Observability Analysis for the INS Error Model with GPS/Uncalibrated Magnetometer Aiding

  • Ronan Arraes Jardim ChagasEmail author
  • Jacques Waldmann


A commercial inertial navigation system (INS) yields time-diverging solutions due to errors in the inertial sensors, which can inhibit long term navigation. To circumvent this issue, a set of non-inertial sensors is used to limit these errors. The fusion between additional data and INS solution is often done by means of an extended Kalman filter using a state-error model. However, the Kalman filter estimates should be used when full observability produces small estimation uncertainty. This paper has analyzed conditions to achieve full observability using as non-inertial sensors a GPS receiver and an uncalibrated magnetometer combined with either a locally horizontal-stabilized IMU or with a strapdown IMU. The magnetometer bias was considered constant and augmented the error-state space. Observability analysis based on concepts of linear algebra provided a geometric insight on the requirements for attaining full observability when assuming piece-wise constant system dynamics. The novel analysis has been validated by covariance analysis of simulation results. Also, simulation results indicate that fusion with uncalibrated magnetometer data without proper processing gives rise to estimation divergence.


Observability analysis INS error model GPS magnetometer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bar-Itzhack, I.Y., Berman, N.: Control Theoretic Approach to Inertial Navigation Systems. Journal of Guidance, Control, and Dynamics 11, 237–247 (1988)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Brammer, K., Siffling, G.: Kalman-Bucy Filters. Artech House Publishers, Boston (1989)Google Scholar
  3. 3.
    Xsens Technologies B.V., Pantheon 6a, P.O. Box 559, 7500 AN Enschede, The Netherlands: MTi-G User Manual and Technical Documentation (2008)Google Scholar
  4. 4.
    Analog Devices, Inc., One Technology Way, P.O. Box 9106, Norwood, MA 02062-9106, U.S.A.: ADIS16400/ADIS16405: Triaxial Inertial Sensor with Magnetometer (2009)Google Scholar
  5. 5.
    Chagas, R.A.J., Waldmann, J.: Geometric Inference-Based Observability Analysis Digest of INS Error Model with GPS/Magnetometer/Camera Aiding. In: 19th Saint Petersburg International Conference on Integrated Navigation Systems. CSRI Elektropribor, JSC, Saint Petersburg, Russia (2012)Google Scholar
  6. 6.
    Goshen-Meskin, D., Bar-Itzhack, I.Y.: Observability Analysis of Piece-Wise Constant Systems - Part II: Application to Inertial Navigation In-Flight Alignment. IEEE Transactions on Aerospace and Electronic Systems 28(4), 1068–1075 (1992)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Lee, J., Park, C.G., Park, H.W.: Multiposition Alignment of Strapdown Inertial Navigation System. IEEE Transactions on Aerospace and Electronic Systems 29(4), 1323–1328 (1993)CrossRefGoogle Scholar
  8. 8.
    Salychev, O.: Applied Inertial Navigation: Problems and Solutions. BMSTU Press, Moscow (2004)Google Scholar
  9. 9.
    Goshen-Meskin, D., Bar-Itzhack, I.Y.: Observability Analysis of Piece-Wise Constant Systems - Part I: Theory. IEEE Transactions on Aerospace and Electronic Systems 28(4), 1056–1067 (1992)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Pinson, J.C.: Inertial Guidance for Cruise Vehicles. In: Leondes, C.T. (ed.) Guidance and Control of Aerospace Vehicles. McGraw-Hill, New York (1963)Google Scholar
  11. 11.
    Chen, C.-T.: Linear System Theory and Design. CBS College Publishing, New York (1984)Google Scholar
  12. 12.
    Chung, D., Park, C.G., Lee, J.G.: Observability Analysis of Strapdown Inertial Navigation System using Lyapunov Transformation. In: 35th IEEE Conference on Decision and Control, pp. 23–28. IEEE Press, New York (1995)Google Scholar
  13. 13.
    Rhee, I., Abdel-Hafez, M.F., Speyer, J.L.: Observability of an Integrated GPS/INS during Maneuvers. IEEE Transactions on Aerospace and Electronic Systems 40(2), 526–535 (2004)CrossRefGoogle Scholar
  14. 14.
    Hong, S., Lee, M.H., Chun, H.-H., Kwon, S.-H., Speyer, J.L.: Observability of Errors States in GPS/INS Integration. IEEE Transactions on Vehicular Technology 54(2), 731–743 (2005)CrossRefGoogle Scholar
  15. 15.
    Lee, M.K., Hong, S., Lee, M.H., Kwon, S., Chun, H.-H.: Observability Analysis of Alignment Erros in GPS/INS. Journal of Mechanical Science and Technology 19(6), 1253–1267 (2005)CrossRefGoogle Scholar
  16. 16.
    Tang, Y., Wu, Y., Wu, M., Wu, W., Hu, X., Shen, L.: INS/GPS Integration: Global Observability Analysis. IEEE Transactions on Vehicular Technology 58(3), 1129–1142 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ronan Arraes Jardim Chagas
    • 1
    Email author
  • Jacques Waldmann
    • 1
  1. 1.Instituto Tecnológico de AeronáuticaSão PauloBrazil

Personalised recommendations