Robust optimal attitude determination of the satellite based on the min-max optimization algorithm

Generally, the determination methods of the satellite orientation are known as attitude determination and attitude estimation. The attitude determination solution of the satellite leads to the Wahba problem. Therefore, at least two independent measurement vectors and two corresponding reference vectors are needed to apply the Wahba problem. These input vectors aren't accurate due to sensor noises, misalignment, and low-order approximations. However, these uncertainties aren't considered in the classic Wahba problem directly. In this case, the estimation error of the Wahba problem depends on the input vectors' accuracy. Hence, modeling error and measurement noise are modeled using Interval analysis. Then, the attitude determination problem is transformed from a single-objective problem to a multi-objective robust optimization problem. Since solving the multi-objective problem with heuristic solvers such as NSGA II is time-consuming, the multi-objective problem was solved using the min-max optimization algorithm. The attitude determination error with the proposed method is reduced (7 times) compared to the quaternion method, and its dependence on the accuracy of the input vectors is reduced (200 times). In fact, while reducing the mean attitude error, the algorithm robustness has increased compared to the uncertainties in the input vectors. Using the min-max algorithm has reduced the execution time of the algorithm (about 600 times) compared to the NSGA II algorithm and is suitable for real-time applications. Based on the results, the proposed method has narrower bounds, so that the mean square error (RMS) is decreased by more than 50% over the q-method.