This paper presents a novel algorithm for quaternion estimation fromsingle-frame vector measurements, which is developed in the realm ofdeterministic constrained least-squares estimation. Hinging on the interpretationof quaternion measurements errors as angular errors in thefour-dimensional Euclidean space, a novel cost function is developed anda minimization problem is formulated under the constraint of the quaternionunit-norm. This approach sheds a new light on the Wahba problem,which is a known constrained least-squares attitude determinationproblem, and on its quaternion-based solution, the q-method. The resultingalgorithm is a batch algorithm that is mathematically equivalentto the q-method. Taking advantage of the gained geometric insight, arecursive algorithm is developed, where the update stage is a rotationin the four-dimensional Euclidean space. The rotation is performed ina plane that is generated by the a priori quaternion estimate and by ameasurement-related quaternion. The rotation angle is empirically designedas a fading memory factor. One highlight of this novel algorithmis the preservation by design of the estimated quaternion unit-norm.Numerical simulations are performed in order to illustrate the performancesof the novel algorithm and to compare it with the q-method. Theproposed approach provides a convenient framework in order to embednorm-preserving quaternion update stages in augmented state estimators.Although developed for the purpose of quaternion estimation, thisapproach could lend itself to norm-preserving estimation algorithms inhigher dimensions.
展开▼
