بهبود دقت مدل انتشار خطای ناوبری اینرسی به منظور افزایش کارایی سیستم ناوبری تلفیقی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری / دانشکده مهندسی برق، دانشگاه صنعتی امیرکبیر

2 عضو هیات علمی / دانشکده مهندسی برق، دانشگاه صنعتی امیرکبیر

3 عضو هیات علمی / دانشکده مهندسی برق و کامپیوتر، دانشگاه کاشان

چکیده

یکی از موضوعاتی که امروزه در حوزه ناوبری از اهمیت وی‍‍ژه­ای برخوردار است، استفاده از معادلات انتشار خطای ناوبری به منظور تلفیق خروجی یک سیستم ناوبری اینرسی با یک اندازه­گیری بیرونی جهت استفاده توأم از مزایای هر دو مکانیزم ناوبری اینرسی و اندازه­گیری خارجی است. مطالعه تحقیقات گذشته نشان می­دهد که معادلات انتشار خطا عموماً در دستگاه جغرافیایی استخراج شده که می­تواند نقاط ضعفی داشته باشد. در این مقاله ضمن بیان چگونگی استخراج معادلات انتشار خطا در دستگاه مماسی، به صورت تحلیلی نشان داده شده است که این معادلات در مقایسه با دستگاه جغرافیایی نه تنها سادگی بیشتری دارند بلکه دقت بالاتری نیز در توصیف انتشار خطای ناوبری اینرسی و در نتیجه افزایش کارایی سیستم ناوبری تلفیقی دارند. در پایان، شبیه­سازی­هایی در دو حالت استفاده از مدل انتشار خطا در دستگاه مماسی و معادلات انتشار خطا در دستگاه جغرافیایی با لحاظ کردن مقادیر فرضی برای شتاب­ها و سرعت­های زاویه­ای و خطای تصادفی سنسورهای یک نمونه IMU واقعی، انجام شده است. نتایج شبیه­سازی­های انجام شده نیز صحت افزایش دقت مدل انتشار خطای پیشنهادی این مقاله را تأیید می­کنند.

کلیدواژه‌ها


عنوان مقاله [English]

Accuracy improvement of inertial navigation error propagation model for increasing efficiency of integrated navigation system

نویسندگان [English]

  • Ayoob Abdoli Hosseinabadi 1
  • mohammad bagher menhaj 2
  • Seyed Ali Zahiripour 3
1 Phd student/ Amirkabir University of Technology
2 Professor, Amirkabir University of Technology, Tehran
3 Faculty of Electrical and Computer Engineering/ university of kashan
چکیده [English]

Todays, one of the topics that is of particular importance in the field of navigation is the use of navigation error propagation equations in order to integrate the output of an inertial navigation system with an external measurement to take advantages of both the inertial navigation mechanism and the external measurement. Study of past research Show that error propagation equations are generally extracted in a geographic frame that can have weaknesses. This paper demonstrates how to extract the error propagation equations in a tangent frame that not only have more simplicity than the geographic frame but also have a higher accuracy in describing the inertial navigation error propagation and thus increase the efficiency of the integrated navigation system. Finally, simulations in two cases using the tangent error propagation model and the geographic error propagation equations are performed by considering the hypothetical values for the acceleration and angular velocities and random error of the sensors. The results of the simulations also confirm the increasing of accuracy of the proposed error propagation model in this paper.ns in this paper also confirm the validity of this issue.

کلیدواژه‌ها [English]

