Two-step optimal filter design for the low-cost attitude and heading reference systems

Two-step optimal filter design for the low-cost attitude and heading reference systems

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This study presents a novel sensing methodology with two optimal condition-based fusion algorithms for attitude estimation, using low-cost micro-machined gyroscopes, accelerometers and magnetometers. The proposed methodology named two-step optimal filter is composed of an optimal filter and fast determination algorithm. The filter is designed as sensor-based Kalman filter, which is augmented by a fuzzy rule to adjust the parameters on line to yield optimal measurements of accelerometers and magnetometers. Then, the fast second estimator of the optimal quaternion algorithm is described to determine the orientations. Meanwhile, adaptation architecture is implemented to yield robust performance, even when the vehicle is subject to strong accelerations or ferromagnetic disturbed. The new construction of attitude estimation algorithm is easy to be implemented, the precise, robustness and efficient are compared with the common methodology. Experimental results are provided for a remotely operational vehicle test and the performance of the proposed filter is evaluated against the output from a conventional filter.


    1. 1)
      • 1. Hong, S.K.: ‘Fuzzy logic based closed-loop strapdown attitude system for unmanned aerial vehicle (UAV)’, Sens. Actuator A, 2003, 107, pp. 109118 (doi: 10.1016/S0924-4247(03)00353-4).
    2. 2)
      • 2. Angelo, M.S.: ‘Estimating three-dimensional orientation of human body parts by inertial/magnetic sensing’, Sensors, 2011, 11, (10), pp. 14891525.
    3. 3)
      • 3. Syed, Z.F., Aggarwal, P., Goodall, C., Niu, X., El-Sheimy, N.: ‘A new multi-position calibration method for MEMS inertial navigation systems’, Meas. Sci. Technol., 2007, 18, pp. 18971907 (doi: 10.1088/0957-0233/18/7/016).
    4. 4)
      • 4. Bonneta, S., Bassompierrea, C., Godina, C., Lesecqa, S., Barraudb, A.: ‘Calibration methods for inertial and magnetic sensors’, Sens. Actuators A, 2009, 156, pp. 302311 (doi: 10.1016/j.sna.2009.10.008).
    5. 5)
      • 5. Lai, Y.C., Jan, S.S., Hsiao, F.B.: ‘Development of a low-cost attitude and heading reference system using a three-axis rotating platform’, Sensors, 2010, 10, pp. 24722491 (doi: 10.3390/s100402472).
    6. 6)
      • 6. Vasconcelos, J.F., Elkaim, G., Silvestre, C.: ‘A geometric approach to strapdown magnetometer calibration in sensor frame’. FAC Workshop on Navigation, Guidance and Control of Underwater Vehicles, Ireland, 2008.
    7. 7)
      • 7. Jafar, K.: ‘Fuzzy calibration of a magnetic compass for vehicular applications’, Mech. Syst. Signal Process., 2010, 11, (5), pp. 115.
    8. 8)
      • 8. Yun, X., Bachmann, E.R.: ‘Design, implementation, and experimental results of a quaternion-based Kalman filter for human body motion tracking’, IEEE Trans. Robot., 2006, 22, pp. 12161227 (doi: 10.1109/TRO.2006.886270).
    9. 9)
      • 9. Angelo, M.S.: ‘Quaternion-based extended Kalman filter for determining orientation by inertial and magnetic sensing’, IEEE Trans. Biomed. Eng., 2006, 53, pp. 13461356 (doi: 10.1109/TBME.2006.875664).
    10. 10)
      • 10. Xsens Technologies, Available:
    11. 11)
      • 11. VectorNav Technologies, Available:
    12. 12)
      • 12. Mahony, R., Hamel, T., Pflimlin, J.M.: ‘Complementary filter design on the special orthogonal group SO (3)’. Proc. IEEE Conf. Decision and Control, Seville, Spain, 2005.
    13. 13)
      • 13. Hamel, T., Mahony, R.: ‘Attitude estimation on SO(3) based on direct inertial measurements’. Proc. Int. Conf. on Robotics and Automation, Orlando, FL, 2006.
