Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-30T22:46:21.064Z Has data issue: false hasContentIssue false

Graph-optimisation-based self-calibration method for IMU/odometer using preintegration theory

Published online by Cambridge University Press:  13 January 2022

Shiyu Bai
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China
Jizhou Lai*
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China
Pin Lyu
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China
Yiting Cen
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China
Bingqing Wang
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China
Xin Sun
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China
*Corresponding author. E-mail:


Determination of calibration parameters is essential for the fusion performance of an inertial measurement unit (IMU) and odometer integrated navigation system. Traditional calibration methods are commonly based on the filter frame, which limits the improvement of the calibration accuracy. This paper proposes a graph-optimisation-based self-calibration method for the IMU/odometer using preintegration theory. Different from existing preintegrations, the complete IMU/odometer preintegration model is derived, which takes into consideration the effects of the scale factor of the odometer, and misalignments in the attitude and position between the IMU and odometer. Then the calibration is implemented by the graph-optimisation method. The KITTI dataset and field experimental tests are carried out to evaluate the effectiveness of the proposed method. The results illustrate that the proposed method outperforms the filter-based calibration method. Meanwhile, the performance of the proposed IMU/odometer preintegration model is optimal compared with the traditional preintegration models.

Research Article
Copyright © The Author(s), 2022. 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.)


