Functional algorithms and attitude determination error equations for strap-down inertial navigation systems

Аuthors

Dmitrochenko L. A.^*, Sachkov G. P.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: nio3@mai.ru

Abstract

One of the main tasks when developing a strap-down inertial navigation system is creation of attitude determination algorithms providing both convenience of numerical realization of the algorithms, and minimization of computing errors. Attitude determination algorithms for strap-down inertial navigation systems and its error equations are considered in the paper. The main purpose of the paper is receiving the functional algorithms allowing direct calculation of aircraft orientation angles in the form of heading, roll, and pitch. It is specified that the use of Rodrigue-Hamilton parameters for orientation angles calculation do not give particular advantages compared to their definition with orientation matrixes. Qualitative differences of the suggested algorithm from the algorithm based on orientation matrixes are noted. The algorithm is convenient when using in the systems that requires calculation of angles of heading, roll, and pitch. The algorithm under consideration also can be applied when carrying out numerical or semi-natural experiments using rotary tables or motion simulators for inertial sensors and inertial navigation system characteristics research. The equations in variations allowing describe errors of strap-down inertial navigation systems in specified tasks are obtained in the paper. Variants of equations set down in relation to the movement along a loxodrome and along a great circle route are given. Dependence between projections of absolute angular rate in various coordinate systems is shown that is actual for various tasks of navigation and orientation of different mobile objects. Possibility of use of the suggested error equations both for platform or strap-down inertial navigation systems is noted.

Keywords:

orientation algorithm, inertial navigation system errors

References

1. Andreev V.D. Teoriya inertsial’noi navigatsii (Theory of inertial navigation), Moscow, Fizmatlit, 1966, vol. 1, 580 p.
2. Appel’ P.E. Teoreticheskaya mekhanika (Theory of mechanics), Moscow, Fizmatlit, 1960, vol. 2, 490 p.
3. Loitsyanskii L.G., Lur’e A.I. Kurs teoreticheskoi mekhaniki (Course of Theoretical Mechanics), Moscow, GITTL, 1955, vol. 2, 596 p.
4. Lur’e A.I. Analiticheskaya mekhanika (Analytical mechanics), Moscow, GITTL, 1961, 824 p.
5. Korn G., Korn T. Spravochnik po matematike (Reference book on mathematics (for scientists and engineers)), Moscow, Nauka, 1973, 832 p.
6. Laptev G.F. Elementy vektornogo ischisleniya (Elements of vector calculation), Moscow, Nauka, 1975, 336 p.

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