Skip to main content

GNSS/INS Tightly Coupled Navigation with Robust Adaptive Extended Kalman Filter


GNSS/INS integrated navigation system is particularly outstanding in providing reliable navigation information for land vehicle applications. However, GNSS measurements are easily disturbed in harsh operating environments, especially the accuracy of integrated navigation system integrated with inertial navigation system will be affected accordingly. Hence, a robust adaptive extended Kalman filter procedure is crucial to maintain the stability and reliability of the system. In this study, a robust factor based on local test of standardized residual vector was proposed to deal with potential gross errors, and an adaptive factor based on position dilution of precision which reflect the satellite geometry was proposed to adjust covariance matrix. The robust adaptive factor function models are established to adjust the dynamic model and abnormal measurements. The test results show that the standard extended Kalman filter cannot always give an optimal solution due to the influence of GNSS measurements and satellite geometry especially in the complex environment, while the proposed method improves the reliability of the integrated navigation system by adopting robust adaptive factor.

This is a preview of subscription content, access via your institution.


δr n :

error vectors of position (m)

δv n :

error vectors of velocity (m/s)

ψ n :

error vectors of attitude (rad/s)


accelerometer error vector (m/s2)

f n :

vectors of specific force (N)


gyro drift (rad/s)

ω n ie :

earth rotation velocity in the n-frame (rad/s)

ω n en :

the rotation vector from the e-frame to the n-frame (rad/s)

ω n in :

the sum of the ω nie and ω nen (rad/s)

\(d{t_{{u_b}}}\) :

receiver clock bias (m)

\(d{t_{{u_d}}}\) :

receiver clock drift (m)

ρ I :

pseudo range measurements from INS (m)

ω G :

pseudo range measurements from GPS (m)

ω̇ I :

pseudo range rate measurements from INS (m/s)

ω̇ G :

pseudo range rate measurements from GPS (m/s)


inertial navigation system


global navigation satellite system


slowly growing errors


fault detection and isolation


kalman filter


autonomous integrity monitoring by extrapolation


multiple-model-based adaptive estimation


extended kalman filter


innovation-based adaptive estimation


residual-based adaptive estimation


position dilution of precision


autonomous integrity monitoring


inertial measurement unit


  • Alfakih, M., Keche, M. and Benoudnine H. (2018). A new Wi-Fi/GPS fusion method for robust positioning in urban environments. Physical Communication, 31, 10–20.

    Article  Google Scholar 

  • Almagbile A. (2019). Geometric and statistical interpretation of correlation between fault tests in integrated GPS/INS systems. J. Applied Geodesy 13, 3, 267–278.

    Article  Google Scholar 

  • Amato, F., Cosentino, C., Mattei, M. and Paviglianiti, G. (2006). A direct/functional redundancy scheme for fault detection and isolation on an aircraft. Aerospace Science and Technology, 10, 338–345.

    Article  MATH  Google Scholar 

  • Angrisano, A., Maratea, A. and Gaglione, S. (2018). A resampling strategy based on bootstrap to reduce the effect of large blunders in GPS absolute positioning. J. Geodesy, 92, 81–92.

    Article  Google Scholar 

  • Bhatti, U. and Ochieng, W. (2009). Detecting multiple failures in GPS/INS integrated system: A novel architecture for integrity monitoring. J. Global Positioning Systems 8, 1, 26–12.

    Article  Google Scholar 

  • Bhatti, U., Ochieng, W. and Feng, S. (2007a). Integrity of an integrated GPS/INS system in the presence of slowly growing errors. Part I: A critical review. GPS Solutions, 11, 173–181.

    Article  Google Scholar 

  • Bhatti, U., Ochieng, W. and Feng, S. (2007b). Integrity of an integrated GPS/INS system in the presence of slowly growing errors. Part II: analysis. GPS Solutions, 11, 183–192.

    Article  Google Scholar 

  • Chen, J., Zhang, S., Cao, Y., Li, H. and Zheng, H. (2020). A robust fault detection algorithm for the GNSS/INS integrated navigation systems. J. Geodesy and Geoinformation Science 3, 1, 12–24.

