Determining a satellite attitude motion on measurements of its angular rate and the strength of the Earth magnetic field using the kinematic model of an attitude motion

The paper presents the technique for determining attitude motion of a satellite by means of processing on board measurements of two vectors - the Earth magnetic field strength and the satellite angular rate. The technique is based on kinematic attitude equations only and can be used for determining both uncontrolled and controlled motion for any external torque acted on a satellite. In the framework of the technique, the measurement data of both type, collected on a time interval about a few hours, are processed simultaneously. The angular rate data are smoothed by discrete Fourier series and those series are substituted in Poisson kinematic equations for elements of the transition matrix which transforms the satellite coupled coordinate system to the orbital one. The equations obtained present the kinematic model of a satellite attitude motion. The solution of the equation, which approximates the real motion, is found by least squares method from the condition of the best agreement between measurement and calculation data of the magnetic strength. The results are given for testing the technique on the measurement data obtained on the satellite Foton-12.