Geodesic
An investigation of algorithms for estimating the inertial orientation of a moving object
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 80-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 investigated. 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 new algorithms are developed using the Picard successive approximation method. These algorithms use the 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. 
@article{ISU_2016_16_1_a7,
     author = {Yu. N. Chelnokov and S. E. Perelyaev and L. A. Chelnokova},
     title = {An investigation of algorithms for estimating the inertial orientation of a moving object},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {80--95},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a7/}
}
TY  - JOUR
AU  - Yu. N. Chelnokov
AU  - S. E. Perelyaev
AU  - L. A. Chelnokova
TI  - An investigation of algorithms for estimating the inertial orientation of a moving object
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2016
SP  - 80
EP  - 95
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a7/
LA  - ru
ID  - ISU_2016_16_1_a7
ER  - 
%0 Journal Article
%A Yu. N. Chelnokov
%A S. E. Perelyaev
%A L. A. Chelnokova
%T An investigation of algorithms for estimating the inertial orientation of a moving object
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2016
%P 80-95
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a7/
%G ru
%F ISU_2016_16_1_a7
Yu. N. Chelnokov; S. E. Perelyaev; L. A. Chelnokova. An investigation of algorithms for estimating the inertial orientation of a moving object. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 80-95. http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a7/

[1] Chelnokov Yu. N., Quaternion and Biquaternion Models and Methods of Mechanics of Solid Bodies and Applications. Geometry and Kinematics of Motion, Fizmatlit, M., 2006, 511 pp. (in Russian)

[2] Chelnokov Yu. N., Perelyaev S. E., Chelnokova L. A., “New SDINS Equations and Algorithms for Orientation with Four-Dimensional Skew-Symmetric Operators”, 14-th Intern. Scientific Conf. “System Analysis, Control and Navigation”, Book of abstracts, MAI-PRINT, M., 2009, 35–36 (in Russian) | MR

[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”, Problems of Critical Situations in Precision Mechanics and Control, Proc. of the Conf., OJSC “Nauka” Publ. Center, Saratov, 2013, 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 Skew-symmetric Operators”, Proc. of the XXI Saint-Petersburg Intern. Conf. on Integrated Navigation Systems, State Research Center of the Russian Federation, Concern CSRI Elektropribor, Saint-Petersburg, 2014, 308–312 (in Russian)

[5] Perelyaev S. E., Chelnokov Yu. N., “New Algorithms for Estimating the Orientation of an Object”, J. Appl. Math. Mech., 78:6 (2014), 778–789 | MR

[6] Gantmakher F. R., Theory of Matrices, Nauka, M., 1967, 576 pp. (in Russian) | MR

[7] Stuelpnagel J., “On the parametrization of the three-dimensional rotation group”, SIAM Review, 6:4 (1964), 422–429 | DOI | MR

[8] Perelyaev S. E., “On the correspondence between the three- and four-dimensional parameters of the three-dimensional rotation group”, Mech. Solids, 44:2 (2009), 204–213 | DOI

[9] Panov A. P., Mathematical Background of Inertial Orientation Theory, Naukova Dumka, Kiev, 1995, 279 pp. (in Russian)

[10] Bortz J. E., “A new mathematical formulation for strapdown inertial navigation”, IEEE Transaction on Aerospace and Electronic Systems, AES-7:1 (1971), 61–66 | DOI

[11] Savage P. G., “Strapdown inertial navigation integration algorithm design. Pt. 1: Attitude algorithms”, J. Guidance, Control and Dynamics, 21:1 (1998), 19–28 | DOI | Zbl

[12] Branetz V. N., Lectures on the Theory of Inertial Navigation Control Systems, MFTI, M., 2009, 304 pp. (in Russian)

[13] Edwards A., “Strapdown Inertial Navigation Systems”, Rocket Technology, 1973, no. 5, 50–57

[14] Besarab P. N., “Estimation of the Orientation Parameters of a Moving Object”, U.S.S.R. Comput. Math. Math. Phys., 14:1 (1974), 242–248 | DOI | MR | Zbl

[15] Branetz V. N., Shmyglevsky I. P., Application of Quaternions in Problems of Orientation of a Rigid Body, Nauka, M., 1973, 320 pp. (in Russian) | MR

[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, 11–20 (in Russian) | MR

[17] Plotnikov P. K., Chelnokov Yu. N., “Comparative Analysis of Accuracy of Algorithms for Estimating the Orientation of an Object in Rodrigues–Hamilton Parameters and Direction Cosines”, Cosmic Research, 17:3 (1979), 371–377