鲁棒EKF在脉冲星导航系统中的应用

doi:10.7527/S1000-6893.2015.0175

电子与控制

本期目录 | 过刊浏览 | 高级检索

前一篇 | 后一篇

鲁棒EKF在脉冲星导航系统中的应用

李敏, 张迎春, 耿云海, 祝宝龙, 李化义

哈尔滨工业大学航天学院, 哈尔滨 150001

收稿日期:2015-04-22 修回日期:2015-06-07 出版日期:2016-04-15 发布日期:2015-07-02
通讯作者: 张迎春,Tel.:0451-86402357 E-mail:zhangyc1@hit.edu.cn E-mail:zhangyc1@hit.edu.cn
作者简介:李敏,男,博士研究生,主要研究方向:脉冲星导航,多传感器网络信息融合。Tel:0451-86402357 E-mail:liminhit@126.com;张迎春,男,教授,博士生导师。主要研究方向:卫星总体设计,控制系统设计,故障诊断,脉冲星导航。Tel:0451-86402357 E-mail:zhangyc1@hit.edu.cn
基金资助:
国家自然科学基金(61473297,61304237)

A robust extended Kalman filter algorithm for X-ray pulsar navigation system

LI Min, ZHANG Yingchun, GENG Yunhai, ZHU Baolong, LI Huayi

School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

Received:2015-04-22 Revised:2015-06-07 Online:2016-04-15 Published:2015-07-02
Supported by:
National Natural Science Foundation of China (61473297,61304237)

摘要/Abstract

摘要：

针对脉冲星导航系统的滤波问题,传统的扩展卡尔曼滤波(EKF)算法存在不能克服系统模型存在不确定性参数以及乘性噪声等缺陷,提出一种鲁棒EKF算法。首先,分析了状态预测误差方程和估计误差方程,利用统计学原理,得到了状态预测方差矩阵和状态估计方差矩阵计算等式。由于系统模型存在不确定性参数,状态预测协方差矩阵和状态估计协方差矩阵无法计算;因此,利用4个重要矩阵不等式,分析并找到预测方差矩阵和状态估计方差矩阵的上界。最后,利用状态估计误差协方差矩阵上界设计状态增益矩阵,使得状态估计协方差矩阵的迹最小。将该算法对脉冲星导航系统进行仿真,仿真结果验证了所提算法的有效性。

关键词: 脉冲星导航系统, 不确定性, 非线性滤波, 鲁棒扩展卡尔曼滤波(EKF), 估计精度

Abstract:

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.

Key words: X-ray pulsar navigation system, uncertainty, nonlinear system filtering, robust extended Kalman filter, estimation accuracy

中图分类号:

V448.22⁺4

李敏, 张迎春, 耿云海, 祝宝龙, 李化义. 鲁棒EKF在脉冲星导航系统中的应用[J]. 航空学报, 2016, 37(4): 1305-1315.

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.

参考文献

[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).

E-mail：hkxb@buaa.edu.cn

关于我们

期刊社服务

专业学科

封面文章

友情链接

主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

鲁棒EKF在脉冲星导航系统中的应用

A robust extended Kalman filter algorithm for X-ray pulsar navigation system

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	陈志远, 李璐祎. 参数不确定性下高效的可靠性灵敏度分析方法[J]. 航空学报, 2022, 43(9): 325881-325881.
[2]	夏侯唐凡, 陈江涛, 邵志栋, 吴晓军, 刘宇. 随机和认知不确定性框架下的CFD模型确认度量综述[J]. 航空学报, 2022, 43(8): 25716-025716.
[3]	李晓阳, 陶昭, 张慰. 基于不确定微分方程的疲劳可靠性建模[J]. 航空学报, 2022, 43(8): 225820-225820.
[4]	罗佳奇, 傅文豪, 曾先, 夏志恒. 雷诺数对高负荷低压涡轮叶栅流动损失的不确定性影响[J]. 航空学报, 2022, 43(7): 125427-125427.
[5]	胡政文, 张保强, 邓振鸿. 概率盒全局灵敏度和活跃子空间跨层降维[J]. 航空学报, 2021, 42(9): 224582-224582.
[6]	方安然, 李旦, 张建秋. 异常值和未知观测噪声鲁棒的非线性滤波器[J]. 航空学报, 2021, 42(7): 324675-324675.
[7]	贾庆轩, 段嘉琪, 陈钢. 机器人在轨装配无标定视觉伺服对准方法[J]. 航空学报, 2021, 42(6): 424063-424063.
[8]	魏科鹏, 胡健, 姚建勇, 邢浩晨, 乐贵高. 航空机电作动器神经网络快速终端滑模控制[J]. 航空学报, 2021, 42(6): 624540-624540.
[9]	董雷霆, 周轩, 赵福斌, 贺双新, 卢志远, 冯建民. 飞机结构数字孪生关键建模仿真技术[J]. 航空学报, 2021, 42(3): 23981-023981.
[10]	刘德元, 刘昊, Frank L LEWIS. 尾座式无人飞行器鲁棒容错编队控制[J]. 航空学报, 2021, 42(2): 324296-324296.
[11]	钟赟, 万路军, 张杰勇. 区间不确定性下的空中作战行动过程优选方法[J]. 航空学报, 2021, 42(2): 324282-324282.
[12]	王娜娜, 解青, 苏星宇, 任祝寅. 湍流燃烧机理和调控的活性子空间分析方法[J]. 航空学报, 2021, 42(12): 625228-625228.
[13]	赵剑, 黄悦琛, 李海阳, 何湘粤. 垂直起降运载火箭返回轨迹不确定性优化[J]. 航空学报, 2021, 42(11): 524829-524829.
[14]	闫文旭, 兰华, 王增福, 金术玲, 潘泉. 基于变分贝叶斯的星载雷达非线性滤波[J]. 航空学报, 2020, 41(S2): 724395-724395.
[15]	刘丹阳, 柯鹏, 杨春信, 马坤昌, 戚晓玲. 基于小波熵的救生伞高速空投最大开伞动载不确定性[J]. 航空学报, 2020, 41(8): 123627-123627.