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In this study, an unscented Kalman filter (UKF) algorithm, which integrates mathematical model of the attitude dynamics with the measurements of inertial measurement unit (IMU) and the magnetometers, is designed. The identified vector is arranged from the Euler angles, angular rates, and the unknown constant components of the external torques (the gravity-gradient, magnetic field pressure and the sun radiation) acting on the pico satellite. Because of the inherent nonlinear dynamics and the nonlinear measurement model caused by the magnetometer measurements, UKF is selected as a filter algorithm. Performance of the proposed algorithm is demonstrated via simulations for a cube pico satellite.