Recursive attitude determination from vector observations Euler angle estimation

This work presents an algorithm that processes a sequence of pairs of measured vectors to obtain a minimum variance estimate of the Euler angles which describe the attitude between two coordinate systems. The measurement equation is nonlinear and, unlike the direction cosine matrix and the quaternion estimation problems, the dynamics of the estimated angles are nonlinear as well. The algorithm can also handle singular cases, thus extending the use of Euler angles to all-attitude vehicles. Results of Monte-Carlo simulations are presented that demonstrate the efficiency of the algorithm. This work is a natural extension of the algorithms that were recently developed for estimating the direction cosine matrix and the quaternion, therefore it completes the set of recursive minimum variance algorithms for estimating the three common forms of expressing attitude.