Increasing the precision and stability of online estimation for a spacecraft's model, due to the simultaneous presence of uncertainty in the system dynamics and noise in the state sensor outputs, is one of the challenges in attitude control. One effective method for estimating such dynamic models is the least squares error method combined with the Kalman filter. To enhance the performance of this estimation method, a new online metaheuristic algorithm based on the development of the Generalized Minimal Residual (GMRES) method is proposed. This algorithm is an iterative-based approach that utilizes information from the previous step and, based on user experience, or employs a novel online metaheuristic technique to determine the number of steps required to solve the system in the Krylov subspace, thereby improving overall convergence to the desired response. To evaluate the accuracy of this estimation method, comparisons are made among simple GMRES, Bi-Conjugate Gradient, Conjugate Gradients Squared, and Bi-Conjugate Gradient Stabilized methods. The results demonstrate that the adaptive online metaheuristic GMRES method exhibits the highest accuracy and stability in response.