Application of Cross-linked Positional Correction in a Strapdown Orientation System

The quaternionic equations describing operation of strapdown inertial orientation system (BISO) consisting of an inertial measurement module (IMU) and an on-board computer, are considered. The IMU contains a three-component angular velocity meter, a linear acceleration sensor and a magnetometer. The aim of the work construction of a system of kinematic equations with asymptotically stable solutions configured for the Shuler period and a low-pass filter with a given bandwidth. This ensures compensation for errors in the initial exposure, tolerance to linear accelerations (ballistic errors), reduction of the noise level in the estimates of orientation parameters in relation to the signals of gyroscopes, accelerometers, and magnetometers and the absence of accumulation of orientation determination errors. The BISO algorithms are based on the Poisson equations in the Rodrigue-Hamilton parameters with additionally introduced terms of cross-positional correction, the signs of which are set based on the requirement of asymptotic stability, while the numerical values of the correction coefficients provide the remaining properties of the algorithms. The range of angular velocities of an object at which the properties of the algorithms are preserved is theoretically substantiated. The results of the work are confirmed by mathematical modeling of the work of the IMU and BISO and full-scale tests of a BISO model with a micromechanical IMU on a vehicle.

1. Matveev V.V., Raspopov V.Ya. Osnovy postroyeniya besplatformennykh inertsial’nykh navigatsionnykh sistem (Fundamentals of constructing Strapdown Inertial Navigation Systems), St. Petersburg, 2009, 280 р. (in Russ.)

2. Anuchin O.N., Emelyantsev G.I. Integrirovannyye sistemy oriyentatsii i navigatsii dlya morskikh podvizhnykh ob”yektov (Integrated Orientation and Navigation Systems for Marine Mobile Objects), St. Petersburg, 2003, 390 р. (in Russ.)

3. Branets V.N., Shmyglevsky I.P. Vvedeniye v teoriyu besplatformennykh inertsial’nykh navigatsionnykh system (Introduction to the Theory of Strapdown Inertial Navigation Systems), Moscow, 1992, 280 р. (in Russ.)

4. Chelnokov Yu.N. Kvaternionyye modeli i metody dinamiki, navigatsii i upravleniya dvizheniyem (Quaternion Models and Methods of Dynamics, Navigation and Motion Control), Moscow, 2011, 560 р. (in Russ.)

5. Plotnikov P.K., Lyuchev S.A. Journal of Instrument Engineering, 1991, no. 10(34), pp. 62–68. (in Russ.)

6. Plotnikov P.K.Giroskopiya i Navigatsiya, 1999, no. 3, pp. 23–35. (in Russ.)

7. Plotnikov P.K. Mechanics of Rigid Bodies, 1999, no. 2, pp. 3–14. (in Russ.)

8. Premerlani W., Bizard Р. Direction Cosine matrix IMU: Theory, 2009, http://http://gentlenav.googlecode.com/files/DCMDraft2.pdf.

9. Zhidkova N.V., Volkov V.L. Sovremennyye problemy nauki i obrazovaniya, 2015, no. 1, pp. 4–14. (in Russ.)

10. Volkov V.L., Zhidkova N.V. Trudy Nizhegorodskogo gosudarstvennogo tekhnicheskogo universiteta im. R.E. Alekseyeva. Mikromekhanicheskiye sistemy, 2015, no. 3, pp. 279–286. (in Russ.)

11. Aleshkin V.V., Zdrazhevskiy R.A., Golovanov P.N., Marusich V.O. Mekhatronika, avtomatizatsiya, upravleniye (Mechatronics, Automation, Control), 2021, no. 9(22), pp. 494–504. (in Russ.)

12. Patent RU 2738342, G01 M 7/00, G01 M 15/00, Sposob avtonomnoy oriyentatsii podvizhnogo ob”yekta s pomoshch’yu inertsial’nogo izmeritel’nogo modulya (Method for Autonomous Orientation of a Moving Object Using an Inertial Measurement Module), V.V. Aleshkin, R.A. Zdrazhevsky, P.N. Golovanov, V.O. Marusich, Patent application no. 2019145337, Priority 30.12.2019. (in Russ.)

13. Aleshkin V.V., Golovanov P.N. Problemy upravleniya, obrabotki i peredachi informatsii (UOPI-2018) (Problems of Management, Processing and Transmission of Information (UPI-2018)), Proc. of the VI Intern. Sci. Conf., Saratov, 2019, рр. 79–84. (in Russ.)