Optimal linear attitude estimator and its recursive algorithm via geometric analysis

Abstract

A new optimal linear attitude estimator is proposed for single-point attitude estimation using geometric approach, and a recursive optimal linear attitude estimator is developed through filtering noisy measurements. Dot and cross products are taken in order to eliminate the unknown parameters of relationships between measurements and Gibbs vector. The optimality criterion, which does not coincide with Wahba’s constrained criterion, yields linear attitude estimate. A prior rotation is adopted to avoid singularity which occurs when the principal angle is close to π. The recursive algorithm is achieved for the purpose of improving attitude accuracy using all past measurements. For long-term space missions, memory fading concept is introduced into recursive optimal linear attitude estimator. The optimal relative weighting is obtained through minimizing error propagation, and an efficient modification is proposed to significantly reduce the sudden increase of attitude error of recursive optimal linear attitude estimator in special cases. Numerical simulations show that the estimate of optimal linear attitude estimator is almost identical with that of the famous QUaternion ESTimator, and the accuracy provided by recursive optimal linear attitude estimator is over an order magnitude higher than that of optimal linear attitude estimator or QUaternion ESTimator in most cases.