Fast initial alignment for inertial navigation system based on high order sliding mode observer and Kalman filter

Document Type : Research Article

Authors

1 Department of Electrical and Computer Engineering, khaje nasir University.

2 faculty of electrical engineering, tarbiat modares university

3 Department of Mechanical Engineering, Imam Hossein University, Tehran, Iran.

4 Department of Aerospace Engineering, Imam Hossein University.

Abstract

The inertial navigation system is a dead reckoning system, thus initial alignment for an inertial navigation system plays an important role in the accuracy of it. In this paper, a novel approach for initial alignment in an inertial navigation system with increased speed and accuracy is proposed. This method has two stages, which integrates the Kalman filter and a high order sliding mode observer. In the inertial navigation system, leveling misalignment angles reach the steady-state faster than the azimuth misalignment angle does, which means the azimuth alignment takes a considerable time for initial alignment. Therefore, in this paper at the first stage estimations of state variables of the system are obtained using the Kalman filter and whenever all variables (except azimuth alignment) reach steady-state, the second stage begins. In the second stage, the estimation which is obtained by the Kalman filter is used as the input to design an equivalent system with unknown inputs for inertial navigation system. A high-order sliding mode observer is then used to estimate the states of a system with an unknown input for estimating the azimuth alignment angle. This method not only increases the speed of estimation but also has comparable accuracy.