    14. 14)
      • 14. Robert, M., Tarek, H., Pflimlin, J.M.: ‘Nonlinear complementary filters on the special orthogonal group’, IEEE Trans. Autom. Control, 2008, 53, (5), pp. 12031218 (doi: 10.1109/TAC.2008.923738).
    15. 15)
      • 15. Martin, P., Salaün, E.: ‘An embedded attitude and heading reference system based on a nonlinear filter’. Informatics in Control, Automation and Robotics, Milan, Italy, 2009.
    16. 16)
      • 16. Bonnabel, S., Martin, P., Rouchon, P.: ‘Non-linear symmetry-preserving observers on lie groups’, IEEE Trans. Autom. Control, 2009, 54, (7), pp. 17091713 (doi: 10.1109/TAC.2009.2020646).
    17. 17)
      • 17. Martin, P., Salaün, E.: ‘Design and implementation of a low-cost observer-based attitude and heading reference system’, Control Eng. Pract., 2010, 18, pp. 712722 (doi: 10.1016/j.conengprac.2010.01.012).
    18. 18)
      • 18. Rehbinder, H., Hu, X.M.: ‘Drift-free attitude estimation for accelerated rigid bodies’, Automatic, 2004, 40, pp. 653659 (doi: 10.1016/j.automatica.2003.11.002).
    19. 19)
      • 19. Harada, T., Mori, T., Sato, T.: ‘Development of a tiny orientation estimation device to operate under motion and magnetic disturbance’, Int. J. Robust Res., 2007, 26, pp. 547559 (doi: 10.1177/0278364907079272).
    20. 20)
      • 20. Lee, J.K., Park, E.J.: ‘A fast quaternion-based orientation optimizer via virtual rotation for human motion tracking’, IEEE Trans. Biomed. Eng., 2009, 56, pp. 15741582 (doi: 10.1109/TBME.2008.2001285).
    21. 21)
      • 21. Tae, S.Y., Sung, K.H., Hyok, M.Y., Sungsu, P.: ‘Gain-scheduled complementary filter design for a MEMS based attitude and heading reference system’, Sensors, 2011, 11, pp. 38163830 (doi: 10.3390/s110403816).
    22. 22)
      • 22. Ah-Lam, L., Kim, J.H.: ‘3-Dimensional pose sensor algorithm for humanoid robot’, Control Eng. Pract., 2010, 18, (10), pp. 11731182 (doi: 10.1016/j.conengprac.2010.06.002).
    23. 23)
      • 23. Rotenberg, D., Luinge, H.J., Baten, C.T.M., Veltink, P.H.: ‘Compensation of magnetic disturbances improves inertial and magnetic sensing of human body segment orientation’, IEEE Trans. Neural Syst. Rehabil. Eng., 2005, 13, pp. 395405 (doi: 10.1109/TNSRE.2005.847353).
    24. 24)
      • 24. L¨otters, J.C., Schipper, J., Veltink, P.H., Olthius, W., Bergveld, P.: ‘Procedure for in-use calibration of triaxial accelerometers in medical applications’, Sens. Actuators A, 1998, 68, pp. 221228 (doi: 10.1016/S0924-4247(98)00049-1).
    25. 25)
      • 25. Titterton, D., Weston, J.: ‘Strapdown inertial navigation technology’ (The American Institute of Aeronautics and Astronautics, 2004, 2nd edn.).
    26. 26)
      • 26. Mohamed, A.H., Schwarz, K.P.: ‘Adaptive Kalman filtering for INS/GPS’, J. Geodesy, 1999, 73, pp. 193203 (doi: 10.1007/s001900050236).
    27. 27)
      • 27. Escamilla-Ambrosio, P.J., Mort, N.: ‘A hybrid Kalman filters fuzzy logic multisensor data fusion architecture with fault tolerant characteristics’. Proc. Int. Conf. Artificial Intelligence, Las Vegas, NV, USA, 2001, pp. 361367.
    28. 28)
      • 28. Wahba, G.: ‘A least squares estimate of satellite attitude’, SIAM Rev., 1965, 7, pp. 409 (doi: 10.1137/1007077).
    29. 29)
      • 29. Markley, F.L., Mortari, D.: ‘Quaternion attitude estimation using vector observations’, J. Astronaut. Sci., 2000, 48, (2), pp. 359380.
    30. 30)
      • 30. Theodor, Y., Shaked, U., Souza, C.E.: ‘A game theory approach to robust discrete-time H∞ estimation’, IEEE Trans. Signal Process., 1994, 42, pp. 14861495 (doi: 10.1109/78.286964).

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