    Google Scholar 

  • Chiang, K. W., Tsai, G. J., Li, Y. and El-Sheimy, N. (2020). Navigation engine design for automated driving using INS/GNSS/3D LiDAR-SLAM and integrity assessment. Remote Sensing 12, 10, 1564.

    Article  Google Scholar 

  • Choi, S. and Hong, D. (2021). Position estimation in urban u-turn section for autonomous vehicles using multiple vehicle model and interacting multiple model filter. Int. J. Automotive Technology 22, 6, 1599–1607.

    Article  Google Scholar 

  • Doostdar, P., Keighobadi, J. and Hamed, M. A. (2020). ING/GNSS integration using recurrent fuzzy wavelet neural networks. GPS Solutions, 24, 29.

    Article  Google Scholar 

  • Gullu, M. and Yilmaz, I. (2010). Outlier detection for geodetic nets using ADALINE learning algorithm. Scientific Research & Essays 5, 5, 440–447.

    Google Scholar 

  • Han, H. and Wang, J. (2017). Robust GPS/BDS/INS tightly coupled integration with atmospheric constraints for long-range kinematic positioning. GPS Solutions, 21, 1285–1299.

    Article  Google Scholar 

  • Hewitson, S. and Wang, J. (2006). GNSS receiver autonomous integrity monitoring (RAIM) performance analysis. GPS Solutions, 10, 155–170.

    Article  Google Scholar 

  • Hewitson, S. and Wang, J. (2010). Extended receiver autonomous integrity monitoring (eRAIM) for GNSS/INS Integration. J. Surveying Engineering, 136, 13–22.

    Article  Google Scholar 

  • Hwang, Y., Jeong, Y., Kweon, I. S. and Choi, S. (2021). Online misalignment estimation of strapdown navigation for land vehicle under dynamic condition. Int. J. Automotive Technology 22, 6, 1723–1733.

    Article  Google Scholar 

  • Jiang, H., Shi, C., Li, T. and Jing, G. (2021). Low-cost GPS/INS integration with accurate measurement modeling using an extended state observer. GPS Solutions, 25, 17.

    Article  Google Scholar 

  • Katriniok, A. and Abel, D. (2016). Adaptive EKF-based vehicle state estimation with online assessment of local observability. IEEE Trans. Control Systems Technology 24, 4, 1368–1381.

    Article  Google Scholar 

  • Knight, N. L. and Wang, J. (2009). A comparison of outlier detection procedures and robust estimation methods in GPS positioning. J. Navigation 62, 4, 699–709.

    Article  Google Scholar 

  • Kottath, R., Narkhede, P, Kumar, V., Karar, V. and Poddar, S. (2017). Multiple model adaptive complementary filter for attitude estimation. Aerospace Science and Technology, 69, 574–581.

    Article  Google Scholar 

  • Lee, J. Y., Kim, H. S., Choi, K. H., Lim, J., Chun, S. and Lee, H. K. (2016). Adaptive GPS/INS integration for relative navigation. GPS Solutions 20, 1, 63–75.

    Article  Google Scholar 

  • Lee, J., Shin, H. and Kim, T. (2018). Optimal combination of fault detection and isolation methods of integrated navigation algorithm for UAV. Int. J. Aeronautical and Space Sciences, 19, 694–710.

    Article  Google Scholar 

  • Li, X., Wang, X., Liao, J., Li, X. and Lyu, H. (2021). Semi-tightly coupled integration of multi-GNSS PPP and S-VINS for precise positioning in GNSS-challenged environments. Satellite Navigation 2, 1, 1–14.

    Article  Google Scholar 

  • Lim, J. H., Choi, K. H., Cho, J. and Lee, H. K. (2017). Integration of GPS and monocular vision for land vehicle navigation in urban area. Int. J. Automotive Technology 18, 2, 345–356.

