以寻北系统Kalman滤波器为研究对象,从滤波噪声在寻北Kalman滤波器中传播机理的角度对其影响进行分析。基于随机可控制性和随机可观测性得到了误差协方差矩阵与噪声统计特性之间的解析表达式,并利用单轴旋转式寻北系统对所提出的基于随机理论的解析分析方法进行验证。实验结果表明,利用基于随机理论的解析分析方法分析寻北系统有效而且适用,并且所得到的解析式能够更全面地表示系统的性能。
The north-finding Kalman filter is studied from the aspect of the propagation mechanism of filtering noises. Explicit analytic expressions of the state error covariance matrix with different noise statistical characteristics are derived based on the stochastic controllability and stochastic observablity theory, and the proposed analytic method is detailed demonstrated on the single-axis rotary inertial navigation system (INS). The experimental results show that, the proposed analytic method is effective and applicable to analyzing the north-finding filter, and the analytic expressions can provide with us more information about the system performance.
2016,38(6): 132-136 收稿日期：2015-10-19
DOI：10.3404/j.issn.1672-7619.2016.06.027
分类号：U666.1
基金项目：国家"863计划"资助项目(2014AAxxx4028E)
作者简介：朱海(1965-),男,博士,教授,主要从事水下导航技术研究。
参考文献：
[1] EL-OSERY A, BRUDER S, LAUGHLIN D. High-accuracy heading determination[C]//Proceedings of the 8th international Conference on System of Systems Engineering. Maui, Hawaii, USA:IEEE, 2013:308-313.
[2] PESHEKHONOV V G. Gyroscopic navigation systems:current status and prospects[J]. Gyroscopy and Navigation, 2011, 2(3):111-118.
[3] GIBSON C, FLUECKIGER K, HOPKINS R, et al. Demonstrating practical inertial navigation:the beginnings and beyond[C]//Proceedings of AIAA Guidance, Navigation, and Control (GNC) Conference. Boston, MA:American Institute of Aeronautics and Astronautics, 2013:5122.
[4] LEE M H, PARK W C, LEE K S, et al. Observability analysis techniques on inertial navigation systems[J]. Journal of System Design and Dynamics, 2012, 6(1):28-44.
[5] GREWAL M S, HENDERSON V D, MIYASAKO R S. Application of kalman filtering to the calibration and alignment of inertial navigation systems[J]. IEEE Transactions on Automatic Control, 1991, 36(1):4-13.
[6] GREWAL M S, ANDREWS A P. Applications of Kalman filtering in aerospace 1960 to the present[J]. IEEE Control Systems, 2010, 30(3):69-78.
[7] LU S L, XIE L, CHEN J B. Reduced-order Kalman filter for RLG SINS initial alignment[C]//Proceedings of 2008 Chinese Control and Decision Conference. Yantai, China:IEEE, 2008:3675-3680.
[8] 杨俊峰, 司文杰. 陀螺随机游走对导弹自瞄准精度的影响[J]. 航天控制, 2012, 30(5):21-24, 47. YANG Jun-feng, SI Wen-jie. The effect of gyro random walk during the process of initial alignment of missile[J]. Aerospace Control, 2012, 30(5):21-24, 47.
[9] ALBO M, BRONSHTEYN B. North finding device, system and method:US, 8151475[P]. 2012-04-10.
[10] LI Z K. Gyrocompass modeling and simulation system (GMSS) and method thereof:US, 20130179134 A1[P]. 2013-07-11.
[11] 高贤志. 陀螺角度随机游走误差对旋转惯导系统的影响[J]. 舰船科学技术, 2014, 36(9):122-124, 135. GAO Xian-zhi. Research on the influence of rotation inertial navigation due to gyro angle random walk error[J], Ship Science and Technology, 2014, 36(9):122-124, 135.
[12] 黄宗升, 秦石乔, 王省书, 等. 恒速偏频激光陀螺寻北仪的研究[J]. 弹箭与制导学报, 2007, 27(5):65-67. HUANG Zong-sheng, QIN Shi-qiao, WANG Xing-shu, et al. The study on north-finder based on constant rate biased RLG[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2007, 27(5):65-67.
[13] GROVES P D. Principles of GNSS, inertial, and multisensor integrated navigation systems[M]. 2nd ed. Boston, London UK:Artech House, 2008:111-129, 140-153.
[14] ROGERS R M. Applied mathematics in integrated navigation systems[M]. 2nd ed. Reston, VA:American Institute of Aeronautics and Astronautics, Inc., 2006:132-161.
[15] 程向红, 郑梅. 捷联惯导系统初始对准中Kalman参数优化方法[J]. 中国惯性技术学报, 2006, 14(4):12-17. CHENG Xiang-hong, ZHENG Mei. Optimization on Kalman filter parameters of SINS during initial alignment[J]. Journal of Chinese Inertial Technology, 2006, 14(4):12-17.
[16] BAR-ITZHACK I Y, PORAT B. Azimuth observability enhancement during inertial navigation system in-flight alignment[J]. Journal of Guidance, Control, and Dynamics, 1980, 3(4):337-344.
[17] PORAT B, BAR-ITZHACK I Y. Effect of acceleration switching during INS in-flight alignment[J]. Journal of Guidance, Control, and Dynamics, 1981, 4(4):385-389.
[18] GELB A. Applied optimal estimation[M]. 16th ed. Cambridge, Massachusetts, USA:MIT Press, 2001:92-154.
[19] 杨晓霞, 阴玉梅. 可观测度的探讨及其在捷联惯导系统可观测性分析中的应用[J]. 中国惯性技术学报, 2012, 20(4):405-409. YANG Xiao-xia, YIN Yu-mei. Discussions on observability and its applications in SINS[J]. Journal of Chinese Inertial Technology, 2012, 20(4):405-409.
[20] YU H P, ZHU H, GAO D Y, et al. A stationary north-finding scheme for an azimuth rotational IMU utilizing a linear state equality constraint[J]. Sensors, 2015, 15(2):4368-4387.
[21] BRITTING K R. Effects of azimuth rotation on gyrocompass systems[C]//Proceedings of the 34th Annual Meeting of the Institute of Navigation. Arlington, TX, USA:ION, 1978:1-13.
