Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T11:29:13.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Lie group based nonlinear state errors for MEMS-IMU/GNSS/magnetometer integrated navigation

Published online by Cambridge University Press:  11 March 2021

Jiarui Cui Open the ORCID record for Jiarui Cui [Opens in a new window] ,
Maosong Wang ,
Wenqi Wu Open the ORCID record for Wenqi Wu [Opens in a new window]  and
Xiaofeng He
Jiarui Cui
Affiliation:
College of Intelligence Science and Technology, National University of Defense Technology, Changsha, Hunan, P.R. China
Maosong Wang*
Affiliation:
College of Intelligence Science and Technology, National University of Defense Technology, Changsha, Hunan, P.R. China
Wenqi Wu
Affiliation:
College of Intelligence Science and Technology, National University of Defense Technology, Changsha, Hunan, P.R. China
Xiaofeng He
Affiliation:
College of Intelligence Science and Technology, National University of Defense Technology, Changsha, Hunan, P.R. China
*
*Corresponding author. E-mail: wangmaosong12@hotmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In the integrated navigation system using extended Kalman filter (EKF), the state error conventionally uses linear approximation to tackle the commonly nonlinear problem. However, this error definition can diverge the filter in some adverse situations due to significant distortion of the linear approximation. By contrast, the nonlinear state error defined in the Lie group satisfies the autonomous equation, which thus has distinctively better convergence property. This work proposes a novel strapdown inertial navigation system (SINS) nonlinear state error defined in the Lie group and derives the SINS equations of the Lie group EKF (LG-EKF) for the MIMU/GNSS/magnetometer integrated navigation system. The corresponding measurement equations are also derived. A land vehicle field test has been conducted to evaluate the performance of EKF, ST-EKF (state transformation extended Kalman filter) and LG-EKF, which verifies LG-EKF's superior estimation accuracy of the heading angle as well as the other two horizontal angles (pitch and roll). The LG-EKF proposed in this paper is unlimited in the choice of sensors, which means it can be applied with both high-end and low-end inertial sensors.

Keywords

integrated navigationnonlinear state errorLG-EKFMIMU/GNSS/magnetometer integration
Type
Research Article
Information
The Journal of Navigation , Volume 74 , Issue 4 , July 2021 , pp. 887 - 900
Check for updates
Copyright
Copyright © The Royal Institute of Navigation 2021

