SINS大失准角传递对准模型的可观测性分析
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摘要
捷联惯导系统(SINS)是在军事、航空等领域有着广泛应用的全自主导航系统,传递对准是确定其导航初值的一项关键技术.针对捷联惯导系统大失准角传递对准模型进行了可观测性分析研究.首先,建立了SINS欧拉角误差模型,并根据水平失准角为小角度的工程实际情况等对误差模型进行了简化;然后,从非线性系统的可观测性分析出发,利用微分几何理论给出系统的可观测矩阵,并给出了系统可观测度定义以及通过奇异值分解分析状态变量可观测度的方法.将该方法应用于SINS大失准角传递对准模型中,对系统进行了"速度"匹配和"速度+姿态"匹配模式下的可观测性和状态可观测度分析;最后,设计了UKF滤波器进行传递对准仿真,仿真结果与可观测分析结论一致,验证了该可观测分析方法的正确性.结果表明,这两种匹配模式下系统均为不完全可观测,并且"速度+姿态"匹配模式下状态变量的可观测度相比"速度"匹配模式下的状态可观测度高.
The strapdown inertial navigation system(SINS) is a self-service navigation system widely used in military, aviation, and other fields, and the transfer alignment is one of the key technologies of SINS. The observability analysis of SINS alignment model of large misalignment angle is studied in this paper. Firstly, the nonlinear SINS error model was deduced and the error model was simplified according to the actual engineering situation. Then, based on the observability analysis method of nonlinear theory, the system observable matrix was built using the differential geometry theory, the definition of the system observable degree and the analysis method of the state variables' observable degree were given, and the method was applied to SINS nonlinear transfer alignment model under two different matching modes. Finally, the unscented Kalman filter(UKF) was designed for the SINS large misalignment angle transfer alignment simulation, and the simulation results verified the observability analysis.
The strapdown inertial navigation system(SINS) is a self-service navigation system widely used in military, aviation, and other fields, and the transfer alignment is one of the key technologies of SINS. The observability analysis of SINS alignment model of large misalignment angle is studied in this paper. Firstly, the nonlinear SINS error model was deduced and the error model was simplified according to the actual engineering situation. Then, based on the observability analysis method of nonlinear theory, the system observable matrix was built using the differential geometry theory, the definition of the system observable degree and the analysis method of the state variables' observable degree were given, and the method was applied to SINS nonlinear transfer alignment model under two different matching modes. Finally, the unscented Kalman filter(UKF) was designed for the SINS large misalignment angle transfer alignment simulation, and the simulation results verified the observability analysis.
引文
[1]王丹力, 张洪钺. 惯导系统初始对准的非线性滤波算法[J]. 中国惯性技术学报, 1999, 7(3): 17WANG Danli, ZHANG Hongyue. Nonlinear filtering algorithm for INS initial alignment[J]. Journal of Chinese Inertial Technology, 1999, 7(3): 17. DOI:10.13695/j.cnki.12-1222/o3.1999.03.004
[2]杨功流, 王丽芬, 袁二凯, 等. 大方位失准角下舰载机快速传递对准技术[J]. 中国惯性技术学报, 2014, 22(1): 45YANG Gongliu, WANG Lifen, YUAN Erkai, et al. Rapid transfer alignment of lager misalignment angle for carrier aircrafts[J]. Journal of Chinese Inertial Technology, 2014, 22(1): 45. DOI:10.13695/j.cnki.12-1222/o3.2014.01.010
[3]郭子伟, 缪玲娟, 赵洪松, 等. 一种改进的类高斯和粒子滤波在大失准角传递对准中的应用[J]. 航空学报, 2013, 34(1): 164GUO Ziwei, MIAO Lingjuan, ZHAO Hongsong, et al. Application of an improved Gaussian-like sum particle filter to large misalignment transfer alignment[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(1): 164. DOI:10.7527/S1000-6893.2013. 0019
[4]刘豹, 唐万生. 现代控制理论[M]. 北京: 机械工业出版社, 2006: 101LIU Bao, TANG Wansheng. Modern control theory[M]. Beijing: China Machine Press, 2006: 101
[5]CHO S Y, LEE H K, LEE H K. Observability and estimation error analysis of the initial fine alignment filter for nonleveling strapdown inertial navigation system[J]. Journal of Dynamic Systems, Measurement, and Control, 2013, 135(2): 021005-1. DOI:10.1115/1.4007552
