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A robust extended Kalman filter algorithm for X-ray pulsar navigation system
Received date: 2015-04-22
Revised date: 2015-06-07
Online published: 2015-07-02
Supported by
National Natural Science Foundation of China (61473297,61304237)
Considering that the traditional extended Kalman filter (EKF) algorithm has low accuracy and poor robustness in the application of the X-ray pulsar navigation system with uncertainty of model parameters, multiplicative noises and additive noises, a robust EKF algorithm is proposed in this paper. The equations for state prediction errors and state estimation errors are established. Then, state prediction error covariance and state estimation error covariance are obtained. However, as there are uncertainties in model parameters, the accurate value of state prediction error covariance and state estimation error covariance cannot be calculated. Hence, the upper bound of the state prediction error covariance and the upper bound of the state estimation error covariance are identified by using four matrix inequalities. The gain matrix is designed by minimizing the upper bound of the state estimation error covariance for all admissible uncertainties. The method is applied to X-ray pulsar navigation system, and simulation results show the effectiveness of the algorithm.
LI Min , ZHANG Yingchun , GENG Yunhai , ZHU Baolong , LI Huayi . A robust extended Kalman filter algorithm for X-ray pulsar navigation system[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016 , 37(4) : 1305 -1315 . DOI: 10.7527/S1000-6893.2015.0175
[1] EMADZADEH A A, SPEYER J L. X-ray pulsar-based relative navigation using epoch folding[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(4):2317-2328.
[2] 帅平, 陈绍龙, 吴一帆. X射线脉冲星导航原理[J]. 宇航学报, 2007, 28(6):1538-1543. SHUAI P, CHEN S L, WU Y F. Navigation principles using X-ray pulsars[J]. Journal of Astronautics, 2007, 28(6):1538-1543(in Chinese).
[3] SHEIKH S I, JPINES D. Spacecraft navigation using X-ray pulsars[J]. Journal of Guidance, Control, and Dynamics, 2006, 29(1):49-62.
[4] OKITA O F, OZAKI Y S. Nonlinearity-compensation extended Kalman filter and its application to target motion[J]. Oki Technical Review, 1997, 63(159):1-12.
[5] JOSEPH J, LAVIOLA J. A comparison of unscented and extended Kalman filtering for estimating quaternion motion[C]//Proceedings of the 2003 American Control Conference. Denver:American Automat Control Council, 2003:2435-2440.
[6] 李理敏, 龚文斌, 刘会杰. 基于自适应扩展卡尔曼滤波的载波跟踪算法[J]. 航空学报, 2012, 33(7):1319-1328. LI L M, GONG W B, LIU H J. A carrier tracking algorithm based on adaptive extended Kalman filter[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(7):1319-1328(in Chinese).
[7] XIONG K, LIU L D, ZHANG H Y. Modified unscented Kalman filtering and its application in autonomous satellite navigation[J]. Aerospace Science and Technology, 2009, 13(4):238-246.
[8] FENG D Z, GUO H H, WANG X. Autonomous orbit determination and its error analysis for deep space using X-ray pulsar[J]. Aerospace Science and Technology, 2014, 32:35-41.
[9] LIU J, FANG J C, KANG Z W. Novel algorithm for X-ray pulsar navigation against Doppler effects[J]. IEEE Transactions on Aerospace and Electronic Systems, 2015, 51(1):228-241.
[10] DONG Z, YOU Z. Finite-horizon robust Kalman filtering for uncertain discrete time-varying systems with uncertain-covariance white noises[J]. IEEE Signal Processing Letter, 2006, 13(8):493-496.
[11] YANG F, WANG Z, HUANG Y S. Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises[J]. IEEE Transactions on Automat Control, 2002, 47(7):1179-1183.
[12] XIONG K, LIU L D, LIU Y W. Nonlinear robust filter design for satellite attitude determination[J]. IET Control Theory Application, 2010, 4(7):1222-1234.
[13] MAHMOUD M S, XIE L, SOH Y C. Robust Kalman filtering for discrete state-delay systems[J]. IEE Proceedings-Control Theory and Applications, 2000, 47(6):613-618.
[14] XIE L, LU L, LIU L. Robust Kalman filtering for uncertain discrete-time systems[J]. IEEE Transactions on Automatic Control, 1994, 39(6):1310-1314.
[15] THEODOR Y, SHAKED U. Robust discrete-time minimum-variance filtering[J]. IEEE Transactions on Signal Processing, 1996, 44(2):181-189.
[16] HOM R A, JOHNSON C R. Topic in matrix analysis[M]. London:Cambridge University Press, 1991:22-50.
[17] 帅平, 陈忠贵, 曲广吉. 关于X射线脉冲星导航的轨道力学问题[J]. 中国科学, 2009, 39(3):556-561. SHUAI P, CHEN Z G, QU G J. Orbital mechanics of X-ray pulsar navigation[J]. Science in China, 2009, 39(3):556-561(in Chinese).
[18] SHEIKH S I, PINES D J. Recursive estimation of spacecraft position and velocity using X-ray pulsar time of arrival measurements[J]. Journal of the Institute of Navigation, 2006, 53(3):149-166.
[19] JULIER S J, UHLAMNN J K, DUNANT-WHYTE H F. A new method for the nonlinear transformation of means and covariance in filters and estimators[J]. IEEE Transactions on Automatic Control, 2000, 45:477-482.
[20] 宫轶松, 归庆明, 李保利. 自适应渐消扩展Kalman粒子滤波方法在组合导航中的应用[J]. 大地测量与地球动力学, 2012, 30(1):99-104. GONG Y S, GUI Q M, LI B L. Adaptive fading extended Kalman particle filtering applied to integrated navigation[J]. Journal of Geodesy and Geodynamics, 2012, 30(1):99-104(in Chinese).
[21] 邓新坪, 郑建华, 高东. 改进UKF在X射线脉冲星导航中的应用研究[J]. 北京理工大学学报, 2012, 32(1):51-56. DENG X P, ZHENG J H, GAO D. Application research of modified unscented kalman filter in X-ray pulsar navigation[J]. Transaction of Beijing Institute of Technology, 2012, 32(1):51-56(in Chinese).
[22] 张共愿, 程咏梅, 杨峰. 预测-校正EKF算法在自主导航中的应用[J]. 宇航学报, 2009, 30(6):2227-2230. ZHANG G Y, CHENG Y M, YANG F. Applying forecast-revise EKF algorithm in autonomous navigation system[J]. Journal of Astronautics, 2009, 30(6):2227-2230(in Chinese).
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