• Olha Sushchenko National Aviation University



accelerometers, attitude and heading reference systems, control and correction moments, dynamically tuned gyros, inertial navigation systems


Purpose: The paper deals with the mathematical description of the gimballed attitude and heading reference systems, which can be applied in design of strategic precision navigation systems. The main goal is to created mathematical description taking into consideration the necessity to use different navigations operating modes of this class of navigation systems. To provide the high accuracy the indirect control is used when the position of the gimballed platform is controlled by signals of gyroscopic devices, which are corrected using accelerometer’s signals. Methods: To solve the given problem the methods of the classical theoretical mechanics, gyro theory, and inertial navigation are used. Results: The full mathematical model of the gimballed attitude and heading reference system is derived including descriptions of different operating modes. The mathematical models of the system Expressions for control and correction moments in the different modes are represented. The simulation results are given. Conclusions: The represented results prove efficiency of the proposed models. Developed mathematical models can be useful for design of navigation systems of the wide class of moving vehicles.

Author Biography

Olha Sushchenko, National Aviation University

Olha Sushchenko (1956). D. Sci., Associate Professor.

Aircraft Control Systems Department of the National Aviation University, Kyiv, Ukraine.

Education: Kyiv Polytechnic Institute, Kyiv, Ukraine (1980).

Research area: systems for stabilization of information and measuring devices.


Wang H.G., Williams T.G. (2008) Strategic inertial navigation systems. IEEE Control Systems Magazine, vol. 28, no. 1, pp. 65 –85. Doi: 10.1109/MCS.2007.910206.

Brozgul L.I. (1989) Dynamychesky nastrayvaemыe hiroskopy. Modely pohreshnostey dlya system navyhatsyy" [Dynamically tuned gyros. Models of errors for navigation systems]. Moscow, Mashinostroenie Publ., 232 p. (In Russian)

Nesterenko O.I., Avrutov V.V. (1995) Matematycheskaya model' malohabarytnoho korrektyruemoho hyrokompasa s dynamychesky nastrayvaemыm hyroskopom [Mathematical model of small-size corrected gyroscopic compass]. Vestnik KPI, issue 24, pp. 242–255. (in Russian)

Zbrutskiy O.V., Nesterenko O.I., Shevchuk A.V. (2001–2002) Matematychna model' odniyeyi skhemy kursokrenopokazhchyka [Mathematical model of one scheme of indicator of heading and roll]. Mekhanika hiroskopichnykh system, issue

–18, pp. 154–167. (In Ukrainian)

Sushchenko O.A. (2014) Features of control by two-axis gimbaled attitude and heading reference system [Proc. 3rd Int. Conf. “Methods and Systems of Navigation and Motion Control]. Kyiv, pp. 190–193.

Sushchenko O.A. (2004) Osoblyvosti upravlinnya systemoyu vyznachennya kursu v rezhymi tochnoho pryvedennya do horyzontu [Features of control of course system in mode of high-precision levelling]. Visnyk NAU, no. 4, pp. 29-32. (in Ukrainian)

Sushchenko O. A. (2013) Optimal synthesis of electronic system for gyroscopic nautical compass stabilization [Proc. 33rd Int. Conf. “Electronics and Nanotechnology (ELNANO)”. Kyiv, pp. 436 – 439.

Hilkert J.M. (2008) Inertially stabilized platform technology. IEEE Control Systems Magazine, vol. 28, no. 1, pp. 26–46.doi:0.1109/MCS.2007.910256.

Smirnov E.L., Yalovenko A.V., Yakushenkov A.A. (1988) Tekhnycheskye sredstva sudovozhdenyya [Technical facilities of ship navigation].Moscow, Transport, 376 p. (in Russian)

Averil B. (1997)Fundamentals of High Accuracy Inertial Navigation, Reston, American Institute of Aeronautics and Astronautics Publ., 325 p.



How to Cite

Sushchenko, O. (2017). MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM. Advances in Aerospace Technology, 71(2), 42–50.