Skip to main content
SpringerLink
Log in

Strapdown Inertial Navigation System Algorithms Based on Geometric Algebra

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

Abstract

This paper develops the strapdown inertial navigation system (SDINS) algorithm by using geometric algebra (GA). The kinematic equation of the motor is derived and applied to design the GA-based navigation kinematic equations. These equations combine the attitude and velocity/position integrations which are treated respectively in the traditional SDINS algorithm, and they can be solved by normal differential equation methods. The consistency of the presented algorithm with the traditional algorithm is justified. Simulations are carried out under both ideal and nonideal inertial sensor configurations. The results show that this proposed algorithm can improve the navigation precision remarkably, and restrain the errors caused by the maneuver of the vehicle apparently. Therefore, it is more suitable for navigation systems with high-precision and high-maneuver requirements.

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. Pitman G. R.: Inertial Guidance. Wiley, New York (1962)

    MATH  Google Scholar 

  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  MATH  Google Scholar 

  3. Savage P. G.: Strapdown inertial navigation integration algorithm design part 2: Velocity and position algorithms. Journal of Guidance, Control, and Dynamics 21(2), 208–221 (1998)

    Article  MATH  Google Scholar 

  4. 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 

  5. Murray R., Li Z., Sastry S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Florida (1994)

    MATH  Google Scholar 

  6. Celledoni E., Owren B.: Lie group methods for rigid body dynamics and time integration on manifolds. Computer Methods in Applied Mechanics and Engineering 192(3–4), 421–438 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Cervantes-Sanchez J. J., Rico-Martinez J. M., Gonzalez-Montiel G., Gonzalez-Galvan E. J.: The differential calculus of screws: theory, geometrical interpretation, and applications. Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science 223(6), 1449–1468 (2009)

    Article  Google Scholar 

  8. 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  Google Scholar 

  9. V. N. Branets and I. P. Shmyglevsky, Introduction to the Theory of Strapdown Inertial Navigation System (In Russian). Nauka, Moscow, 1992.

  10. Daniilidis K.: Hand-eye calibration using dual quaternions. International Journal of Robotics Research 18, 286–298 (1999)

    Article  Google Scholar 

  11. Bayro-Corrochano E.: Motor algebra for 3d kinematics: The case of the handeye calibration. Journal of Mathematical Imaging and Vision, 13, 79–100 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bayro-Corrochano E.: Modeling the 3d kinematics of the eye in the geometric algebra framework. Pattern Recognition 36(12), 2993–3012 (2003)

    Article  MATH  Google Scholar 

  13. Bayro-Corrochano E.: Conformal geometric algebra for robotic vision. Journal of Mathematical Imaging and Vision 24, 55–81 (2006)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  15. J. Zamora-Esquivel and E. Bayro-Corrochano, Kinematics and diferential kinematics of binocular robot heads. In Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, Florida, (2006), 4130–4135.

  16. Zamora-Esquivel J., Bayro-Corrochano E.: Robot perception and handling actions using the conformal geometric algebra framework. Adv. Appl. Clifford Algebras 20, 959–990 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Berman S., Liebermann D. G., Flash T.: Application of motor algebra to the analysis of human arm movements. Robotica 26, 435–451 (2008)

    Article  Google Scholar 

  18. Rosenhahn B.: Pose estimation of 3D free-form contours. International Journal of Computer Vision 62(3), 267–289 (2005)

    Article  Google Scholar 

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

    Google Scholar 

  20. Hestenes D.: New Foundations for Classical Mechanics, 2nd ed. Kluwer Academic, Dordrecht (1999)

    MATH  Google Scholar 

  21. 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 

  22. I. Y. Bar-Itzhack, Navigation computation in terrestrial strapdown inertial navigation system. IEEE Transactions on Aerospace and Electronic Systems AES-13 (6) (1977), 679–689.

  23. D. H. Titterton and J. L. Weston, Strapdown Inertial Navigation Technology. Peregrinus Ltd. on behalf of the Institute of Electrical Engineers, New York, 1997.

  24. Wu Y., Wang P., Hu X.: Algorithm of earth-centered earth-fixed coordinates to geodetic coordinates. IEEE Transactions on Aerospace and Electronic Systems 39(4), 1457–1461 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Automation, College of Mechatronics Engineering and Automation, National University of Defense Technology, Yanwachi 47, Dongfeng Road, Kaifu Region, Changsha, Hunan, 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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, D., Wang, Z. Strapdown Inertial Navigation System Algorithms Based on Geometric Algebra. Adv. Appl. Clifford Algebras 22, 1151–1167 (2012). https://doi.org/10.1007/s00006-012-0326-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-012-0326-8

Keywords

Search

Navigation