Estimating the inertia tensor of the geostationary satellite Yamal on the base of the telemetry information

The paper presents the method and the results of estimating the inertia tensor of the satellite Yamal on the base of the telemetry information about its attitude motion and the total angular momentum of flywheel. The information about an attitude motion is time sequences of the quaternion of the satellite attitude with respect to an inertial coordinate system and the satellite angular rate. Basing on the information, we reconstruct the satellite motion using splines. Such an approximation is used in the linear differential equations, which describe the variation of the total angular momentum of flywheels during the motion. Solutions of the equations depend linearly upon inertia tensor components and satellite geometric parameters. We find estimations of these quantities from the condition of the best approximation of angular momentum measurement data by those solutions using the least squares method. The method was applied for processing real telemetry data. The errors of estimating the diagonal (the most large) inertia tensor components were in limits of 5–17% if the telemetry data were referred to sunny part of the orbit and 4–8% if the data were refereed to the shady part.