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), 1614–1624.10.2514/1.G001025CrossRefGoogle Scholar
Barrau, A. and Bonnabel, S. (2017a). The invariant extended Kalman filter as a stable observer. IEEE Transactions on Automatic Control, 62(4), 1797–1812.10.1109/TAC.2016.2594085CrossRefGoogle Scholar
Barrau, A. and Bonnabel, S. (2017b). Three examples of the stability properties of the invariant extended Kalman filter. IF AC-PapersOnLine, 50(1), 431–437.10.1016/j.ifacol.2017.08.061CrossRefGoogle Scholar
Barrau, A. and Bonnabel, S. (2020). Extended Kalman Filtering With Nonlinear Equality Constraints: A Geometric Approach. IEEE Transactions on Automatic Control, 65(6), 2325–2338.10.1109/TAC.2019.2929112CrossRefGoogle Scholar
Brossard, M., Bonnabel, S. and Barrau, A. (2018). Invariant Kalman filtering for visual inertial SLAM. International Conference on Information Fusion, 2021–2028.Google Scholar
Brossard, M., Barrau, A. and Bonnabel, S. (2019). RINS-W: Robust Inertial Navigation System on Wheels. 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2068–2075.10.1109/IROS40897.2019.8968593CrossRefGoogle Scholar
Cui, C., Zhao, J. and Hu, J. (2019). Improving robustness of the MAV yaw angle estimation for low-cost INS/GPS integration aided with tri-axial magnetometer calibrated by rotating the ellipsoid model. IET Radar, Sonar & Navigation, 14(1), 61–70.Google Scholar
Groves, P. D. (2013). Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems. London: Artech House.Google Scholar
Hartley, R., Ghaffari, M. and Eustice, R. M. (2020). Contact-aided invariant extended Kalman filtering for robot state estimation. The International Journal of Robotics Research, 39(4), 402–430.10.1177/0278364919894385CrossRefGoogle Scholar
He, R., Hu, X., Zhang, L., He, X. and Han, G. (2020). A combination orientation compass based on the information of polarized skylight/geomagnetic/MIMU. IEEE Access, 8, 10879–10887.10.1109/ACCESS.2019.2939591CrossRefGoogle Scholar
Huang, G., Mourikis, A. I. and Roumeliotis, S. I. (2010). Observability-based rules for designing consistent EKF SLAM estimators. The International Journal of Robotics Research, 29(5), 502–528.10.1177/0278364909353640CrossRefGoogle Scholar
Jang, J. S. and Liccardo, D. (2007). Small UAV automation using MEMS. IEEE Aerospace and Electronic Systems Magazine, 22(5), 30–34.10.1109/MAES.2007.365332CrossRefGoogle Scholar
Leclerc, J. (2007). MEMs for aerospace navigation. IEEE Aerospace and Electronic Systems Magazine, 22(10), 31–36.10.1109/MAES.2007.4385708CrossRefGoogle Scholar
Liang, H., Bai, H. and Liu, N. (2020). Polarized skylight compass based on a soft-margin support vector machine working in cloudy conditions. Applied Optics, 59(5), 1271–1279.10.1364/AO.381612CrossRefGoogle ScholarPubMed
Miao, C., Cao, J. and Ou, Y. (2014). MEMS-SINS/GPS/magnetometer integrated navigation system for small unmanned aerial vehicles. Applied Mechanics and Materials, 568–570, 976–986.10.4028/www.scientific.net/AMM.568-570.976CrossRefGoogle Scholar
Ravish, G., Jigyasha, M. and Pannaga, N. (2013). MEMS technology and application in defense navigation system. International Journal of Engineering Research and Technology (IJERT), 2(10), 1903–1909.Google Scholar
Robert, E. and Perrot, T. (2017). Invariant Filtering Versus Other Robust Filtering Methods Applied to Integrated Navigation. 24th Saint Petersburg International Conference on Integrated Navigation Systems, 1–7.10.23919/ICINS.2017.7995604CrossRefGoogle Scholar
Schmidt, S. F. (1966). Application of state-space methods to navigation problems. Advances in Control Systems, 3, 293–340.10.1016/B978-1-4831-6716-9.50011-4CrossRefGoogle Scholar
Sebesta, K. D. and Boizot, N. (2014). A real-time adaptive high-gain EKF, applied to a quadcopter inertial navigation system. IEEE Transactions on Industrial Electronics, 61(1), 495–503.10.1109/TIE.2013.2253063CrossRefGoogle 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
Wang, M., Wu, W., He, X. and Pan, X. (2019a). State Transformation Extended Kalman Filter for SINS Based Integrated Navigation System. 2019 DGON Inertial Sensors and Systems (ISS). IEEE.10.1109/ISS46986.2019.8943781CrossRefGoogle Scholar
Wang, M., Wu, W., He, X. and Pan, X. (2019b). Further explanation and application of state transformation extended Kalman filter. Journal of Chinese Inertial Technology, 27(4), 500–509.Google Scholar
Wang, M., Wu, W., He, X., Li, Y. and Pan, X. (2019c). Consistent ST-EKF for long distance land vehicle navigation based on SINS/OD integration. IEEE Transactions on Vehicular Technology, 68(11), 10525–10534.10.1109/TVT.2019.2939679CrossRefGoogle Scholar
Wu, J. (2019). Real-time magnetometer disturbance estimation via online nonlinear programming. IEEE Sensors Journal, 19(12), 4405–4411.10.1109/JSEN.2019.2901925CrossRefGoogle Scholar
Wu, J., Liu, M., Huang, Y., Jin, C., Wu, Y. and Yu, C. (2020). SE(n)++: An Efficient Solution to Multiple Pose Estimation Problems. IEEE Transactions on Cybernetics, 1–12.Google Scholar
Wu, J., Zhou, Z., Chen, J., Fourati, H. and Li, R. (2016). Fast complementary filter for attitude estimation using low-cost MARG sensors. IEEE Sensors Journal, 16(18), 6997–7007.10.1109/JSEN.2016.2589660CrossRefGoogle Scholar
Wu, Y., Zou, D. and Liu, P. (2018). Dynamic magnetometer calibration and alignment to inertial sensors by Kalman filtering. IEEE Transactions on Control Systems and Technology, 26(2), 716–723.10.1109/TCST.2017.2670527CrossRefGoogle Scholar
Xiang, X., Ming, L., Cao, G. and Xu, D. (2019). Real-time calibration method for three-axis magnetometer based on adaptive parameter estimation. Journal of Chinese Inertial Technology, 27(3), 384–389.Google Scholar