Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-19T14:16:33.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiplicative extended Kalman filter ignoring initial conditions for attitude estimation using vector observations

Published online by Cambridge University Press:  12 January 2023

Lubin Chang
Lubin Chang*
Affiliation:
College of Electrical Engineering, Naval University of Engineering, Wuhan, Hubei, P.R. China
*
E-mail: changlubin@163.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group-affine and its error state model should be trajectory-independent. Moreover, with such a trajectory-independent error state model, the linear Kalman filter is still effective for large initialisation errors. However, the measurement model of the traditional MEKF is dependent on the attitude prediction, which is therefore trajectory-dependent. This is also the main reason why the performance of traditional MEKF is degraded for large initialisation errors. Through substitution of the attitude prediction related term with vector observations in the body frame, a trajectory-independent measurement model is derived for MEKF. Meanwhile, MEKFs with reference attitude error definition and with global state formulating on special Euclidean group have also been studied, with the main focus on derivation of the trajectory-independent measurement models. Extensive Monte Carlo simulations of spacecraft attitude estimation implementations demonstrate that the performance of MEKFs can be much improved with trajectory-independent measurement models.

Keywords

inertial navigationlie groupmultiplicative extended Kalman filterattitude estimation
Type
Research Article
Information
The Journal of Navigation , Volume 76 , Issue 1 , January 2023 , pp. 62 - 76
Check for updates
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Institute of Navigation

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andrle, M. S. and Crassidis, J. L. (2015). Attitude estimation employing common frame error representations. Journal of Guidance Control and Dynamics, 38(9), 1614–1624.CrossRefGoogle Scholar
Barrau, A. (2015). Non-linear state error based extended Kalman filters with applications to navigation. Thesis, MINES Paristech, Paris, France.Google Scholar
Barrau, A. and Bonnabel, S. (2014). Intrinsic filtering on Lie groups with applications to attitude estimation. IEEE Transactions on Automatic Control, 60(2), 436–449.CrossRefGoogle Scholar
Barrau, A. and Bonnabel, S. (2015). An EKF-SLAM algorithm with consistency properties. arXiv preprint, arXiv:1510.06263.Google Scholar
Barrau, A. and Bonnabel, S. (2017). The invariant extended Kalman filter as a stable observer. IEEE Transactions on Automatic Control, 62(4), 1797–1812.CrossRefGoogle Scholar
Chang, L. B. (2020). SE(3) based extended Kalman filter for spacecraft attitude estimation. arXiv preprint, arXiv:2003.12978.Google Scholar
Cheng, Y. and Crassidis, J. L. (2010). Particle filtering for attitude estimation using a minimal local-error representation. Journal of Guidance, Control, and Dynamics, 33(4), 1305–1310.10.2514/1.47236CrossRefGoogle Scholar
Crassidis, J. L. and Junkins, J. L. (2012). Optimal Estimation of Dynamic Systems (2nd ed.). Boca Raton, FL: CRC Press, Chap. 3, pp. 153–154, Chap. 7, pp. 421–424.Google Scholar
Crassidis, J. L. and Markley, F. L. (2003). Unscented filtering for spacecraft attitude estimation. Journal of Guidance, Control, and Dynamics, 26(4), 536–542.CrossRefGoogle Scholar
Crassidis, J. L., Markley, F. L. and Cheng, Y. (2007). Survey of nonlinear attitude estimation methods. Journal of Guidance, Control, and Dynamics, 30(1), 12–28.CrossRefGoogle Scholar
Cui, J., Wang, M., Wu, W. and He, X. (2021). Lie group based nonlinear state errors for MEMS-IMU/GNSS/magnetometer integrated navigation. The Journal of Navigation, 1–14. doi:10.1017/S037346332100014XGoogle Scholar
Gai, E., Daly, K., Harrison, J. and Lemos, L. (1985). Star-sensor-based satellite attitude/attitude rate estimator. Journal of Guidance, Control, and Dynamics, 8(5), 560–565.CrossRefGoogle Scholar
Gui, H. and de Ruiter, A. H. J. (2018). Quaternion invariant extended Kalman filtering for spacecraft attitude estimation. Journal of Guidance, Control, and Dynamics, 41(4), 863–878.CrossRefGoogle Scholar
Hartley, R., Ghaffari, M., Eustice, R. M. and Grizzle, J. W. (2020). Contact-aided invariant extended Kalman filtering for robot state estimation. The International Journal of Robotics Research, 39(4), 402–430.CrossRefGoogle Scholar
Lefferts, E. J., Markley, F. L. and Shuster, M. D. (1982). Kalman filtering for spacecraft attitude estimation. Journal of Guidance, Control, and Dynamics, 5(5), 417–429.CrossRefGoogle Scholar
Li, M. and Mourikis, A. I. (2012). Improving the Accuracy of EKF-Based Visual-Inertial Odometry. 2012 IEEE International Conference on Robotics and Automation, St. Paul, MN, 828–835.CrossRefGoogle Scholar
Markley, F. L. (2003). Attitude error representations for Kalman filtering. Journal of Guidance, Control, and Dynamics, 26(2), 311–317.10.2514/2.5048CrossRefGoogle Scholar
Markley, F. L. and Crassidis, J. L. (2014). Fundamentals of Spacecraft Attitude Determination and Control. New York: Microcosm Press and Springer.CrossRefGoogle Scholar
Mueller, M. W., Hehn, M. and Andrea, R. (2017). Covariance correction step for Kalman filtering with an attitude. Journal of Guidance, Control, and Dynamics, 40(9), 2301–2306.10.2514/1.G000848CrossRefGoogle Scholar
Wang, M., Wu, W., He, X., Li, Y. and Pan, X. (2019). Consistent ST-EKF for long distance land vehicle navigation based on SINS/OD integration. IEEE Transactions on Vehicular Technology, 68(11), 10525–10534.CrossRefGoogle Scholar
Wang, M., Wu, W., Zhou, P. and He, X. (2018). State transformation extended Kalman filter for GPS/SINS tightly coupled integration. GPS Solutions, 22(4), 1–12.10.1007/s10291-018-0773-3CrossRefGoogle Scholar