Keywords

Main Subjects

References

[1] R.M. Rogers, Applied mathematics in integrated navigation systems, American Institute of Aeronautics and Astronautics, 2007.
[2] R.M. Rogers, Applied mathematics in integrated navigation systems. American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia, USA,  (2003).
[3] D. Titterton, J.L. Weston, J. Weston, Strapdown inertial navigation technology, IET, 2004.
[4] N. El-Sheimy, S. Nassar, A. Noureldin, Wavelet de-noising for IMU alignment, IEEE Aerospace and Electronic Systems Magazine, 19(10) (2004) 32-39.
[5] R. Kalman, A new approach to linear filtering and prediction theory, Trans. ASME, J. Basic Eng., 83 (1961) 95-108.
[6] J. Li, N. Song, G. Yang, R. Jiang, Fuzzy adaptive strong tracking scaled unscented Kalman filter for initial alignment of large misalignment angles, Review of Scientific Instruments, 87(7) (2016) 075118.
[7] Y. Zhang, L. Luo, T. Fang, N. Li, G. Wang, An improved coarse alignment algorithm for odometer-aided sins based on the optimization design method, Sensors, 18(1) (2018) 195.
[8] J.G. Park, J.G. Lee, C.G. Park, SDINS/GPS in-flight alignment using GPS carrier phase rate, GPS Solutions, 8(2) (2004) 74-81.
[9] S. Han, J. Wang, A novel initial alignment scheme for low-cost INS aided by GPS for land vehicle applications, The Journal of Navigation, 63(4) (2010) 663-680.
[10] F. Jiancheng, Y. Sheng, Study on innovation adaptive EKF for in-flight alignment of airborne POS, IEEE Transactions on Instrumentation and Measurement, 60(4) (2011) 1378-1388.
[11] D. Gu, N. El-Sheimy, T. Hassan, Z. Syed, Coarse alignment for marine SINS using gravity in the inertial frame as a reference, in:  2008 IEEE/ION Position, Location and Navigation Symposium, IEEE, 2008, pp. 961-965.
[12] P.M. Silson, Coarse alignment of a ship's strapdown inertial attitude reference system using velocity loci, IEEE Transactions on Instrumentation and Measurement, 60(6) (2011) 1930-1941.
[13] K. Taizhong, F. Jiancheng, W. Wei, Quaternion-optimization-based in-flight alignment approach for airborne POS, IEEE Transactions on Instrumentation and Measurement, 61(11) (2012) 2916-2923.
[14] J. Li, J. Xu, L. Chang, F. Zha, An improved optimal method for initial alignment, The Journal of Navigation, 67(4) (2014) 727-736.
[15] Y. Wu, X. Pan, Velocity/position integration formula part I: Application to in-flight coarse alignment, IEEE Transactions on Aerospace and Electronic Systems, 49(2) (2013) 1006-1023.
[16] L. Chang, J. Li, S. Chen, Initial alignment by attitude estimation for strapdown inertial navigation systems, IEEE Transactions on Instrumentation and Measurement, 64(3) (2014) 784-794.
[17] G. Cheng, S. Cao, L. Guo, W. Chen, Initial alignment of Inertial Navigation System based on a predictive iterated Kalman filter, in:  2018 37th Chinese Control Conference (CCC), IEEE, 2018, pp. 4655-4660.
[18] X. Xu, J. Lu, T. Zhang, A Fast-Initial Alignment Method With Angular Rate Aiding Based on Robust Kalman Filter, IEEE Access, 7 (2019) 51369-51378.
[19] W. Li, W. Wu, J. Wang, L. Lu, A fast SINS initial alignment scheme for underwater vehicle applications, The Journal of Navigation, 66(2) (2013) 181-198.
[20] Z. Chuanbin, T. Weifeng, J. Zhihua, A novel method improving the alignment accuracy of a strapdown inertial navigation system on a stationary base, Measurement Science and Technology, 15(4) (2004) 765.
[21] X. Wang, Fast alignment and calibration algorithms for inertial navigation system, Aerospace Science and Technology, 13(4-5) (2009) 204-209.
[22] Y. Huang, Y. Zhang, X. Wang, Kalman-filtering-based in-motion coarse alignment for odometer-aided SINS, IEEE Transactions on instrumentation and measurement, 66(12) (2017) 3364-3377.
[23] T. Du, L. Guo, J. Yang, A fast initial alignment for SINS based on disturbance observer and Kalman filter, Transactions of the Institute of Measurement and Control, 38(10) (2016) 1261-1269.
[24] M. Hou, R. Patton, Optimal filtering for systems with unknown inputs, IEEE transactions on Automatic Control, 43(3) (1998) 445-449.
[25] Y. Cheng, H. Ye, Y. Wang, D. Zhou, Unbiased minimum-variance state estimation for linear systems with unknown input, Automatica, 45(2) (2009) 485-491.
[26] J. NASH, R, J. D'APPOLITO, K. ROY, Error analysis of hybrid aircraft inertial navigation systems, in:  Guidance and Control Conference, 1972, pp. 848.
[27] F.J. Bejarano, L. Fridman, High order sliding mode observer for linear systems with unbounded unknown inputs, International Journal of Control, 83(9) (2010) 1920-1929.
[28] K.R. Britting, Inertial navigation systems analysis,  (1971).
[29] C. Broxmeyer, C. Leondes, Inertial navigation systems, in, American Society of Mechanical Engineers Digital Collection, 1964.
[30] I. Guidance, GR Pitman, Jr., Ed, in, John Wiley & Sons, Inc., New York, 1962.
[31] C.T. Leondes, Guidance and control of aerospace vehicles, McGraw-Hill New York, 1963.
[32] D.O. Benson, A comparison of two approaches to pure-inertial and Doppler-inertial error analysis, IEEE Transactions on Aerospace and Electronic Systems, (4) (1975) 447-455.
[33] J.A. D'Appolito, The evaluation of Kalman filter designs for multisensor integrated navigation systems, Air Force Avionics Laboratory, 1971.
[34] C. Hutchinson, H. Wondergem, An error analysis technique for inertial navigation systems and Kalman filters, MASSACHUSETTS UNIV AMHERST SCHOOL OF ENGINEERING, 1968.
[35] A. Yavnai, I.Y. Bar-Itzhack, Self-contained updating of ground inertial navigation system, Israel Journal of Technology, 18 (1980) 304-313.
[36] L. Fridman, A. Levant, J. Davila, High-order sliding modes observer for linear systems with unbounded unknown inputs, IFAC Proceedings Volumes, 42(17) (2009) 216-221.
[37] F.J. Bejarano, L. Fridman, Unbounded unknown inputs estimation based on high-order sliding mode differentiator, in:  Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, IEEE, 2009, pp. 8393-8398.
[38] H.L. Trentelman, A.A. Stoorvogel, M. Hautus, Control theory for linear systems, Springer Science & Business Media, 2012.
[39] B. Molinari, A strong controllability and observability in linear multivariable control, IEEE Transactions on Automatic Control, 21(5) (1976) 761-764.
[40] A. Levant, Higher-order sliding modes, differentiation and output-feedback control, International journal of Control, 76(9-10) (2003) 924-941.
 
Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 6
September 2021
Pages 3571-3586

Files

Share

How to cite

Statistics