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A Novel Constrained Filter Integrated with an Extended Kalman Filter in Underground Pipeline Navigation Using MEMS IMU


To produce a 3D map of the Tehran’s first gas transfer pipeline (Tehran—Kuhnamak), a methodology has been developed in this research, in which a strapdown inertial navigation system (SINS) based on micro-electro-mechanical system (MEMS) and inertial measurement unit (IMU) is applied on pipeline inspection gauges (PIGs) to sense data every 4 millimeters of 111 kilometers of the whole pipeline. The navigation solution is based on an extended Kalman filter (EKF) using Allan variance (AVAR) to analyze and tune the EKF initial inputs. A new constrained PIG filter (CPF) is proposed in this paper in integration with EKF, in which two Euler angles (pitch and yaw) of the PIG are updated due to non-holonomic state constraints between pipe junctions. Besides, 98 magnetic control points have been used to increase robustness about every kilometer, which is coordinated by GPS. Furthermore, odometer measurements have been employed as measurements in the EKF. The results show that using such a hybrid approach has improved the PIG positioning accuracy by about 81% compared with that of the Basic EKF. In addition, positioning accuracy in comparison with the latest methods like EKF/pipeline junctions (PLJ) has increased by 32%. Furthermore, the proposed method is 55% better than EKF/PLJ in the algorithm runtime.

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  1. Guan, L., Cong, X., Sun, Y., Gao, Y., Iqbal, U., and Noureldin, A., Enhanced MEMS SINS aided pipeline surveying system by pipeline junction detection in small diameter pipeline, IFAC-PapersOnLine, 2017, vol. 50, no. 1, pp. 3560–3565.

    Article  Google Scholar 

  2. Murray, I. and Dawson, J., Evaluating pipeline integrity using ILI mapping data, Proc. 9th Pipeline Technology Conference 2014, Berlin, Germany, 2014.

  3. Guan, l., Gao, Y., Osman, A., Iqbal, U. and Noureldin, A., Analysis of rolling motion effect on SINS error modeling in PIG, Proc. 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS), 2016, pp. 681–686.

  4. Li, R., Cai, M., Shi, Y., Feng, Q. and Chen, P., Technologies and application of pipeline centerline and bending strain of In-line inspection based on inertial navigation, Transactions of the Institute of Measurement and Control, 2018, vol. 40, pp. 1554–1567.

    Article  Google Scholar 

  5. Santana, D.D.S., Maruyama, N. and Furukawa, C.M., Estimation of trajectories of pipeline PIGs using inertial measurements and non linear sensor fusion, Proc. 2010 9th IEEE/IAS International Conference on Industry Applications—INDUSCON 2010, 2010, pp. 1–6.

  6. Arribas, J., Moragrega, A., Fernández-Prades, C. and Closas, P., Low-cost GNSS/INS/Odometric sensor fusion platform for ground intelligent transportation systems, Proc. 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, 2017, pp. 436–455.

  7. Jin, S. and Ping, Y., Research on the describing of trajectory for subsea pipeline based on inertial navigation system, Proc. 2011 IEEE Power Engineering and Automation Conference, 2011, pp. 463–468.

  8. Yadav, S.M., Shastri, S.K., Chakravarthi, G.B., Kumar, V., Rao, A.D. and Agrawal, V.K., A fast, parallel algorithm for fully overlapped Allan variance and total variance for analysis and modeling of noise in inertial sensors, IEEE Sensors Letters, 2018, vol. 2, pp. 1–4.

    Article  Google Scholar 

  9. El-Sheimy, N., Hou, H. and Niu, X., Analysis and modeling of inertial sensors using Allan variance, IEEE Transactions on Instrumentation and Measurement, 2007, vol. 57, pp. 140–149.

    Article  Google Scholar 

  10. Ghafil, H.N. and Jármai, K., Spatial representations, in Optimization for Robot Modelling with MATLAB, Springer, 2020, pp. 55–68.

