Analysis of Attitude Reference System Accuracy versus Rotation Angle Sensor Errors

Navigation instruments


Liang Q. 1*, Litvinenko Y. A.2, Stepanov O. A.2

1. St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 49, Kronverkskiy av , St. Petersburg, 197101, Russia
2. Concern «Elektropribor», 30, Malaya Posadskaya str., Saint Petersburg 197046, Russia



At present, various methods of compensation for errors in orientation systems and Inertial Navigation Systems (INS) based on the rotation modulation technique are widely used. This method can enhance the autonomy of orientation system and navigation system and allows the system to operate for a long time even on relatively coarse sensors.

The data processing problem of attitude and heading reference system based on rotation modulation technique is studied in this article. A novel orientation system consisting of two micromechanical IMUs mounted on two separate rotary platforms with orthogonal axes is proposed. It can improve attitude system performance while reducing requirements for external sensors. This structure allows estimate errors of angular rate sensors without dynamic motion model of the object and any other external information. Though, in this case, the accuracy of the orientation system under consideration depends not only on the IMU measurement errors, but also on the encoder measurement errors of the angular positions of the platforms.

The error of the angle sensor consists of two components: constant and random error. Based on covariance analysis, the accuracy of the gyroscope errors was estimated employing various error level of angle sensors. It has been proved that the constant error component of the angle sensor has the same effect as misalignment angles, and the random error component affects the accuracy of the orientation system in the way similar to gyro measurement noise. The resulting data is very useful for designing the attitude and heading reference system based on two units of micromechanical gyroscopes, especially for selecting the type of micromechanical gyroscopes and angle measurement sensors.


micromechanical unit, modulation rotation, orientation system, angle sensors errors


  1. Zel’dovich S.M., Maltinskii M.I., Okon I.M., Ostromukhov Ya.G. Avtokompensatsiya instrumental’nykh pogreshnostei girosistem (Auto compensation of gyro systems’ instrumental errors), Leningrad, Sudostroenie, 1976, 255 p.

  2. Ishibashi S., Tsukioka S., Sawa T. et al. The rotation control system to improve the accuracy of an inertial navigation system installed in an autonomous underwater vehicle, IEEE, Proceedings of the Symposium on Underwater Technology and Workshop on Scientific Use of Submarine Cables and Related Technologies, Tokyo, Japan, April 2007, pp. 495 – 498.

  3. Sun F., Sun W., Guo Z. Auto-compensation method of SINS based on IMU rotation, Chinese Journal of Scientific Instrument, 2009, issue 12, vol. 30, URL:

  4. Peshekhonov V.G. Gyroscopic Systems: Current Status and Prospects, Gyroscopy and Navigation, 2011, no. 1, pp. 3 – 16.

  5. Yuan Z., Zhao L. Error Analysis of Rotary SINS Sensor, Sensors & Transducers, September 2013, issue 9, vol.156, pp. 35 – 39.

  6. Stepanov A.P., Emelyantsev G.I., Blazhnov B.A. Efficiency of IMU modulation rotations in a marine FOG-based SINS, Gyroscopy and Navigation, 2015, no. 4 (91), pp. 42 – 54.

  7. Tuktarev N.A., Grishin D.V., Busurin V.I., Akhmedova S.K. Trudy MAI, 2016, no. 88, available at:

  8. Ren Q., Wang B., Deng Z., Fu M. A multi-position self-calibration method for dual-axis rotational inertial navigation system, Sensors and Actuators A: Physical, 2014, vol. 219, pp 24 – 31.

  9. Zheng Z., Han S., Zheng K. An eight-position self-calibration method for a dual-axis rotational inertial navigation system, Sensors and Actuators A: Physical, 2015, vol. 232, pp. 39 – 48.

  10. Lyan Ts., Litvinenko Yu.A. Materialy XVIII konferentsii molodykh uchenykh s mezhdunarodnym uchastiem «Navigatsiya i upravlenie dvizheniem», Saint-Petersburg, 15-18 marta 2016, pp. 556 – 564.

  11. Stepanov O.A. Osnovy teorii otsenivaniya s prilozheniyami k zadacham obrabotki navigatsionnoi informatsii. Vvedenie v teoriyu otsenivaniya (Fundamentals of Estimation Theory with Applications to the Problems of Navigation Information Processing. Introduction to the Estimation Theory), Saint-Petersburg, Elektropribor, 2010, 509 p.

  12. Zhao Lin, Wang Xiaoxu, Li Liang, Sun Min. Nonlinear System Filtering theory. Beijing, National Defense Industry Press, 2012, pp. 111 – 119.

  13. Ma Jianhong, Sun Yutong, Hao Yongqin. The comparison between resolver encoders and photoelectric encoders, Navigation and control, Jun. 2016, vol. 15 (3), pp. 89 – 94.

  14. Zheng L., Tang Q., Ma X., and Zhang Y. High-precision static and dynamic angular measurements with a ring laser gyro, Proceedings of SPIE, 1996, vol. 2899, pp. 50 – 53.

  15. Bournachev M., Filatov Y., Goncharov N., Loukianov D., Pavlov P. Dynamic goniometers based on ring laser and optical encoder. Ultra precision measurements, Proceedings of the 4-th Euspen International Conference, Glasgow, Scotland, UK, 2004, pp. 318 – 319.

  16. Qin S., Huang Z., Wang X. Optical Angular Encoder Installation Error Measurement and Calibration by Ring Laser Gyroscope, IEEE Transactions on instrumentation and measurement, 2010, vol. 59 (3), pp. 506 – 511.

  17. Wang X. Errors and precision analysis of subdivision signals for photoelectric angle encoders, Optics and Precision Engineering, 2012, vol. 20, no. 2, pp. 379 – 386.

  18. C. Wang, G. Zhang, S. Guo, and J. Jiang. Auto correction of interpolation errors in optical encoders, Proceedings of SPIE, 1996, vol. 2718, pp. 439 – 447.

  19. S. Ye Accurate measurement about photoelectric shift. Chengdu, Science and Technology Press, 2003, 230 p.

  20. Z. Huang, S. Qin, X. Wang, and D. Zhan. Error analysis of optical angular encoder and calibration with ring laser gyro // Chin J. Sci Instrument, Oct. 2007, vol. 28, no. 10, pp. 1866 – 1869.

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