Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Chelnokov Y. N., Perelyaev S. E., Chelnokova L. A. An Investigation of Algorithms for Estimating the Inertial Orientation of a Moving Object. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 1, pp. 80-95. DOI: 10.18500/1816-9791-2016-16-1-80-95, EDN: VUSOFL

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.03.2016
Full text:
download
(downloads: 195)
Language: 
Russian
Heading: 
Mechanics
UDC: 
531 (075.8); 629.7.05(075)
DOI: 
10.18500/1816-9791-2016-16-1-80-95
EDN: 
VUSOFL

An Investigation of Algorithms for Estimating the Inertial Orientation of a Moving Object

Autors: 
Chelnokov Yurii Nikolaevich, Saratov State University
Perelyaev Sergei Egororovich, "AeroSpetsProekt" Ltd.
Chelnokova Lyudmila Aleksandrovna, Institute of Precision Mechanics and Control, Russian Academy of Sciences (IPTMU RAS)
Abstract: 

The new and known strapdown INS algorithms for high-precision estimation of the orientation parameters of a moving object (Rodrigues–Hamilton (Euler) parameters) in the inertial frame are nvestigated. The new algorithms are based upon using the classical Hamilton rotation quaternion, quaternion with zero scalar part, which is correlated to the classical rotation quaternion via the quaternion equivalent of Cayley formula, and also the new quaternion differential equation for the inertial orientation of a moving object. The newalgorithms are developed using thePicard successive approximation method. These algorithms usethe integral raw information about absolute angular motion of an object as input data. It is demonstrated that the new algorithms are superior to the known algorithms of the same order regarding accuracy and complexity.

Key words: 
moving object
Rodrigues – Hamilton (Euler) parameters
inertial orientation
Hamilton quaternion
quaternion matrix
Cayley formula
four-dimensional skew-symmetric operator
References: 
  1. Chelnokov Yu. N. Quaternion and Biquaternion Models and Methods of Mechanics of Solid Bodies and its Applications. Geometry and Kinematics of Motion. Moscow, Fizmatlit, 2006. 511 p. (in Russian).
  2. Chelnokov Yu. N., Perelyaev S. E., Chelnokova L. A. New SDINS Equations and Algorithms for Orientation with Four-Dimensional SkewSymmetric Operators. Book of abstracts, 14-th Intern. Scientific Conf. “System Analysis, Control and Navigation”. Мoscow, MAI-PRINT, 2009, pp. 35–36 (in Russian).
  3. Chelnokov Yu. N., Perelyaev S. E., Chelnokova L. A. Differential Kinematic Equations of the Angular Motion of a Solid in Four-dimensional Skew-symmetric Operators and the new Strapdown INS algorithms for orientation. Proc. of the Conf. “Problems of Critical Situations in Precision Mechanics and Control”. Saratov, OJSC “Nauka” Publ. Center, 2013, pp. 315–320 (in Russian).
  4. Chelnokov Yu. N., Perelyaev S. E. New Equations and Algorithms of Orientation and Navigations for Strapdown INS with Four-dimensional Skewsymmetric Operators. Proc. of the XXI SaintPetersburg Intern. Conf. on Integrated Navigation Systems. Saint-Petersburg, State Research Center of the Russian Federation, Concern CSRI Elektropribor, 2014, pp. 308–312 (in Russian).
  5. Perelyaev S. E., Chelnokov Yu. N. New Algorithms for Estimating the Orientation of an Object. J. Appl. Math. Mech., 2014, vol. 78, iss. 6, pp. 778–789.
  6. Gantmakher F. R. Theory of Matrices. Moscow, Nauka, 1967, 576 p. (in Russian).
  7. Stuelpnagel J. On the parametrization of the threedimensional rotation group. SIAM Review, 1964, vol. 6, no. 4, pp. 422–430.
  8. Perelyaev S. E. On the correspondence between the three- and four-dimensional parameters of the three-dimensional rotation group. Mech. Solids, 2009, vol. 44, iss. 2, pp. 204–213.
  9. Panov A. P. Mathematical Background of Inertial Orientation Theory. Kiev, Naukova Dumka, 1995, 279 p. (in Russian).
  10. Bortz J. E. A new mathematical formulation for strapdown inertial navigation. IEEE Trans. On Aerospace and Electronic Systems, 1971, vol. AES-7, no. 1, pp. 61-66.
  11. Savage P. O. Strapdown inertial navigation integration algorithm design. Pt. 1: Attitude algorithms. J. Guidance, Control and Dynamics, 1998, vol. 21, no. 1, pp. 19–28.
  12. Branetz V. N. Lectures on the Theory of Inertial Navigation Control Systems. Moscow, MFTI, 2009, 304 p. (in Russian).
  13. Edwards A. Strapdown Inertial Navigation Systems. Rocket Technology, 1973, no. 5, pp. 50–57.
  14. Besarab P. N. Estimation of the Orientation Parameters of a Moving Object. U.S.S.R. Comput. Math. Math. Phys., 1974, vol. 14, no 1, p. 242-248. DOI: https://doi.org/10.1016/0041-5553(74)90156-6.
  15. Branetz V. N, Shmyglevsky I. P. Application of Quaternions in Problems of Orientation of a Rigid Body. Moscow, Nauka, 1973, 320 p. (in Russian).
  16. Chelnokov Yu. N. On Estimating the Orientation of an Object in Rodrigues – Hamilton Parameters Using its Angular Velocity. Izv. Akad. Nauk. Mekh. Tverd. Tela, 1977, no. 3, pp. 11–20 (in Russian).
  17. Plotnikov P. K., Chelnokov Yu. N. Comparative Analysis of Accuracy of Algorithms for Estimating the Orientation of an Object in RodriguesHamilton Parameters and Direction Cosines. Cosmic Research, 1979, vol. 17, iss. 3, pp. 371–377.
Received: 
22.11.2015
Accepted: 
25.02.2016
Published: 
31.03.2016
  • 1188 reads