    Book  Google Scholar 

  11. Hou, H., Modeling inertial sensors errors using Allan variance, Master of Science Thesis, University of Calgary, Department of Geomatics Engineering, Calgary, 2004.

  12. Barreda Pupo, L., Characterization of errors and noises in MEMS inertial sensors using Allan variance method, Master of Science Thesis, Universitat Politècnica de Catalunya, Barcelona, 2016.

  13. Sahli, H., MEMS-based aided inertial navigation system for small diameter pipelines, PhD Thesis, University of Calgary, 2016.

  14. Sahli, H. and El-Sheimy, N., A novel method to enhance pipeline trajectory reconstruction using pipeline junctions, Sensors, 2016, vol. 16, no. 4, pp. 567.

    Article  Google Scholar 

  15. El-Sheimy, N., Sahli, H. and Moussa, A., Methods and systems to enhance pipeline trajectory reconstruction using pipeline junctions, Patent of the US, no. US 2017/0138524 A1, 2017.

  16. Guan, L., Xu, X., Gao, Y., Liu, F., Rong, H., Wang, M. et al., Micro-Inertial-Aided High-Precision Positioning Method for Small-Diameter PIG Navigation, IntechOpen, 2018.

    Google Scholar 

  17. Zhang, M., Li, K., Hu, B. and Meng, C., Comparison of Kalman filters for inertial integrated navigation, Sensors, 2019, vol. 19, no. 6, p. 1426.

    Article  Google Scholar 

  18. Ji, M., Liu, J., Xu, X., Guo, Y. and Lu, Z., Improved pedestrian positioning with inertial sensor based on adaptive gradient descent and double-constrained extended Kalman filter, Complexity, 2020, vol. 2020, ID 4361812.

  19. IEEE Standard 952-1997: Specification Format Guide and Test Procedure for Single-Axis Interferometric Fiber Optic Gyros, IEEE Standards Board, 1998.

  20. Gonzalez, R., Giribet, J. and Patino, H., An approach to benchmarking of loosely coupled low-cost navigation systems, Mathematical and Computer Modelling of Dynamical Systems, 2015, vol. 21, no. 3, pp. 272–287.

    Article  Google Scholar 

  21. Noureldin, A., Karamat, T.B. and Georgy, J., Fundamentals of Inertial Navigation, Satellite-Based Positioning and Their Integration, Springer Science & Business Media, 2012.

    Google Scholar 

  22. Titterton, D.H. and Weston, J.L., Strapdown Inertial Navigation Technology, 2nd Edition, Stevenage: Institution of Electrical Engineers, The American Institute of Aeronautics and Astronautics, 2004.

  23. Groves, P.D., Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, Artech House, 2013.

    MATH  Google Scholar 

  24. Vavilova, N., Golovan, A., Kozlov, A., Nikitin, I., Panyov and A., Parusnikov, N., A navigation system of a pipeline inspection system for oil and gas pipelines: the results of the development and testing, Proc. 22nd St. Petersburg International Conference on Integrated Navigation Systems, St. Petersburg: Concern CSRI Elektropribor, 2015.



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The data for research have been provided by Segal Processing Engineering Company [25] which is the first indigenous and national manufacturer of PIG in Iran. The operator and owner of the mentioned gas pipeline is Iranian Gas Transmission Company (IGTC) [26].

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Correspondence to I. H. Afshar, M. R. Delavar or B. Moshiri.

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Some or all data, models, or codes used during the study were provided by a third party. Direct requests for these materials may be made to the provider as indicated in the Acknowledgements.

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Afshar, I.H., Delavar, M.R. & Moshiri, B. A Novel Constrained Filter Integrated with an Extended Kalman Filter in Underground Pipeline Navigation Using MEMS IMU. Gyroscopy Navig. 13, 7–22 (2022).

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  • EKF
  • odometer
  • navigation constraint
  • CPF
  • PLJ
  • SINS