Chang, L., Niu, X. J. and Liu, T. Y. (2020). GNSS/IMU/ODO/LiDAR-SLAM integrated navigation system using IMU/ODO pre-integration. Sensors, 20(17), 4702.CrossRefGoogle ScholarPubMed
Chiu, H. P., Zhou, X. S., Carlone, L., Dellaert, F., Samarasekera, S. and Kumar, R. (2014). Constrained Optimal Selection for Multi-sensor Robot Navigation using Plug-and-Play Factor Graphs. 2014 IEEE International Conference on Robotics and Automation (ICRA). Hong Kong, China, 663–670.CrossRefGoogle Scholar
Dang, Z. Q., Wang, T. M. and Pang, F. M. (2018). Tightly-coupled Data Fusion of VINS and Odometer based on Wheel Slip Estimation. 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO). Kuala Lumpur, Malaysia, 1613–1619.CrossRefGoogle Scholar
Dellaert, F. and Kaess, M. (2017). Factor graphs for robot perception. Foundations and Trends ® in Robotics, 6(1–2), 1139.CrossRefGoogle Scholar
Forster, C., Carlone, L., Dellaert, F. and Scaramuzza, D. (2017). On-Manifold Preintegration for Real-Time Visual--Inertial Odometry. IEEE Transactions on Robotics, 33(1), 121.CrossRefGoogle Scholar
Gao, J. X., Li, K. and Chen, Y. P. (2017). Study on integration of FOG single-axis rotational INS and odometer for land vehicle. IEEE Sensors Journal, 18(2), 752763.CrossRefGoogle Scholar
Gao, Z. Z., Ge, M. R., Li, Y., Shen, W. B., Zhang, H. P. and Schuh, H. (2018). Railway irregularity measuring using Rauch-Tung-Striebel smoothed multi-sensors fusion system: Quad-GNSS PPP, IMU, odometer, and track gauge. GPS Solutions, 22(2), 36.CrossRefGoogle Scholar
Geiger, A., Lenz, P., Stiller, C. and Urtasun, R. (2013). Vision meets robotics: The kitti dataset. The International Journal of Robotics Research, 32(11), 12311237.CrossRefGoogle Scholar
Georgy, J., Karamat, T., Iqbal, U. and Noureldin, A. (2011). Enhanced MEMS-IMU/odometer/GPS integration using mixture particle filter. GPS solutions, 15(3), 239252.CrossRefGoogle Scholar
He, Y. J., Guo, Y., Ye, A. X. and Yuan, K. (2017). Camera-Odometer Calibration and Fusion using Graph based Optimization. 2017 IEEE International Conference on Robotics and Biomimetics (ROBIO). Macau, China, 1624–1629.CrossRefGoogle Scholar
Indelman, V., Williams, S., Kaess, M. and Dellaert, F. (2013). Information fusion in navigation systems via factor graph based incremental smoothing. Robotics and Autonomous Systems, 61(8), 721738.CrossRefGoogle Scholar
Li, Z. K., Wang, J., Li, B. H., Gao, J. X. and Tan, X. L. (2014). GPS/INS/Odometer integrated system using fuzzy neural network for land vehicle navigation applications. The Journal of Navigation, 67(6), 967.CrossRefGoogle Scholar
Li, L. L., Sun, H. X., Yang, S., Ding, X. W., Wang, J., Jiang, J. L., Pu, X. H., Ren, C. H., Hu, N. and Guo, Y. C. (2018). Online calibration and compensation of total odometer error in an integrated system. Measurement, 123, 6979.CrossRefGoogle Scholar
Liu, Z. B., El-Sheimy, N. and Qin, Y. Y. (2016). Low-Cost INS/Odometer Integration and Sensor-to-Sensor Calibration for Land Vehicle Applications. Proceedings of the IAG/CPGPS International Conference on GNSS+(ICG+ 2016). Shanghai, China.Google Scholar
Liu, J. X., Gao, W. and Hu, Z. Y. (2019). Visual-inertial Odometry Tightly Coupled with Wheel Encoder Adopting Robust Initialization and Online Extrinsic Calibration. 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Macau, China, 5391–5397.CrossRefGoogle Scholar
Mascaro, R., Teixeira, L., Hinzmann, T., Siegwart, R. and Chli, M. (2018). GOMSF: Graph-Optimization based Multi-Sensor Fusion for Robust UAV Pose Estimation. 2018 IEEE International Conference on Robotics and Automation (ICRA). Brisbane, Australia, 1421–1428.Google Scholar
Nemec, D., Šimák, V., Janota, A., Hruboš, M. and Bubeníková, E. (2019). Precise localization of the mobile wheeled robot using sensor fusion of odometry, visual artificial landmarks and inertial sensors. Robotics and Autonomous Systems, 112, 168177.CrossRefGoogle Scholar
Qin, T., Li, P. L. and Shen, S. J. (2018). Vins-mono: A robust and versatile monocular visual-inertial state estimator. IEEE Transactions on Robotics, 34(4), 10041020.CrossRefGoogle Scholar
Quan, M. X., Piao, S. H., Tan, M. L. and Huang, S. S. (2019). Tightly-coupled monocular visual-odometric SLAM using wheels and a MEMS gyroscope. IEEE Access, 7, 9737497389.CrossRefGoogle Scholar
Seo, J. W., Lee, H. K., Lee, J. G. and Park, C. G. (2006). Lever arm compensation for GPS/INS/odometer integrated system. International Journal of Control, Automation, and Systems, 4(2), 247254.Google Scholar
Strasdat, H., Montiel, J. M. M. and Davison, A. J. (2012). Visual SLAM: Why filter? Image and Vision Computing, 30(2), 6577.CrossRefGoogle Scholar
Wang, Q. Z., Fu, M. Y., Deng, Z. H. and Ma, H. B. (2012). A Comparison of Loosely-Coupled Mode and Tightly-Coupled Mode for INS/VMS. American Control Conference (ACC). Montréal, Canada, 6346–6351.Google Scholar
Wang, X. F., Chen, H. Y., Li, Y. J. and Huang, H. L. (2019). Online extrinsic parameter calibration for robotic camera–encoder system. IEEE Transactions on Industrial Informatics, 15(8), 46464655.CrossRefGoogle Scholar
Wen, W. S, Kan, Y. C. and Hsu, L. T. (2019a). Performance Comparison of GNSS/INS Integrations Based on EKF and Factor Graph Optimization. Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019). Miami, USA, 3019-3032.Google Scholar
Wen, W. S., Bai, X. W., Kan, Y. C. and Hsu, L. T. (2019b). Tightly coupled GNSS/INS integration via factor graph and aided by fish-eye camera. IEEE Transactions on Vehicular Technology, 68(11), 1065110662.CrossRefGoogle Scholar
Wu, Y. (2014). Versatile Land Navigation using Inertial Sensors and Odometry: Self-Calibration, In-motion Alignment and Positioning. 2014 DGON Inertial Sensors and Systems (ISS). Karlsruhe, Germany, 1–19.Google Scholar
Wu, Y. X., Goodall, C. and El-Sheimy, N. (2010). Self-calibration for IMU/Odometer Land Navigation: Simulation and Test Results. Proceedings of the 2010 International Technical Meeting of The Institute of Navigation, USA: San Diego, 839849.Google Scholar
Yuan, C., Lai, J. Z., Lyu, P., Shi, P., Zhao, W. and Huang, K. (2018). A novel fault-tolerant navigation and positioning method with stereo-camera/micro electro mechanical systems inertial measurement unit (MEMS-IMU) in hostile environment. Micromachines, 9(12), 626.CrossRefGoogle Scholar
Zhang, P. H., Hancock, C. M., Lau, L., Roberts, G. W. and de Ligt, H. (2019). Low-cost IMU and odometer tightly coupled integration with Robust Kalman filter for underground 3-D pipeline mapping. Measurement, 137, 454463.CrossRefGoogle Scholar
Zhao, H. S., Miao, L. J. and Shao, H. J. (2017). Adaptive two-stage Kalman filter for SINS/odometer integrated navigation systems. The Journal of Navigation, 70(2), 242261.CrossRefGoogle Scholar