ESOQ: A closed-form solution to the Wahba problem
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A closed-form solution to the problem of optimal spacecraft attitude estimation based on vector observation, known as the Wahba problem, is presented. The algorithm first provides the closed-form expressions of a 4 4 matrix eigenvalues and then computes the eigenvector associated with the greatest of them (representing the optimal quaternion) using two different methods. The first method uses a vector cross-product in a four-dimensional space, while the second uses an equivalent technique requiring a 3 3 nonsingular matrix inversion. The resulting "EStimator of the Optimal Quaternion" (ESOQ) algorithm does not present any singularities and allows an easy identification of the approaching of the unresolvable condition of quasi-parallel observed vectors. Numerical accuracy tests, showing the average and the variance of the maximum attitude errors, are presented. Speed numerical tests, which demonstrate ESOQ as the fastest optimal attitude estimation algorithm to date, validate ESOQ as the most suitable algorithm when a fast and optimal attitude determination is required.
