Spacecraft Attitude Rate Estimation From Geomagnetic Field Measurements

Methods are developed 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 detumbling, 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 momentum 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 five of the six inertia matrix elements, and two error states of the measured magnetic field direction. It uses an initial rate estimate from the deterministic algorithm to avoid divergence. The algorithms have been tested using data from a spinning sounding rocket. They achieve initial accuracies in the range 2-7 deg/s when the rocket spins at about 80 deg/s, and their accuracies improve to 1-2 deg/s after the spin rate decays to 20 deg/s. These results indicate a lower bound on the ratio of the error to the nominal spin rate, which suggests that dynamic modeling error is the dominant source of uncertainty.