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Attitude determination using a single sensor observation: analytic quaternion solutions and property discussion

Attitude determination using a single sensor observation: analytic quaternion solutions and property discussion

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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.

References

    1. 1)
      • 1. Markley, F.L., Crassidis, J.L.: ‘Fundamentals of spacecraft attitude determination and control’ (Springer, 2014), vol. 33.
    2. 2)
      • 2. Li, W., Wang, J.: ‘Effective adaptive Kalman filter for MEMS-IMU/magnetometers integrated attitude and heading reference systems’, J. Navig., 2012, 66, (01), pp. 99113.
    3. 3)
      • 3. Suh, Y.S.: ‘Orientation estimation using a quaternion-based indirect Kalman filter with adaptive estimation of external acceleration’, IEEE Trans. Instrum. Meas., 2010, 59, (12), pp. 32963305.
    4. 4)
      • 4. Suh, Y.S.: ‘A smoother for attitude and position estimation using inertial sensors with zero velocity intervals’, IEEE Sens. J., 2012, 12, (5), pp. 12551262.
    5. 5)
      • 5. Zhou, Z., Li, Y., Liu, J., et al: ‘Equality constrained robust measurement fusion for adaptive Kalman-filter-based heterogeneous multi-sensor navigation’, IEEE Trans. Aerosp. Electron. Syst., 2013, 49, (4), pp. 21462157.
    6. 6)
      • 6. Zhou, Z., Li, Y., Zhang, J., et al: ‘Integrated navigation system for a low-cost quadrotor aerial vehicle in the presence of rotor influences’, J. Surv. Eng., 2016, 4, (May), pp. 113.
    7. 7)
      • 7. Markley, F.L., Mortari, D.: ‘How to estimate attitude from vector observations’, Adv. Astronaut. Sci., 2000, 103, (PART III), pp. 19791996.
    8. 8)
      • 8. Wahba, G.: ‘A least squares estimate of satellite attitude’, 1965, p. 409.
    9. 9)
      • 9. Shuster, M.D., Oh, S.D.: ‘Three-axis attitude determination from vector observations’, J. Guid. Control Dyn., 1981, 4, (1), pp. 7077.
    10. 10)
      • 10. Markley, F.L.: ‘Attitude determination using vector observations – a fast optimal matrix algorithm’, J. Astronaut. Sci., 1993, 41, (2), pp. 261280.
    11. 11)
      • 11. Mortari, D.: ‘ESOQ: a closed-form solution to the Wahba problem’, J. Astronaut. Sci., 1997, 45, (2), pp. 195204.
    12. 12)
      • 12. Gong, D., Shao, X., Li, W., et al: ‘Optimal linear attitude estimators via geometric analysis’, J. Zhejiang Univ. SCIENCE A, 2011, 12, (11), pp. 873882.
    13. 13)
      • 13. Psiaki, M.L., Hinks, J.C.: ‘Numerical solution of a generalized Wahba problem for a spinning spacecraft’, J. Guid. Control Dyn., 2012, 35, (3), pp. 764773.
    14. 14)
      • 14. Yang, Yaguang: ‘Attitude determination using Newton's method on Riemannian manifold’, Proc. Inst. Mech. Eng. G J. Aerosp. Eng., 2015, 229, (14), pp. 27372742.
    15. 15)
      • 15. Yang, Y., Zhou, Z.: ‘An analytic solution to Wahbas problem’, Aerosp. Sci. Technol., 2013, 30, (1), pp. 4649.
    16. 16)
      • 16. Shuster, M.D., Natanson, G.: ‘Quaternion computation from a geometric point of view’, 1993, pp. 545556.
    17. 17)
      • 17. Valenti, R.G., Dryanovski, I., Xiao, J.: ‘A linear Kalman filter for MARG orientation estimation using the algebraic quaternion algorithm’, IEEE Trans. Instrum. Meas., 2016, 65, (2), pp. 467481.
    18. 18)
      • 18. Yang, Y.: ‘Spacecraft attitude determination and control: quaternion based method’, Annu. Rev. Control, 2012, 36, (2), pp. 198219.
    19. 19)
      • 19. Salychev, O.S.: ‘Applied inertial navigation: problems and solutions’ (BMSTU Press Moscow, Russia, 2004).
    20. 20)
      • 20. Wu, J., Zhou, Z., Chen, J., et al: ‘Fast complementary filter for attitude estimation using low-cost MARG sensors’, IEEE Sens. J., 2016, 16, (18), pp. 69977007.
    21. 21)
      • 21. Jennings, A., McKeown, J.J.: ‘Matrix computation’ (John Wiley & Sons Inc, 1992).
    22. 22)
      • 22. Sabatini, A.M.: ‘Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation’, Sensors, 2011, 11, (10), pp. 91829206.
    23. 23)
      • 23. Pittelkau, M.E.: ‘Rotation vector in attitude estimation’, J. Guid. Control Dyn., 2003, 26, (6), pp. 855860.
    24. 24)
      • 24. Savage, P.G.: ‘Strapdown analytics’ (Strapdown Associates Maple Plain, MN, 2000), vol. 2.
    25. 25)
      • 25. Titterton, D., Weston, J.L.: ‘Strapdown inertial navigation technology’ (IET, 2004), vol. 17.
    26. 26)
      • 26. Diebel, J.: ‘Representing attitude: Euler angles, unit quaternions, and rotation vectors’, Matrix, 2006, 58, pp. 135.
    27. 27)
      • 27. Groves, P.D.: ‘Principles of gnss, inertial, and multisensor integrated navigation systems (second edition)’, 2013.
    28. 28)
      • 28. Marantos, P., Koveos, Y., Kyriakopoulos, K.J.: ‘UAV state estimation using adaptive complementary filters’, IEEE Trans. Control Syst. Technol., 2016, 24, (4), pp. 12141226.
    29. 29)
      • 29. Markley, F.L.: ‘Fast quaternion attitude estimation from two vector measurements’, J. Guid. Control Dyn., 2002, 25, (2), pp. 411414.
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