Accuracy estimation of the technique for reconstructing the spacecraft attitude motion by measurements of its angular rate and Earth magnetic field strength

The reconstruction technique is based on processing the measurements of two vectors: the spacecraft angular rate and the strength of the Earth magnetic field. The processing technique uses kinematical equations of the attitude motion of a rigid body. In its framework, the measurement data of both types, collected on a time interval, are processed jointly. The angular rate data are smoothed by suitable functions and those functions are substituted in kinematical equations for components of the quaternion, which defines a transformation of the spacecraft coupled coordinate system to inertial one. The equations obtained present the kinematical model of a spacecraft attitude motion. The solution of the equations, which approximates the real motion, is found by the least squares method from the condition of the best agreement between measurement and calculation data of the magnetic strength. The accuracy of the technique was investigated by processing measurements obtained on board Service Module of ISS. The reconstruction of ISS attitude motion was compared with telemetry data of its real motion. The errors of reconstruction of the motion in orbital orientation did not exceed 0.6$^\circ$, the errors of reconstruction of rotations did not exceed 1.2$^\circ$.