Skip to main content
Log in

Solving the Autonomous Initial Navigation Task for Strapdown Inertial Navigation System on the Perturbed Basis Using Rodriguez—Hamilton Parameters

  • Flight Dynamics and Control of Flight Vehicles
  • Published:
Russian Aeronautics Aims and scope Submit manuscript

Abstract

The paper attempts to solve the initial orientation task for perturbed-basis strapdown inertial navigation systems (SINS) of aircraft with most general assumptions about the character of the angular motion of the basis and the accelerations perturbing the SINS. The solution has been attained in the form of generalized Kalman filter using the vector of Rodriguez—Hamilton parameters as the state vector, and the measurement vector of the SINS accelerometers as the observation vector. A practical example serves to illustrate the high precision and convergence rate of estimation process of the aircraft SINS initial orientation parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sokolov, S.V. and Pogorelov, V.A., Stokhasticheskaya otsenka, upravlenie i identifikatsiya v vysokotochnykh navigatsionnykh sistemakh (Stochastic Evaluation, Control and Identification in High-Precision Navigation Systems), Moscow: Fizmatlit, 2016.

    Google Scholar 

  2. Sokolov, S.V. and Pogorelov, V.A., Osnovy sinteza mnogostrukturnykh besplatformennykh navigatsionnykh sistem (Fundamentals of Multi-Structural Strapdown Navigation System Synthesis), Moscow: Fizmatlit, 2009.

    Google Scholar 

  3. Rozenberg, I.N., Sokolov, S.V., Umanskii, V.I., and Pogorelov, V.A., Teoreticheskie osnovy tesnoi integratsii inertsial’no-sputnikovykh navigatsionnykh sistem (Theoretical Basis of Close Integration of Inertial Satellite Navigation Systems), Moscow: Fizmatlit, 2018.

    Google Scholar 

  4. Shen, Kai, Neusypin, K.A., Selezneva, M.S., and Proletarskii, A.V., Research on High-Precision Measurement Systems of Modern Aircraft, Izv. Vuz. Av. Tekhnika, 2018, vol. 61, no. 2, pp. 124–130 [Russian Aeronautics (Engl. Transl.), vol. 61, no. 2, pp. 279–286].

    Google Scholar 

  5. Emaletdinova, L.Yu., Gainutdinova, A.V., and Gainutdinova, T.Yu., An Algorithm for Calibrating the Three-Axis Magnetometer, Izv. Vuz. Av. Tekhnika, 2017, vol. 60, no. 1, pp. 128–134 [Russian Aeronautics (Engl. Transl.), vol. 60, no. 1, pp. 134–140].

    Google Scholar 

  6. Malyutin, D.M. and Malyutina, M.D., Information-Measuring and Control System of Unmanned Aerial Vehicles Based on High-Accuracy Micromechanical Sensitive Elements, Izv. Vuz. Av. Tekhnika, 2014, vol. 57, no. 2, pp. 39–43 [Russian Aeronautics (Engl. Transl.), vol. 57, no. 2, pp. 162–168].

    Google Scholar 

  7. Savel’ev, V.M. and Antonov, D.A., Exhibition of Strapdown Inertial Navigation System of Unmanned Flying Vehicle on Mobile Basis, Trudy MAI, 2011, no. 45, URL: http://trudymai.ru/published.php?ID=25328&;PAGEN_2=2.

  8. Pogorelov, V.A., Chub, E.G., and Yakovlev, K.Yu., Modeling the Motion of an Uncompensated Gyrostabilized Platform in the Rodrigues—Hamilton Parameters, Izv. Vuz. Av. Tekhnika, 2012, vol. 55, no. 3, pp. 69–72 [Russian Aeronautics (Engl. Transl.), vol. 55, no. 3, pp. 315–319].

    Google Scholar 

  9. Dzhandzhava, G.I., Avgustov, L.I., Babichenko, A.V., Orekhov, M.I., Sukhorukov, S.Ya., and Shkred, V.K., Navigatsiya letatel’nykh apparatov v okolozemnom prostranstve (Navigation of Flying Vehicles in Circumterrestrial Space), Moscow: Nauchtekhlitizdat, 2015.

    Google Scholar 

  10. Lukasevich, V.I., Sokolov, S.V., and Pogorelov, V.A., Non-Linear Stochastic Filtering of Angular Motion Parameters of Distributed Antenna by Satellite Measurements, Datchiki i Sistemy, 2015, no. 5(192), p. 8–17.

  11. Kleusberg, A., Mathematics of Attitude Determination with GPS, GPS World, 1995, vol. 6, no. 9, pp. 72–78.

    Google Scholar 

  12. Nadler, A. and Bar-Itzhack, I.Y., An Efficient Algorithm for Attitude Determination Using GPS, Proc. of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998), Nashville, TN, 1998. P. 1783–1789.

  13. Mahony, R., Hamel, T., and Pflimlin, J.-Ml., Nonlinear Complementary Filters on the Special Orthogonal Group, IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2008, 53 (5), pp.1203–1217.

    Article  MathSciNet  MATH  Google Scholar 

  14. Euston, M., Coote, P.W., Mahony, R., Kim, J., and Hamel, T., A Complementary Filter for Attitude Estimation of a Fixed-Wing UAV, Proc. 2008 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2008, Nice, France, pp. 340–345.

    Google Scholar 

  15. Crassidis, J.L., Markley, F.L., and Cheng, Y., Survey of Nonlinear Attitude Estimation Methods, Journal of Guidance, Control, and Dynamics, 2007, vol. 30, no. 1, pp. 12–28.

    Article  Google Scholar 

  16. Gebre-Egziabher, D., Hayward, R.C., and Powell, J.D., Design of Multi-Sensor Attitude Determination Systems, IEEE Transactions on Aerospace and Electronic Systems, 2004, vol. 40, no. 2, pp. 627–649.

    Article  Google Scholar 

  17. Matveev, V.V. and Raspopov, V.Ya., Pribory i sistemy orientatsii, stabilizatsii i navigatsii na MEMS datchikakh (Instruments and Systems for Orientation, Stabilization and Navigation on MEMS Sensors), Tula: TulGU, 2017.

    Google Scholar 

  18. Sinitsyn, I.N., Fil’try Kalmana i Pugacheva (Kalmann and Pugachev Filters), Moscow: Logos, 2006.

    Google Scholar 

  19. Noureldin, A., Karamat, T.B., and Georgy, J., Fundamentals of Inertial Navigation, Satellite-based Positioning and Their Integration, Heidelberg — New York — Dordrecht — London: Springer, 2013.

    Book  Google Scholar 

Download references

Acknowledgements

This work was supported by RUDN 5–100 Program and the Russian Foundation for Basic Research project no. 18-07-00126. The results were used in implementing State Order no. 1.11772.2018/11.12.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Pogorelov.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sokolov, S.V., Pogorelov, V.A. & Shatalov, A.B. Solving the Autonomous Initial Navigation Task for Strapdown Inertial Navigation System on the Perturbed Basis Using Rodriguez—Hamilton Parameters. Russ. Aeronaut. 62, 42–51 (2019). https://doi.org/10.3103/S1068799819010069

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068799819010069

Keywords

Navigation