Mohammad Ghesmati^{1}, Jafar Heyrani Nobari^{2}, Mohammadreza Arvan ^{}^{1}, Abdorreza Kashaninia^{1}

2- K. N. Toosi University of Technology

This paper deals with analyzing gyroscope drift error in the position-independent navigation algorithm of a stable platform inertial system. Most of the stable platform navigation algorithms proposed in the literature have drawbacks of estimating position rates for alignment commands. Not only the estimating position rates are the basic source of position errors, but they also make the alignment commands and their implementation more complicated. The major advantage of the proposed design is that the angular velocity commands of gyroscopes are independent of the system position and are proportional to accelerations’ integrals, all of which eliminate, the errors resulted from the estimation of the longitude and latitude rates. In this paper, the stable platform system is modeled, and plate alignment procedure is determined and the initial conditions of navigation phase are calculated. In stationary conditions, the position error propagation for the fixed gyroscope drift is obtained analytically. The position error of the proposed algorithm propagates linearly with time, while in the strapdawn algorithm; this error propagates as the cube of time.

Type of Article: Research paper |
Subject:
Special

Received: 2018/03/14 | Accepted: 2018/10/19 | Published: 2019/08/15

Received: 2018/03/14 | Accepted: 2018/10/19 | Published: 2019/08/15

1. [1] Jekeli, C., Inertial Navigation Systems with Geodetic Applications, Walter de Gruyter, New York, 2001. [DOI:10.1515/9783110800234]

2. [2] Izmailov, E. A., "Modern tendencies in development of inertial sensors and aircraft systems", Trudy FGUP NPTs AP, Sistemy i Pribory Upravleniya, No. 1, 2010, pp. 30-43.

3. [3] Kuznetsov, A. G., Portnov, B. I., Izmailov, E. A., "Two Classes of Aircraft Strapdown Inertial Navigation Systems on Laser Gyros: Development and Test Results", Gyroscopy and Navigation, Vol. 5, No. 4, 2014, pp. 187-194. [DOI:10.1134/S2075108714040087]

4. [4] Zhang DR, Bin YE, Dang J., "Flight test performance error analysis of the platform inertial navigation system", Flight Dynamics, Vol. 29, No. 1, 2011, pp. 74-77.

5. [5] George, R., Pitman, JR., Inertial Guidance, John Wiley & Sons, New York, 1962.

6. [6] Britting, K.R., Inertial Navigation Systems Analysis, John Wiley & Sons, New York, 1971.

7. [7] Britting, K. R. "Analysis of Space Stabilized Inertial Navigation Systems", M.I.T. Experimental Astronomy Laboratory, RE-35, 1968.

8. [8] Britting, K. R. "Error Analysis of Strapdown and Local Level Inertial Systems Which Compute in Geographic Coordinates", M.I.T. Measurement Systems Laboratory, RE-52, 1969.

9. [9] Broxmeyer, C., Inertial Navigation Systems, McGraw-Hill, New York, 1964. [DOI:10.1115/1.3629763]

10. [10] Wiryadinata, R., Wahyunggoro, O., Widada, W., Sunarno, M., Santoso, I. "Modification of strapdown inertial navigation system algorithm for rocket flight test", Journal of Theoretical and Applied Information Technology, Vol. 72, No. 2, 2015, pp. 273-279.

11. [11] Zhenhuan, W., Xijun, C., Qingshuang, Z. "Comparison of strapdown inertial navigation algorithm based on rotation vector and dual quaternion", Chinese Journal of Aeronautics, Vol. 26, No. 2, 2013, pp. 442-448. [DOI:10.1016/j.cja.2013.02.022]

12. [12] Maria de Fátima Alves Nunes Bento, Development and Validation of an IMU/GPS/Galileo Integration Navigation System for UAV, PhD Thesis, University of Munich, Munich, Germany, 2013.

13. [13] MacKenzie, D. "Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance", Massachusetts Institute of Technology, 1993.

14. [14] Britting, K. R. "PACE II space-stabilized inertial navigation system", M.I.T. Instrumentation Lab., Vol. 1, No. 4, 1968.

