Fast Linear Quaternion Attitude Estimator Using Vector Observations

As a key problem for multisensor attitude determination, Wahba's problem has been studied for almost 50 years. Different from existing methods, this paper presents a novel linear approach to solve this problem. We name the proposed method the fast linear attitude estimator (FLAE) because it is faster than known representative algorithms. The original Wahba's problem is extracted to several 1-D equations based on quaternions. They are then investigated with pseudoinverse matrices establishing a linear solution to n-D equations, which are equivalent to the conventional Wahba's problem. To obtain the attitude quaternion in a robust manner, an eigenvalue-based solution is proposed. Symbolic solutions to the corresponding characteristic polynomial are derived, showing higher computation speed. Simulations are designed and conducted using test cases evaluated by several classical methods, e.g., Shuster's quaternion estimator, Markley's singular value decomposition method, Mortari's second estimator of the optimal quaternion, and some recent representative methods, e.g., Yang's analytical method and Riemannian manifold method. The results show that FLAE generates attitude estimates as accurate as that of several existing methods, but consumes much less computation time (about 50% of the known fastest algorithm). Also, to verify the feasibility in embedded application, an experiment on the accelerometer-magnetometer combination is carried out where the algorithms are compared via C++ programming language. An extreme case is finally studied, revealing a minor improvement that adds robustness to FLAE, inspired by Cheng et al.