Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-27T00:28:30.528Z Has data issue: false hasContentIssue false
  • English
  • Français

Attitude reconstruction from strap-down rate gyros using power series

Published online by Cambridge University Press:  04 March 2021

Habib Ghanbarpourasl Open the ORCID record for Habib Ghanbarpourasl [Opens in a new window]
Habib Ghanbarpourasl*
Affiliation:
Mechatronics Department, University of Turkish Aeronautical Association, Ankara, Turkey
*
E-mail: habib.ghanbarpour@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

Keywords

attitude reconstructiontime varying linear systemsquaternion updatequaternions’ numerical integrationconing error compensation
Type
Research Article
Information
The Journal of Navigation , Volume 74 , Issue 4 , July 2021 , pp. 763 - 781
Check for updates
Copyright
Copyright © The Royal Institute of Navigation 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bortz, J. E. (1971). A new mathematical formulation for strapdown inertial navigation. IEEE Transactions on Aerospace and Electronic Systems, 7(1), 61–66.10.1109/TAES.1971.310252CrossRefGoogle Scholar
Garg, S. C., Morrow, L. D. and Mamen, R. (1978). Strapdown navigation technology: A literature survey. Journal of Guidance and Control, 1(3), 161–172.10.2514/3.55760CrossRefGoogle Scholar
Gilmore, J. P. (1980). Modular strapdown guidance unit with embedded microprocessors. Journal of Guidance and Control, 3(1), 3–10.10.2514/3.55940CrossRefGoogle Scholar
Hairer, E., Nørsett, S. P. and Wanner, G. (1993). Solving ordinary differential equations I. Nonstiff problems, Volume 8 of Springer Series in Computational Mathematics.Google Scholar
Ignagni, M. B. (1990). Optimal strapdown attitude integration algorithms. Journal of Guidance, Control, and Dynamics, 13(2), 363–369.10.2514/3.20558CrossRefGoogle Scholar
Ignagni, M. B. (1996). Efficient class of optimized coning compensation algorithms. Journal of Guidance, Control, and Dynamics, 19(2), 424–429.10.2514/3.21635CrossRefGoogle Scholar
Ignagni, M. B. (1998). Duality of optimal strapdown sculling and coning compensation algorithms. Navigation, 45(2), 85–95.10.1002/j.2161-4296.1998.tb02373.xCrossRefGoogle Scholar
Jekeli, C. (2012). Inertial Navigation Systems with Geodetic Applications. Walter de Gruyter, Berlin, New York.Google Scholar
Jordan, J. W. (1969). An Accurate Strapdown Direction Cosine Algorithm. National Aeronautics and Space Administration, Cambridge, MA, United States.Google Scholar
Kunovský, J. (2015). Modern Taylor Series Method. 2015 IEEE 13th International Scientific Conference on Informatics. IEEE, 1–8.10.1109/Informatics.2015.7377798CrossRefGoogle Scholar
Lee, J. G., Yoon, Y. J., Mark, J. G. and Tazartes, D. A. (1990). Extension of strapdown attitude algorithm for high-frequency base motion. Journal of Guidance, Control, and Dynamics, 13(4), 738–743.10.2514/3.25393CrossRefGoogle Scholar
McKern, R. A. (1968). A study of transformation algorithms for use in a digital computer. Doctoral dissertation, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
Miller, R. B. (1983). A new strapdown attitude algorithm. Journal of Guidance, Control, and Dynamics, 6(4), 287–291.10.2514/3.19831CrossRefGoogle Scholar
Minor, J. (1965). August. Low-Cost Strapdown Inertial Systems. Guidance Control Conference, 117–123.Google Scholar
Muller, J.-M., Brisebarre, N., De Dinechin, F., Jeannerod, C.-P., Lefevre, V., Melquiond, G., Revol, N., Stehlé, D. and Torres, S. (2018). Handbook of Floating-Point Arithmetic. Vol. 1. Boston, MA: Birkhäuser.10.1007/978-3-319-76526-6CrossRefGoogle Scholar
Musoff, H. and Murphy, J. H. (1995). Study of strapdown navigation attitude algorithms. Journal of Guidance, Control, and Dynamics, 18(2), 287–290.10.2514/3.21382CrossRefGoogle Scholar
Roscoe, K. M. (2001). Equivalency between strapdown inertial navigation coning and sculling integrals/algorithms. Journal of Guidance, Control, and Dynamics, 24(2), 201–205.10.2514/2.4718CrossRefGoogle Scholar
Savage, P. (1966). A New Second-Order Solution for Strapped-Down Attitude Computation. Guidance and Control Conference, 1805.10.2514/6.1966-1805CrossRefGoogle Scholar
Savage, P. (1998a). Strapdown inertial navigation integration algorithm design part 1: Attitude algorithms. Journal of Guidance, Control, and Dynamics, 21(1), 19–28.10.2514/2.4228CrossRefGoogle Scholar
Savage, P. G. (1998b). Strapdown inertial navigation integration algorithm design part 2: Velocity and position algorithms. Journal of Guidance, Control, and Dynamics, 21(2), 208–221.10.2514/2.4242CrossRefGoogle Scholar
Savage, P. G. (2010). Coning algorithm design by explicit frequency shaping. Journal of Guidance, Control, and Dynamics, 33(4), 1123–1132.10.2514/1.47337CrossRefGoogle Scholar
Savage, P. (2017). Down-summing Rotation Vectors for Strapdown Attitude Updating (SAI WBN-14019). Maple Plain, MN: Strapdown Associates, Inc. http://strapdownassociates.com/Rotation%20Vector%20Down_Summing.pdf.Google Scholar
Song, M., Wu, W. and Pan, X. (2013). Approach to recovering maneuver accuracy in classical coning algorithms. Journal of Guidance, Control, and Dynamics, 36(6), 1872–1881.10.2514/1.60121CrossRefGoogle Scholar
Wilcox, J. C. (1967). A new algorithm for strapped-down inertial navigation. IEEE Transactions on Aerospace and Electronic Systems, 3(5), 796–802.10.1109/TAES.1967.5408867CrossRefGoogle Scholar
Wu, Y. (2018). RodFIter: Attitude reconstruction from inertial measurement by functional iteration. IEEE Transactions on Aerospace and Electronic Systems, 54(5), 2131–2142.10.1109/TAES.2018.2808078CrossRefGoogle Scholar
Wu, Y. and Litmanovich, Y. A. (2019). Strapdown attitude computation: functional iterative integration versus Taylor series expansion. arXiv preprint arXiv:1909.09935.Google Scholar
Wu, Y. and Yan, G. (2019). Attitude reconstruction from inertial measurements: QuatFIter and its comparison with RodFIter. IEEE Transactions on Aerospace and Electronic Systems, 55(6), 3629–3639.10.1109/TAES.2019.2910360CrossRefGoogle Scholar
Wu, Y., Cai, Q. and Truong, T. K. (2018). Fast RodFIter for attitude reconstruction from inertial measurements. IEEE Transactions on Aerospace and Electronic Systems, 55(1), 419–428.10.1109/TAES.2018.2866034CrossRefGoogle Scholar
Yan, G., Weng, J., Yang, X. K. and Qin, Y. Y. (2017). An accurate numerical solution for strapdown attitude algorithm based on Picard iteration. Journal of Astronautics, 38(12), 1308–1313.Google Scholar