Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-01T02:29:25.443Z Has data issue: false hasContentIssue false
  • English
  • Français

A Novel Robust Sparse-Grid Quadrature Kalman Filter Design for HCV Transfer Alignment Against Model Parameter Uncertainty

Published online by Cambridge University Press:  28 November 2017

Hongmei Chen  and
Jianjuan Liu
Hongmei Chen*
Affiliation:
(School of Electrical Engineering, Henan University of Technology, Zhengzhou 450000, PR China)
Jianjuan Liu
Affiliation:
(School of Electrical Engineering, Henan University of Technology, Zhengzhou 450000, PR China)
*
(E-mail: chenhongmei_seu@163.com)
Get access Rights & Permissions [Opens in a new window]

Abstract

A novel robust scheme for Transfer Alignment (TA) is proposed for improving the accuracy of the navigation of a Hypersonic Cruise Vehicle (HCV). The main goal is to instil robustness in the safety and accuracy of the attitude determination, despite mode uncertainties. This article focuses on Robust Sparse-Grid Quadrature Filtering (R-SGQF) using two given robust factors for norm-bounded model uncertainties in non-linear systems. Missile dynamic and measurement model uncertainties are established to validate TA technologies. The nominal stability of the R-SGQF is defined by estimating error dynamics. The technique gives sufficient conditions for the R-SGQF in terms of two parameterised Riccati equations. Robust stability is analysed using Lyapunov theory and the accuracy level of the Sparse-Grid Quadrature (SGQ) algorithm. Embedding the SGQ technique into the robust filter structure, R-SGQF is not only of robust stability against uncertainty but also of higher accuracy. The simulation results of the TA algorithm demonstrate that attitude determinations validate the effectiveness of the R-SGQF algorithm.

Keywords

Transfer alignmentModel parameter uncertaintyRobust stabilitySparse-grid quadrature Kalman Filtering
Type
Research Article
Information
The Journal of Navigation , Volume 71 , Issue 3 , May 2018 , pp. 625 - 648
Copyright
Copyright © The Royal Institute of Navigation 2017 

