Attitude determination using a single sensor observation: analytic quaternion solutions and property discussion. Issue 6 (1st September 2017)

• Record Type: Journal Article
• Authors: Wu, Jin; Zhou, Zebo; Li, Rui; Yang, Long; Fourati, Hassen
• Is Part Of: IET science, measurement & technology. Volume 11:Issue 6(2017)
• Page Start: 731
• Page End: 739
• Publication Date: 2017-09-01
• Subjects: attitude measurement -- sensors -- linear matrix inequalities -- inverse problems -- probability -- accelerometers -- vectors -- eigenvalues and eigenfunctions -- decomposition; analytic quaternion solution -- property discussion -- rotation equation -- quadratic quaternion form -- linear matrix equation -- pseudoinverse matrix -- elementary row operation -- single sensor observation -- variance analysis -- probabilistic characters -- accelerometer attitude determination system -- gravity‐determination ability -- rotation vector -- eigenvalue decomposition; Measurement -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Periodicals; Nanotechnology -- Periodicals; Electromagnetism -- Periodicals; Medical instruments and apparatus -- Periodicals; 621.3
• DOI: 10.1049/iet-smt.2016.0202
• Languages: English
• ISSNs: 1751-8822

Abstract

Abstract : This study solves the attitude determination problem based on a single sensor observation. The rotation equation is transformed into a quadratic quaternion form and is then derived to a linear matrix equation with pseudoinverse matrices. The analytic solutions to the equation are computed via elementary row operations. The solutions show that the attitude determination from a single sensor observation has infinite solutions and the general one is governed by two limiting quaternions. Accordingly, the variance analysis is given in view of probabilistic characters. The authors explore the experimental results via the accelerometer attitude determination system. The properties of the two limiting quaternions are investigated in the experiment. The results show that the gravity‐determination abilities of the two limiting quaternions are quite different. Using the rotation vector and eigenvalue decomposition of the attitude matrix, the authors prove that one limiting quaternion is better than another one geometrically. The singularity analysis is also performed revealing the non‐existence of singularities for limiting quaternions. The above findings are novel, which are quite different from the conclusions made in a previously published study.