    Article  Google Scholar 

  • Miao, L. and Shi, J. (2014). Model-based robust estimation and fault detection for MEMS-INS/GPS integrated navigation systems. Chinese J. Aeronautics 27, 4, 947–954.

    Article  Google Scholar 

  • Park, C. H. and Kim, N. H. (2014). Precise and reliable positioning based on the integration of navigation satellite system and vision system. Int. J. Automotive Technology 15, 1, 79–87.

    Article  Google Scholar 

  • Roysdon, P. F. and Farrell, J. A. (2017). Robust GPS-INS outlier accommodation: A soft-thresholded optimal estimator. IFAC-PapersOnLine 50, 1, 3574–3579.

    Article  Google Scholar 

  • Shen, C., Zhang, Y., Guo, X., Chen, X. and Liu, J. (2020). Seamless GPS/inertial navigation system based on self-learning square-root cubature Kalman filter. IEEE Trans. Industrial Electronics 68, 1, 499–508.

    Article  Google Scholar 

  • Srilatha, V., Dutt, I., Sasi, G., Swapna, S., Swarna, R., Rajkumar, G. and Usha, C. (2009). Investigation of GDOP for precise user position computation with all satellites in view and optimum four satellite configurations. The J. Indian Geophysical Union 13, 3, 139–148.

    Google Scholar 

  • Trigo, G. F., Theil, S., Vandersteen, J., Bennani, S. and Roux, C. (2019). Robust tightly coupled hybrid navigation for space transportation. J. Spacecraft and Rockets 56, 2, 596–609.

    Article  Google Scholar 

  • Yang, L. and Shen, Y. (2020). Robust M estimation for 3D correlated vector observations based on modified bifactor weight reduction model. J. Geodesy, 94, 31.

    Article  Google Scholar 

  • Yang, L., Nie, Y. and Shen, Y. (2019). Characteristic analysis of 3D outlier detection method for GNSS network adjustments. J. Surveying Engineering 145, 4, 04019014.

    Article  Google Scholar 

  • Yang, Y. and Gao, W. (2006). An optimal adaptive Kalman filter. J. Geodesy 80, 4, 177–183.

    Article  MATH  Google Scholar 

  • Yang, Y., He, H. and Xu, G. (2001). Adaptively robust filtering for kinematic geodetic positioning. J. Geodesy 75, 2, 109–116.

    Article  MATH  Google Scholar 

  • Yoon, J. H., Eben, L. S. and Ahn, C. (2016). Estimation of vehicle sideslip angle and tire-road friction coefficient based on magnetometer with GPS. Int. J. Automotive Technology 17, 3, 427–435.

    Article  Google Scholar 

  • Yu, H., Han, H., Wang, J., Xiao, H. and Wang, C. (2020). Single-frequency GPS/BDS RTK and INS ambiguity resolution and positioning performance enhanced with positional polynomial fitting constraint. Remote Sensing 12, 15, 2374.

    Article  Google Scholar 

  • Zhang, Q., Zhao, L., Zhao, L. and Zhou, J. (2018). An improved robust adaptive Kalman filter for GNSS precise point positioning. IEEE Sensors J. 18, 10, 4176–4186.

    Article  Google Scholar 

  • Zhong, L., Liu, J., Li, R. and Wang, R. (2017). Approach for detecting soft faults in GPS/INS integrated navigation based on LS-SVM and AIME. J. Navigation 70, 3, 561–579.

    Article  Google Scholar 

Download references


This research was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 19KJB510028), the National Natural Science Foundation of China (Grant No. 61803188) and the Doctoral Scientific Research Startup Foundation of Jinling Institute of Technology (Grant No. jit-b-201603) and Postdoctoral Foundation of Jiangsu Province (Grant No. 2021K463C).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Youlong Wu.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wu, Y., Chen, S. & Yin, T. GNSS/INS Tightly Coupled Navigation with Robust Adaptive Extended Kalman Filter. Int.J Automot. Technol. 23, 1639–1649 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key Words

  • GNSS/INS integrated navigation
  • Extended Kalman filter
  • Robust
  • Adaptive
  • Dilution of precision