A New Online Meta-Heuristic Adaptive GMRES Method to Estimate the Attitude and the Model of a Satellite

Increasing precision and stability in the online estimation of a spacecraft's model, due to the uncertainty and noise is one of the challenges in the attitude control of the space systems. The least squares error method in combination with the Kalman filter is one of the effective methods for estimating these types of dynamic models. Based on the development of the GMRES (generalized minimal residual) methods, in order to increase the performance of the estimation method, a newonline meta-heuristic algorithm is proposed. The algorithm is an iterative-based method that uses previous step information based on user experience, or a new online meta-heuristic method which determines the number of steps to solve the matrix equations system in the Krylov subspace and improves overall convergence to the response. In order to evaluate the accuracy of this estimation method, the GMRES, Bi-CG (Bi Conjugate Gradient), CGS (Conjugate Gradients Squared), BI-CGSTAB (Bi Conjugate Gradient Stabilized) methods are compared that the online meta-heuristic GMRES method shows the highest accuracy and stability in the estimation.