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... wheels. Neither algorithm requires a model of the Earth's magnetic field. The deterministic algorithm solves a nonlinear least-squares problem for the unknown angular momentum component along the magnetic field direction. The extended Kalman filter estimates the attitude rate vector, corrections to 5 of the 6 inertia matrix elements, and 2 error states of the measured magnetic field direction. It uses an initial rate estimate from the deterministic algorithm in order to avoid divergence.