Measuring attitude with a gradiometer
Abstract
This paper explores using a gravity gradiometer to measure the attitude of a satellite, given that the gravity field is accurately known. Since gradiometers actually measure a combination of the gradient and attitude rate and acceleration terms, the answer is far from obvious. The paper demonstrates that it can be done and at microradian accuracy. The technique employed is dynamic estimation, based on the momentum biased Euler equations. The satellite is assumed nominally planet pointed, and subject to control, gravity gradient, and partly radom drag torques. The attitude estimator is unusual. While the standard method of feeding back measurement residuals is used, the feedback gain matrix isn't derived from Kalman theory. instead, it's chosen to minimize a measure of the terminal covariance of the error in the estimate. This depends on the gain matrix and the power spectra of all the process and measurement noises. An integration is required over multiple solutions of Lyapunov equations.
 Publication:

Flight Mechanics/Estimation Theory Symposium
 Pub Date:
 May 1994
 Bibcode:
 1994fmet.symp..315S
 Keywords:

 Attitude (Inclination);
 Covariance;
 Error Analysis;
 Feedback;
 Gradients;
 Gravitational Fields;
 Gravity Gradiometers;
 Momentum Theory;
 Power Spectra;
 Bias;
 Differential Equations;
 Drag;
 Estimating;
 Statistical Analysis;
 Torque;
 Spacecraft Design, Testing and Performance