Quaternion estimator algorithm information

The quaternion estimator algorithm (QUEST) is an algorithm designed to solve Wahba's problem, that consists of finding a rotation matrix between two coordinate systems from two sets of observations sampled in each system respectively. The key idea behind the algorithm is to find an expression of the loss function for the Wahba's problem as a quadratic form, using the Cayley–Hamilton theorem and the Newton–Raphson method to efficiently solve the eigenvalue problem and construct a numerically stable representation of the solution.

The algorithm was introduced by Malcolm D. Shuster in 1981, while working at Computer Sciences Corporation.^[1] While being in principle less robust than other methods such as Davenport's q method or singular value decomposition, the algorithm is significantly faster and reliable in practical applications,^[2][3] and it is used for attitude determination problem in fields such as robotics and avionics.^[4][5][6]