Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2014-6pp.560-567

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S.E. Perelyayev and Yu.N. Chelnokov, "New algorithms for determining the inertial orientation of an object," J. Appl. Math. Mech. 78 (6), 560-567 (2014)
Year 2014 Volume 78 Issue 6 Pages 560-567
Title New algorithms for determining the inertial orientation of an object
Author(s) S.E. Perelyayev (Moscow, Russia,
Yu.N. Chelnokov (Moscow, Russia)
Abstract Kinematic equations and algorithms for the operation of strapdown inertial navigation systems intended for the high-accuracy determination of the inertial orientation parameters (the Euler (Rodrigues-Hamilton) parameters) of a moving object are considered. Together with classical orientation equations, Hamilton's quaternions and new kinematic differential equations in four-dimensional (quaternion) skew-symmetric operators are used that are matched with the classical rotation quaternion and the quaternion rotation matrix using Cayley's formulae. New methods for solving the synthesized kinematic equations are considered: a one-step quaternion orientation algorithm of third-order accuracy and two-step algorithms of third- and fourth-order accuracy in four-dimensional skew-symmetric operators for calculating the parameters of the spatial position of an object. The algorithms were constructed using the Picard method of successive approximations and employ primary integral information from measurements of the absolute angular velocity of the object as the input information, and have advantages over existing algorithms of a similar order with respect to their accuracy and simplicity.
Received 28 February 2014
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