Reconstruction of spacecraft Progress attitude motion by measurements of their angular rate and electric current from solar batteries

In 2011 – 2012, the spacecraft Progress-M-11M, Progress-M-13M, and Progress-M-14М tried out the mode of single-axis solar orientation in their autonomous flight before docking to ISS. At the beginning of the oriented motion, the spacecraft rotated around the normal to solar batteries with angular rate 2 deg./s and the normal was directed to the Sun. The oriented motion lasted for $1\div2$ orbit revolutions. Each spacecraft had two seances of the single-axis solar orientation mode. This mode will be used perhaps for carrying out some scientific experiments specifically the experiments with convection sensor DACON-M. To interpret the experimental results one needs to have the reconstruction of the spacecraft attitude motion during experiments. The motion in the single-axis solar orientation mode was reconstructed by measurements of the spacecraft angular rate and the electric current from its solar batteries. The measurement data, collected in a time interval about a few hours, were processed simultaneously by statistical methods and integration of the spacecraft attitude motion equations. The estimations of the mathematical model parameters and initial conditions of the attitude motion were obtained as a result of such processing. We described in this paper some results obtained.