15. [15] Wang, B., Ren, Q., Deng, Z.H., Fu, M.Y., "A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system", IEEE Trans. Ind. Electron., Vol. 62, No.4, 2015, pp. 2353-2362. [DOI:10.1109/TIE.2014.2361671]

16. [16] Gao, W., Zhang, Y., Wang, J.G, "Research on initial alignment and self-calibration of rotary strapdown inertial navigation systems", Sensors, Vol. 15, No. 2, 2015, pp. 3154-3171. [DOI:10.3390/s150203154]

17. [17] Fang, J., Qin, J., "Advances in atomic gyroscopes: A view from inertial navigation applications", Sensors, Vol. 12, No. 5, 2012, pp. 6331-6346. [DOI:10.3390/s120506331]

18. [18] Wang, H.G., Williams, T.C., "Strategic inertial navigation systems-High-accuracy inertially stabilized platforms for hostile environments", IEEE Control Syst., Vol. 28, No.1, 2008, pp. 65-85. [DOI:10.1109/MCS.2007.910206]

19. [19] Quan, W., Lv, L., Liu, B., "Modeling and optimizing of the random atomic spin gyroscope drift based on the atomic spin gyroscope", Rev. Sci. Instrum., Vol. 85, No. 11, 2014. [DOI:10.1063/1.4900946]

20. [20] Duan, L., Quan, W., Jiang, L., Fan, W., Ding, M., Hu, Z., Fang, J., "Common-mode noise reduction in an atomic spin gyroscope using optical differential detection", Appl. Opt., Vol. 56, No. 27, 2017, pp. 7734-7740. [DOI:10.1364/AO.56.007734]

21. [21] Zou, S., Zhang, H., Chen, X., "Modeling and filter algorithm analysis of all-optical atomic spin gyroscope's random drift", In Proceedings of the 2015 IEEE Metrology for Aerospace (MetroAeroSpace), Benevento, Italy, June 2015, pp. 207-219. [DOI:10.1109/MetroAeroSpace.2015.7180684]

22. [22] Zou, S., Zhang, H., Chen, X., Chen, Y., Fang, J., "A novel calibration method research of the scale factor for the all-optical atomic spin inertial measurement device", J. Opt. Soc. Korea, Vol. 19, No.4, 2015, pp. 415-420. [DOI:10.3807/JOSK.2015.19.4.415]

23. [23] Jiang, L., Quan, W., Li, R., Duan, L., Fan, W., Wang, Z., Liu, F., Xing, L., Fang, J., "Suppression of the cross-talk effect in a dual-axis K-Rb-21Ne comagnetometer", Phys. Rev. A, Vol. 95, No. 6, 2017. [DOI:10.1103/PhysRevA.95.062103]

24. [24] Qingzhong, C., Gongliu, Y., Wei, Q., Ningfang, S., Yongqiang, Tu., Yiliang, L., "Error Analysis of the K-Rb-21Ne Comagnetometer Space-Stable Inertial Navigation System", Sensors, Vol. 18, No. 2, 2018. [DOI:10.3390/s18020670]

25. [25] Gao, Z., Error Propagation Property of Inertial Navigation System. In Inertial Navigation System Technology, Tsinghua University Press, Beijing, China, 2012.

26. [26] Wu, Q., Han, F, "New optimal approach to space-stable inertial navigation system", In Proceedings of the 2011 10th International Conference on Electronic Measurement & Instruments (ICEMI), Chengdu, China, August 2011, pp. 296-299.