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

REFERENCES

Agniel, R.G. and Jury, E.I. (1971). Almost sure boundedness ofrandomly sampled systems. SIAM Journal on Control, 9(3), 372–384.CrossRefGoogle Scholar
Babacan, E.K., Ozbek, L. and Efe, M. (2008). Stability of the Extended Kalman Filter When the States are Constrained. IEEE Transactions on Automatic Control, 53(11), 2707–2711.CrossRefGoogle Scholar
Boutayeb, M. and Aubry, D. (1999). A Strong Tracking Extended Kalman Observer for Nonlinear Discrete-Time Systems. IEEE Transactions on Automatic Control, 44(8), 1550–1556.Google Scholar
Boutayeb, M., Rafaralahy, H. and Darouach, M. (1997). Convergence Analysis of the Extended Kalman Filter Used as an Observer for Nonlinear Deterministic Discrete-Time Systems. IEEE Transactions on Automatic Control, 42, (4), 581–586.CrossRefGoogle Scholar
Chang, L., Li, K. and Hu, B. (2015). Huber's M-estimation based Process Uncertainty Robust Filter for Integrated INS/GPS. IEEE Sensors Journal, 15(6), 3367–3374.CrossRefGoogle Scholar
Chattaraj, S., Mukherjee, A. and Chaudhuri, S.K. (2013). Transfer Alignment Problem: Algorithms and Design Issues. Gyroscopy and Navigation, 4(3), 130–146.CrossRefGoogle Scholar
Chen, H., Cheng, X., Dai, C. and Han, X. (2014). Accuracy, Efficiency and Stability Analysis of Sparse-grid Quadrature Kalman Filter in Near Space Hypersonic Vehicles. IEEE/Institute of Navigation (ION) Positioning, Location and Navigation Symposium, Monterey, CA, May, 27–33.CrossRefGoogle Scholar
Chen, H., Cheng, X., Dai, C. and Liu, L. (2015). Robust Stability Analysis of H∞-SGQKF and its Application to Transfer Alignment. Signal Processing, 117, 310–321.Google Scholar
Grimble, M. J. and Ahmed, E. S. (1990). A Solution of the H∞ Optimal Linear Filtering Problem for Discrete-Time Systems. IEEE Transactions on Acoustics, Speech and Signal Processing, 38, 7, 1092–1104.Google Scholar
Heiss, F. and Winschel, V. (2008). Likelihood approximation by numerical integration on sparse grids. Journal of Econometrics, 144, 62–80.Google Scholar
Hounkpevi, F.O. and Yaz, E.E. (2007). Robust minimum variance linear state estimators for multiple sensors with different failure rates. Automatica, 43, 1274–1280.Google Scholar
Hu, J., Wang, Z.D., Gao, H., and Stergioulas, L.K. (2012). Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements. Automatica, 48, 2007–2015.CrossRefGoogle Scholar
Huang, R., Patwardhan, S.C. and Biegler, L.T. (2012). Robust stability ofnonlinear model predictive control based on extended Kalman filter. Journal of Process Control, 22, 1, 82–89.Google Scholar
Huang, R., Patwardhan, S.C. and Biegler, L.T. (2013). Robust stability ofnonlinear model predictive control with extended Kalman filter and target setting. International Journal Robust and Nonlinear Control, 23, 1240–1264.Google Scholar
Ishihara, J.Y., Terra, M.H. and Campos, J.C.T. (2006). Robust Kalman filter for descriptor systems. IEEE Transactions on Automatic Control, 51(8), 1354–1358.Google Scholar
Jia, B. and Xin, M. (2013). Sparse-grid quadrature H∞ Filter for Discrete-Time Systems with Uncertain Noise Statistics. IEEE Transactions on Aerospace and Electronic Systems, 49(3), 1626–1636.Google Scholar
Jia, B., Xin, M. and Cheng, Y. (2012). Sparse-grid quadrature nonlinear filtering. Automatica, 48(2), 327–341.Google Scholar
Julier, S. S. (2002). The Scaled Unscented Transformation. Proceedings of the 2002 American Control Conference, 4555–4559.Google Scholar
Lewis, F.L. (1986). Optimal estimation. New York: Wiley.Google Scholar
Li, L. and Xia, Y. (2013). Unscented Kalman Filter Over Unreliable Communication Networks with Markovian Packed Dropouts. IEEE Transactions on Automatic Control, 58(12), 3224–3230.Google Scholar
Li, L. and Xia, Y. (2015). Stochastically stability of the unscented Kalman filter with intermittent observation. Automatica, 53, 149–154.Google Scholar
Li, W. and Jia, Y. (2010). H-infinity filtering for a class of nonlinear discrete-time systems based on unscented transform. Signal Processing, 90(12), 3301–3307.CrossRefGoogle Scholar
Marthinus, C. H. (2013). Flight Test Results of a MEMS IMU Based Transfer Alignment Algorithm for Short Range Air-to-Air Missiles. Guidance, Navigation, and Control Conference, Boston, MA, pp. 19–22.Google Scholar
McClintona, C.R., Rauscha, V.L., Shaw, R.J., Methac, U. and Natfield, C. (2005). Hyper-X: Foundation for future hypersonic launch vehicles. Acta Astronautica 57, 614–622.CrossRefGoogle Scholar
Pehlivanoğlu, A. G. and Ercan, Y. (2013). Investigation of flexure effect on transfer alignment performance. Journal of Navigation, 66(1), 1–15.Google Scholar
Piché, R., Sarkka, S. and Hartikainen, J. (2012). Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate Student-t distribution. In Machine Learningfor Signal Processing (MLSP). International Workshop on. IEEE, Santander, Spain, Sept, 1–6.Google Scholar
Reif, K., and Unbehauen, R. (1999), The extended Kalman filter as an exponential observer for nonlinear systems. IEEE Transactions on Signal Processing, 47(8), 2324–2328.Google Scholar
Reif, K., Günther, S., Yaz, E., and Unbehauen, R. (1999). Stochastic Stability of the Discrete-Time Extended Kalman Filter. IEEE Transactions on Automatic Control, 44(4), 714–728.CrossRefGoogle Scholar
Rondeau, C.M. and Jorris, T.R. (2013). 2005X-51A Scramjet Demonstrator Program: Waverider Ground and Flight Test. SFTE 44th International/SETP Southwest Flight Test Symposium, 28 Oct–1 Nov, Ft Worth, TX, 1–14.Google Scholar
Rong, W., Zhi, X., Jianye, L. and Lijuan, S. (2016). Robust inertial-astronomic attitude determination algorithm with adaptive star geometrical error model for HCVs. Journal Aerospace Engineering, 29(2), 04015048.Google Scholar
Savage, P.G. (2007). Strapdown Analytics. Strapdown Associates, Inc., Second Edition.Google Scholar
Savage, P.G. (2014). Modifying The Kalman Filter Measurement To Mitigate Second Order Error Amplification In INS Velocity Matching Alignment Applications. SAI-WBN-14005, Strapdown Associates, Inc., July, 15.Google Scholar
Seo, J., Yu, M.J., Park, C.G. and Gyu, J. (2006). An Extended Robust H∞ Filter for Nonlinear Constrained Uncertain Systems. IEEE Transactions on Signal Processing, 54(1), 14471–4475.CrossRefGoogle Scholar
Simon, D. (2006). Optimal state estimation Kalman, H∞, and nonlinear approaches. Hoboken, New Jersey: John Wiley & Sons.Google Scholar
Souto, R.F., Ishihara, J.Y. and Araujo, B.G. (2009). A robust extended Kalman filter for discrete-time systems with uncertain dynamics, measurements and correlated noise. In IEEE American Control Conference, St. Louis, MO, June, 1888–1893.Google Scholar
Wang, F. and Balakrishnan, V. (2002). Robust Kalman filters for linear time-varying systems with stochastic parametric uncertainties. IEEE Transactions on Signal Processing, 50(4), 803–813.CrossRefGoogle Scholar
Welch, G. and Bishop, G. (2001). An Introduction to the Kalman Filter. Notes ACM SIGGRAPH Tutorial Kalman Filter.Google Scholar
Xie, L., Yeng, C. S., Soh, Y. C. and Carlos, de S, E.. (1994). Robust Kalman Filtering for Uncertain Discrete-Time Systems. IEEE Transaction on Automatic Control, 39(6), 1310–1314.Google Scholar
Xiong, K., Liu, L., Liu, Y. Kai, X. and Liu, Y. (2010). Non-linear robust filter design for satellite attitude determination. IET Control Theory Applications, 4(7), 1222–1234.CrossRefGoogle Scholar
Xiong, K., Liu, L., Liu, Y. Kai, X. and Liu, Y. (2011). Robust extended Kalman filtering for nonlinear systems with multiplicative noises. Optimal Control Applications and Methods, 32(1), 47–63.Google Scholar
Xiong, K., Zhang, H. and Liu, L. (2008). Adaptive robust extended Kalman filter for nonlinear stochastic systems. IET Control Theory&Applications, 2(3), 239–250.Google Scholar
Xiong, K., Zhang, H.Y. and Chan, C.W. (2006). Performance evaluation of UKF-based nonlinear filtering. Automatic, 42, 261–270.CrossRefGoogle Scholar