Symmetry preserving nonlinear observer for attitude estimation with magnetometer only

This paper addresses designing a nonlinear symmetry observer for nano-satellite attitude determination with only Three-Axis Magnetometer (TAM). Hence, two nested filters are delineated to compensate for the lack of data and to solve the observability problem. In the first filter, the magnetic field derivative is estimated by the extended Kalman filter. Subsequently, the magnetic field and its derivative are applied in the second filter. The proposed methodology relies on invariant observers under the action of a Lie group to estimate the attitude and angular velocity simultaneously. Later, the invariant error dynamic equations are utilized in designing the observer. Consequently, the desired performance of this proposed observer tuned by periodic Riccati differential equation is validated through both simulation and exponential stability proof.