Satellite attitude dynamics and estimation with the implicit midpoint method

We describe the application of the implicit midpoint integrator to the problem of attitude dynamics for low-altitude satellites without the use of quaternions. Initially, we consider the satellite to rotate without external torques applied to it. We compare the numerical solution with the exact solution in terms of Jacobi’s elliptic functions. Then, we include the gravity-gradient torque, where the implicit midpoint integrator proves to be a fast, simple and accurate method. Higher-order versions of the implicit midpoint scheme are compared to Gauss–Legendre Runge–Kutta methods in terms of accuracy and processing time. Finally, we investigate the performance of a parameter-adaptive Kalman filter based on the implicit midpoint integrator for the determination of the principal moments of inertia through observations.