Skip to main content
SpringerLink
Log in

Strapdown INS/GPS Integrated Navigation Using Geometric Algebra

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

A strapdown inertial navigation system (INS)/global positioning system (GPS) integrated navigation Kalman filter in terms of geometric algebra (GA) is proposed. Two error models, i.e., the additive GA error (AGAE) model and the multiplicative GA error (MGAE) model, are developed on the ground of the GA-based strapdown INS model. The AGAE model describes the navigation error by means of perturbation. In contrast, the MGAE model which is indirectly derived from the AGAE one, can physically represent the difference between the computed frame and the true frame. Subsequently, one Kalman filter is constructed on the basis of the MGAE model of the strapdown INS and the error model of GPS. A variety of simulations are carried out to test the proposed Kalman filter. The results show that the Kalman filter can reduce the navigation error remarkably.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Christensen and N. Fogh, Inertial navigation system. Aalborg university, Tech. Rep. 08gr1030a, 2008.

  2. Savage P. G.: Strapdown inertial navigation integration algorithm design part 1: Attitude algorithms. Journal of Guidance, Control, and Dynamics. 21(1), 19–28 (1998)

    Article  ADS  Google Scholar 

  3. Ignagni M. B.: Duality of optimal strapdown sculling and coning compensation algorithms. Navigation: Journal of The Institute of Navigation. 45(2), 85–95 (1998)

    Google Scholar 

  4. Wu Y., Hu X., Hu D., Li T., Lian J.: Strapdown inertial navigation system algorithms based on dual quaternion. IEEE Transactions on Aerospace and Electronic Systems. 41(1), 110–132 (2005)

    Article  ADS  MATH  Google Scholar 

  5. Wu Y., Hu X., Wu M., Hu D.: Strapdown inertial navigation using dual quarternion algebra: Error analysis. IEEE Transactions on Aerospace and Electronic Systems. 42(1), 259–266 (2006)

    Article  ADS  Google Scholar 

  6. Savage P. G.: A unified mathematical framework for strapdown algorithm design. Journal of Guidance, Control, and Dynamics. 29(2), 237–249 (2006)

    Article  ADS  Google Scholar 

  7. Wu Y.: Comment on a unified mathematical framework for strapdown algorithm design. Journal of Guidance, Control, and Dynamics. 29(6), 1482–1484 (2006)

    ADS  Google Scholar 

  8. P. G. Savage, Reply by the author to y. wu et al. Journal of Guidance, Control, and Dynamics, 29 (6) (2006) 1485.

  9. J. W. Jordan, An accurate strapdown direction cosine algorithm. NASA, Tech. Rep. TN-D-5384, 1969.

  10. J. E. Bortz, A new mathematical formulation for strapdown inertial navigation. IEEE Transactions on Aerospace and Electronic Systems, AES-7 (1) (1971) 61–66.

    Google Scholar 

  11. Miller R. B.: A new strapdown attitude algorithm. Journal of Guidance, Control, and Dynamics. 6(4), 287–291 (1983)

    Article  ADS  Google Scholar 

  12. D. Wu and Z. Wang, Strapdown inertial navigation system algorithms based on geometric algebra. Adv. Appl. Clifford Algebras, 22 (2012) 1151–1167.

    Google Scholar 

  13. Wu D., Wang Z.: Strapdown Inertial Navigation Using Geometric Algebra: Screw Blade Algorithm. Positioning. 3(2), 13–20 (2012)

    Article  Google Scholar 

  14. D. Hestenes, New Foundations for Classical Mechanics, 2nd ed. Kluwer Academic, Dordrecht, 1999.

  15. Candy L., Lasenby J.: On finite rotations and the noncommutativity rate vector. IEEE Transactions on Aerospace and Electronic Systems. 42(2), 938–943 (2010)

    Article  ADS  Google Scholar 

  16. E. Bayro-Corrochano, Geometric Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action. Springer Verlag, London, 2010.

  17. L. Dorst, D. Fontijne, and S. Mann, Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry. Morgan Kaufmann, San Francisco, 2007.

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

Download references

Author information

Authors and Affiliations

  1. Institute of Automation, National University of Defense Technology, Changsha, 410073, China

    Dimin Wu & Zhengzhi Wang

Authors
  1. Dimin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengzhi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dimin Wu.

Additional information

This work was supported by the National Natural Science Foundation of China (60835005).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, D., Wang, Z. Strapdown INS/GPS Integrated Navigation Using Geometric Algebra. Adv. Appl. Clifford Algebras 23, 767–785 (2013). https://doi.org/10.1007/s00006-013-0395-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-013-0395-3

Keywords

Search

Navigation