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

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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. 
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     title = {An investigation of algorithms for estimating the inertial orientation of a moving object},
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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/