  • Inertial navigation
  • Integrated navigation
  • navigation error propagation
  • Tangent Frame
  • geographic frame
[1] R. Kenneth, Sc. D. Britting, Inertial navigation System analysis, New York: Wiley, 1971.
[2] R.G.Brown. Kalman filter modeling, In      Proceedings of the 16th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, pp. 261–272, 1984
[3] R.G. Brown, Integrated navigation systems and Kalman filtering: A perspectiv. Navigation, Journal of the Institute of Navigation, Vol. 19, No. 4, pp. 355–362, 1972
[4] R. G. Brown, Y. C. Hwang, Introduction to random signals and applied Kalman filtering, Second Edition, New York: Wiley, 1992.
[5] G. J. Geier, Delayed state Kalman filter equations for delta range measurement processing, Technical Report GPSPFP, Cambridge, 1976.
[6] M. S. Grewal, A. P. Andrews, Kalman Filtering: Theory and Practice using Matlab, Second Edition, New York: Wiley, 2001.
[7] P. Hwang, R. Brown, GPS navigation: Combining pseudorange with continuous carrier phase using a Kalman filter. Navigation, Journal of the Institute of Navigation, Vol. 37, No. 2, pp. 181–196, 1990.
[8] C. W. Marquis, Integration of differential GPS and inertial navigation using a complementary Kalman filter, Master’s thesis, Naval Postgraduate School, 1993.
[9] D. Simon, Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches, New York: Wiley, 2006.
[10] A. Van Dierendonck, J. McGraw, and R. Brown, Relationship between Allan variances and Kalman filter parameters, In Proceedings of the 16th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, pp. 273-293, 1984.
[11] Y. Yang, J. A. Farrell, Two antennas GPS-aided INS for attitude determination, IEEE Transactions on Control Systems Technology,  Vol. 11, No. 6, pp.905–918, 2003.
[12] C. W. Marquis, Integration of differential GPS and inertial navigation using a complementary Kalman filter, Master’s thesis, Naval Postgraduate School, 1993.
[13] F. Van Graas and M. Braasch, GPS interferometric attitude and heading determination: Initial flight test results. Navigation: Journal of the Institute of Navigation, Vol. 38, No. 4, pp.297–316, 1991.
[14] A. Van Dierendonck, S. Russell, E. Kopitzke, M. Birnbaum, The GPS navigation message, Navigation: Journal of the Institute of Navigation,, Vol. 25, No. 2, pp. 147-165, 1978.
[15] D. Pietraszewski, J. Spalding, C. Viehweg, L. luft, U.S. Coast Guard differential GPS navigation field test findings, Navigation: Journal of the Institute of Navigation, Vol. 35, No. 1, pp.  55-72, 1988.
[16] W. S. Widnall and P. A. Grundy, Inertial navigations system error models, Technical Report, Intermetrics Inc, 1973.
[17] R. E.  Mortenson, Strapdown guidance error analysis, IEEE Transactions on Aerospace and Electronic Systems, Vol. 10, No. 4, pp.451–457, 1994.
[18] Y. F. Jiang, Y. P. Lin, Error estimation of INS ground aalignment through observability analysis, IEEE Transactions on Aerospace and Electronic Systems, Vol. 28, No. 1, pp.92–96, 1992.
[19] R. G. Brown, D. J. Winger, Error analysis of an integrated inertial/Doppler-satellite system with continuous and multiple satellite coverage, Technical report, Engineering Research Institute, Iowa State University, January 1971.
[20] C. Jekeli, Inertial Navigation Systems with Geodetic Applications, Walter de Gruyter Berlin, New York, 2001.
[21] A. Barrau, S.Bonnabel, A Mathematical Framework for IMU Error Propagation with Applications to Preintegration, IEEE International Conference on Robotics and Automation (ICRA), 2020
[22] J. Zhang, J. Li, Y. Huang, C. Hu, K. Feng and X. Wei, Analysis and Compensation of Installation Errors for Rotating Semi-Strapdown Inertial Navigation System,  IEEE Access, Vol. 7, pp. 101019-101030, 2019.
[23] H. XiongD. DaiY. ZhaoX. WangJ.  ZhengD. Zhan, An Analysis of the Attitude Estimation Errors Caused by the Deflections of Vertical in the Integration of Rotational INS and GNSS, Sensors, Vol.19, No. 7, 2019.
[24] X. Zheng, N. Ma, C. Gao, W. Jing, Propagation mechanism analysis of navigation errors caused by initial state errors for long-range vehicles, Aerospace Science and Technology, Vol. 67, pp. 378-386, 2017
[25] X. Liu, X. Xu, Y. Liu, L. Wang, A Method for SINS Alignment with Large Initial Misalignment Angles Based on Kalman Filter with Parameters Resetting, Mathematical Problems in Engineering, Open Access, Vol. 2014, 2014.
[26] J. Li, P. Dang, Y. Li, B. Gu, A General Euler Angle Error Model of Strapdown Inertial Navigation Systems, Applied Sciences, Vol. 8, No. 1, 2018.
[27] Z. Long-Jie, X. Xiao-fang, L. De-dong, W. Yan, Error Analysis of Strapdown Inertia Navigation System in Tactical Missiles, Procedia Engineering, Vol. 15, pp. 1456-1460, 2011
[28] C. Huang, G. Yi, Q. Zeng, N. Yi, The establishment and analysis of the high-order error model of platform inertial navigation system in mobile conditions, 35th Chinese Control Conference (CCC), 2016.
[29] X. Liu, J. Sima, Y. Huang, X. Liu, P. Zhang, A Simplified Kalman Filter for Integrated Navigation System with Low-Dynamic Movement, Mathematical Problems in Engineering, Vol. 2016,  2016.
[30] H. Rahimi, A. A. Nikkhah, Improving the speed of initial alignment for marine strapdown inertial navigation systems using heading control signal feedback in extended Kalman filter, International Journal of Advaced Robotics Systems, Vol. 17, No. 1, 2020.
[31] E. bekir, Introduction to Modern Modern Navigation Systems, World Scientific Publishing, Singapore, 2007.