Implicit Augmented UKF and Its Application to the Stellar Refraction Navigation
Publication: Journal of Aerospace Engineering
Volume 31, Issue 4
Abstract
Stellar refraction navigation is an effective method for autonomous celestial navigation of satellites. Compared with the refraction apparent height, a better navigation performance can be achieved via the stellar refraction angle. Nevertheless, this causes the measurement model to become an implicit function, in which the measurements and states are restricted to implicit equations. The available filters, applied to a system with an implicit measurement model, are based on linearization, which needs to compute the Jacobian matrices and introduces linearization errors. In this paper, a type of unscented Kalman filter (UKF), referred to as an implicit augmented unscented Kalman filter (IAUKF), is proposed, in which the state is augmented via the measurement. The zero is regarded as the equivalent measurement vector for updating the estimation of the augmented state as well as its covariance matrix. The performance of the IAUKF is tested and demonstrated via simulation. Simulations reveal that the navigation performance of the IAUKF is better than that of the implicit extended Kalman filter (IEKF), the implicit augmented extended Kalman filter (IAEKF), the iterative IEKF, and the implicit UKF.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research presented in this paper has been supported by the National Natural Science Foundation of China (61233005, 61503013) and the National Basic Research Program of China (973 Program 2014CB744202). The authors wish to express their gratitude to all members of the Science & Technology on Inertial Laboratory and the Fundamental Science on Novel Inertial Instrument & Navigation System Technology Laboratory for their valuable comments.
References
Anthony, J. 1992. “Air force Phillips laboratory autonomous space navigation experiment.” In AF Space Command Space Surveillance Workshop, 16–19. Washington, DC: AIAA.
Chowdhary, G., and R. Jategaonkar. 2010. “Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter.” Aerosp. Sci. Technol. 14 (2): 106–117.
Fang, Q., and S. X. Huang. 2013. “UKF for integrated vision and inertial sensors based on three-view geometry.” IEEE Sens. J. 13 (7): 2711–2719.
Gounley, R., R. White, and E. Gai. 1984. “Autonomous satellite navigation by stellar refraction.” J. Guidance Control Dyn. 7 (2): 129–134.
Hu, G. G., S. S. Gao, and Y. M. Zhong. 2015. “A derivative UKF for tightly coupled INS/GPS integrated navigation.” ISA Trans. 56 (May): 135–144.
Johnston, L. A., and V. Krishnamurthy. 2001. “Derivation of a sawtooth iterated extended Kalman smoother via the AECM algorithm.” IEEE Trans. Signal Process. 49 (9): 1899–1909.
Julier, S. J., and J. K. Uhlmann. 1996. A general method for approximating nonlinear transformations of probability distributions. Oxford, UK: Univ. of Oxford.
Julier, S. J., and J. K. Uhlmann. 2004. “Unscented filtering and nonlinear estimation.” Proc. IEEE 92 (3): 401–422.
Kandepu, R., B. Foss, and L. Imsland. 2008. “Applying the unscented Kalman filter for nonlinear state estimation.” J. Process Control 18 (7): 753–768.
Kolas, S., B. A. Foss, and T. S. Schei. 2009. “Noise modeling concepts in nonlinear state estimation.” J. Process Control 19 (7): 1111–1125.
Lair, J. L., P. Duchon, P. Riant, and G. Muller. 1988. “Satellite navigation by stellar refraction.” Acta Astronautica 17 (10): 1069–1079.
Lillestrand, R. L., and J. E. Carroll. 1963. “Horizon-based satellite navigation systems.” IEEE Trans. ANE 10 (3): 247–270.
Ning, X. L., F. Wang, and J. C. Fang. 2016. “Implicit UKF and its observability analysis of satellite stellar refraction navigation system.” Aerosp. Sci. Technol. 54 (Jul): 49–58.
Ning, X. L., L. H. Wang, X. B. Bai, and J. C. Fang. 2013. “Autonomous satellite navigation using starlight refraction angle measurements.” Adv. Space Res. 51 (9): 1761–1772.
Psiaki, M. L. 2011. “Absolute orbit and gravity determination using relative position measurements between two satellites.” J. Guidance Control Dyn. 34 (5): 1285–1297.
Qian, H. M., L. Sun, J. N. Cai, and W. Huang. 2014. “A starlight refraction scheme with single star sensor used in autonomous satellite navigation system.” Acta Astronautica 96 (Mar–Apr): 45–52.
Rehbinder, H., and B. K. Ghosh. 2003. “Pose estimation using line-based dynamic vision and inertial sensors.” IEEE Trans. Autom. Control 48 (2): 186–199.
Sazdovski, V., A. Kitanov, and I. Petrovic. 2015. “Implicit observation model for vision aided inertial navigation of aerial vehicles using single camera vector observations.” Aerosp. Sci. Technol. 40 (Jan): 33–46.
Soatto, S., R. Frezza, and P. Perona. 1996. “Motion estimation via dynamic vision.” IEEE Trans. Autom. Control 41 (3): 393–413.
Steffen, R. 2013. “Robuster iterativer Kalman-Filter mit implizierten Beobachtungsgleichungen” [A robust iterative Kalman filter based on implicit measurement equations]. Photogrammetrie-Fernerkundung-Geoinformation 2013 (4): 323–332.
Steffen, R., and C. Beder. 2007. “Recursive estimation with implicit constraints.” In Pattern recognition, 194–203. Berlin, Heidelberg: Springer.
Uhlmann, J., S. Julier, and H. F. Durrant-Whyte. 2000. “A new method for the nonlinear transformation of means and covariances in filters and estimations.” IEEE Trans. Autom. Control 45 (3): 477–482.
Wang, X. L., and S. Ma. 2009. “A celestial analytic positioning method by stellar horizon atmospheric refraction.” Chin. J. Aeronaut. 22 (3): 293–300.
Wang, X. L., J. Xie, and S. Ma. 2010. “Starlight atmospheric refraction model for a continuous range of height.” J. Guidance Control Dyn. 33 (2): 634–637.
Webb, T. P., R. J. Prazenica, A. J. Kurdila, and R. Lind. 2007. “Vision-based state estimation for autonomous micro air vehicles.” J. Guidance Control Dyn. 30 (3): 816–826.
White, R. L., S. W. Thurman, and F. A. Barnes. 1985. “Autonomous satellite navigation using observations of starlight atmospheric refraction.” Navig. J. Inst. Navig. 32 (4): 317–333.
Yang, B., F. Si, F. Xu, and W. L. Zhou. 2014. “Adaptive measurement model of navigation by stellar refraction based on multiple models switching.” J. Navig. 67 (4): 673–685.
Zhan, R., and J. Wan. 2007. “Iterated unscented Kalman filter for passive target tracking.” IEEE Trans. Aerosp. Electron. Syst. 43 (3): 1155–1163.
Zhao, Y., S. S. Gao, J. Zhang, and Q. N. Sun. 2014. “Robust predictive augmented unscented Kalman filter.” Int. J. Control Autom. Syst. 12 (5): 996–1004.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Aug 2, 2017
Accepted: Jan 8, 2018
Published online: Apr 25, 2018
Published in print: Jul 1, 2018
Discussion open until: Sep 25, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.