ESOQ - A CLOSED-FORM SOLUTION TO THE WAHBA PROBLEM

A closed-form solution to the problem of optimal spacecraft attitude e stimation based on vector observation, known as the Wahba problem, is presented. The algorithm first provides the closed-form expressions of a 4 x 4 matrix eigenvalues and then computes the eigenvector associat ed with the greatest of them (representing the optimal quaternion) usi ng two different methods. The first method uses a vector cross-product in a four-dimensional space, while the second uses an equivalent tech nique requiring a 3 x 3 nonsingular matrix inversion. The resulting '' EStimator of the Optimal Quaternion'' (ESOQ) algorithm does not presen t any singularities and allows an easy identification of the approachi ng of the unresolvable condition of quasi-parallel observed vectors. N umerical accuracy tests, showing the average and the variance of the m aximum attitude errors, are presented. Speed numerical tests, which de monstrate ESOQ as the fastest optimal attitude estimation algorithm to date, validate ESOQ as the most suitable algorithm when a fast and op timal attitude determination is required.