27. [27] Kim, M.S., Yu, S.B., Lee, W.S., "Development of a high-precision calibration method for inertial measurement unit", Int. J. Precis. Eng. Manuf., Vol. 15, No. 3, 2016, pp. 567-575. [DOI:10.1007/s12541-014-0372-3]

28. [28] Yuan, B.L., Liao, D., Han, S.L., "Error compensation of an optical gyro INS by multi-axis rotation", Meas. Sci. Technol., Vol. 23, No. 2, 2012. [DOI:10.1088/0957-0233/23/2/025102]

29. [29] Song, N.F., Cai, Q.Z., Yang, G.L., Yin, H.L., "Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system", Meas. Sci. Technol.. Vol. 24, No. 11, 2013. [DOI:10.1088/0957-0233/24/11/115002]

30. [30] Nie, Q., Gao, X.Y., Liu, Z., "Research on accuracy improvement of INS with continuous rotation", In Proceedings of the IEEE International Conference on Information and Automation, Zhuhai, China, June 2009, pp. 849-853.

31. [31] Gao, Y.B., Guan, L.W., Wang, T.J., Kuang, H., "Position accuracy analysis for single-axis rotary FSINS", Chin. J. Sci. Instrum., Vol. 35, 2014, pp. 794-800.

32. [32] Liu, F., Wang, W., Wang, L., Feng, P.D., "Error analyses and calibration methods with accelerometers for optical angle encoder in rotational inertial navigation systems", Appl. Opt., Vol. 52, No. 32, 2013, pp. 7724-7731. [DOI:10.1364/AO.52.007724]

33. [33] Ren, Q., Wang, B., Deng, Z.H., Fu, M.Y., "A multi-position self-calibration method for dual-axis rotational inertial navigation system", Sens. Actuators A Phys., Vol. 219, No. 3, 2014, pp. 24-31. [DOI:10.1016/j.sna.2014.08.011]

34. [34] Zhang, Q., Wang, L., Liu, Z., Feng, P., "An Accurate Calibration Method Based on Velocity in a Rotational Inertial Navigation System", Sensors, Vol. 15, 2015, pp. 18443-18458. [DOI:10.3390/s150818443]

35. [35] Hao, Y., Gong, J., Gao, W., and Li, L. "Research on the dynamic error of strapdown inertial navigation system", in Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA '08), 2008, pp. 814-819.

36. [36] Gomez-Estern, F., and Gordillo, F. "Error analysis in strapdown INS for aircraft assembly lines", in Proceedings of the 10th International Conference on Control, Automation, Robotics and Vision (ICARCV '08), 2008, pp. 184-189. [DOI:10.1109/ICARCV.2008.4795514]

37. [37] Gao, W., Cao, B., Ben, Y., and Xu, B. "Analysis of gyro's slope drift affecting inertial navigation system error", in Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA '09), 2009, pp. 3757-3762.

38. [38] Musoff, H., and Murphy, J. H. "Study of strapdown navigation attitude algorithms", Journal of Guidance, Control, and Dynamics, Vol. 18, No. 2, 1995, pp. 287-290. [DOI:10.2514/3.21382]

39. [39] Wang, J., Gu, H. "Compensation algorithm of device error for rate strapdown inertial navigation system", in Proceedings of the 1st International Conference on Intelligent Networks and Intelligent Systems (ICINIS '08), 2008, pp. 667-670. [DOI:10.1109/ICINIS.2008.137]

40. [40] Qiao, Y.-H., Liu, Y., Su, B.-K., and Zeng, M. "Test method for error model coefficients of pendulous integrating gyro accelerometer on centrifuge", Journal of Astronautics, Vol. 28, No. 4, 2007, pp. 854-931.

41. [41] Huang, C., Yi, G., Zen, Q., "Accuracy Evaluation Method of Stable Platform Inertial Navigation System Based on Quantum Neural Network", NeuroQuantology, Vol. 16, No. 6, 2018, 613-618. [DOI:10.14704/nq.2018.16.6.1569]

42. [42] Grewal, M. S., Henderson, V. D., Miyasako, R. S. "Application of Kalman Filtering to the Calibration and Alignment of Inertial Navigation Systems", IEEE Trans. Automat. Contr., Vol. 36, No. 1, 1991. [DOI:10.1109/9.62283]

43. [43] کارساز علی، خالوزاده حمید، "آناليز خطاي يک سيستم كنترل آتش خاص"، مجله کنترل، دوره 1، شماره 1، زمستان 1385، صفحات 55 تا 68