[6]赵琳, 李亮, 孙明, 等. 基于SVD的SINS多位置对准可观测性分析[J]. 中国惯性技术学报, 2008, 16(5): 523ZHAO Lin, LI Liang, SUN Ming, et al. Analysis on observability of SINS multi-position alignment based on singular value decomposition[J]. Journal of Chinese Inertial Technology, 2008, 16(5): 523. DOI:10.13695/j.cnki.12-1222/o3.2008. 05.009
[7]张庆, 高延滨, 张勤拓. 机载战术武器传递对准可观测性分析[J]. 华中科技大学学报(自然科学版), 2010, 38(11): 68ZHANG Qing, GAO Yanbin, ZHANG Qintuo. Analyzing the observability of transfer alignment of airborne tactical weapons[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2010, 38(11): 68. DOI:10.13245/j.hust. 2010.11.005
[8]周卫东, 蔡佳楠, 孙龙, 等. GPS/SINS超紧组合导航系统可观测性分析[J]. 北京航空航天大学学报, 2013, 39(9): 1157ZHOU Weidong, CAI Jianian, SUN Long, et al. Observability analysis of GPS/SINS ultra-tightly coupled system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(9): 1157. DOI:10.13700/j.bh.1001-5965.2013.09.006
[9]程建华, 陈岱岱, 王冰玉, 等. 基于可观测度分析的传递对准精度评估方法[J]. 系统工程与电子技术, 2015, 37(4): 895CHENG Jianhua, CHEN Daidai, WANG Bingyu, et al. Approach of transfer alignment accuracy evaluation based on observability degree analysis[J]. Systems Engineering and Electronics, 2015, 37(4): 895. DOI:10.3969/j.issn.1001-506X.2015.04.26
[10]王丹力, 张洪钺. 几种可观测性分析方法及在惯导中的应用[J]. 北京航空航天大学学报, 1999, 25(3): 342WANG Danli, ZHANG Hongyue. Methods for the analysis of observability and their application to INS initial alignment[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(3): 342. DOI:10.13700/j.bh.1001-5965.1999.03.057
[11]HERMANN R, ARTHUR J K. Nonliner controllability and observability[J]. IEEE Transactions on Automatic Control, 1977, 22(5): 728. DOI:10.1109/TAC.1977.1101601
[12]YIM J R, CRASSIDIS J L, JUNKINS J L. Autonomous orbit navigation of interplanetary spacecraft[D]. Texas: Texas A&M University, 2002. DOI:10.2514/6.2000-3936
[13]崔平远, 常晓华, 崔祜涛. 基于可观测性分析的深空自主导航方法研究[J]. 宇航学报, 2011, 32(10): 2115CUI Pingyuan, CHANG Xiaohua, CUI Hutao. Research on observability analysis-based autonomous navigation method for deep space[J]. Journal of Astronautics, 2011, 32(10): 2115. DOI:10.3873/j.issn.1000-1328.2011.10.004
[14]梅春波, 秦永元, 游金川. SINS 基于非线性量测的大失准角初始对准算法[J]. 宇航学报, 2016, 37(3): 291MEI Chunbo, QIN Yongyuan, YOU Jinchuan. Nonlinear measurement based SINS initial alignment algorithm under large misalignment angle[J]. Journal of Astronautics, 2016, 37(3): 291. DOI:10.3873/j.issn. 1000-1328.2016.03.007
[15]严恭敏, 严卫生, 许德民. 简化UKF滤波在SINS大失准角初始对准中的应用[J]. 中国惯性技术学报, 2008, 16(3): 253YAN Gongmin, YAN Weisheng, XU Demin. Application of simplified UKF in SINS initial alignment for large misalignment angles[J]. Journal of Chinese Inertial Technology, 2008, 16(3): 253. DOI:10.13695/j.cnki.12-1222/o3.2008.03.006
[2]杨功流, 王丽芬, 袁二凯, 等. 大方位失准角下舰载机快速传递对准技术[J]. 中国惯性技术学报, 2014, 22(1): 45YANG Gongliu, WANG Lifen, YUAN Erkai, et al. Rapid transfer alignment of lager misalignment angle for carrier aircrafts[J]. Journal of Chinese Inertial Technology, 2014, 22(1): 45. DOI:10.13695/j.cnki.12-1222/o3.2014.01.010
[3]郭子伟, 缪玲娟, 赵洪松, 等. 一种改进的类高斯和粒子滤波在大失准角传递对准中的应用[J]. 航空学报, 2013, 34(1): 164GUO Ziwei, MIAO Lingjuan, ZHAO Hongsong, et al. Application of an improved Gaussian-like sum particle filter to large misalignment transfer alignment[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(1): 164. DOI:10.7527/S1000-6893.2013. 0019
[4]刘豹, 唐万生. 现代控制理论[M]. 北京: 机械工业出版社, 2006: 101LIU Bao, TANG Wansheng. Modern control theory[M]. Beijing: China Machine Press, 2006: 101
[5]CHO S Y, LEE H K, LEE H K. Observability and estimation error analysis of the initial fine alignment filter for nonleveling strapdown inertial navigation system[J]. Journal of Dynamic Systems, Measurement, and Control, 2013, 135(2): 021005-1. DOI:10.1115/1.4007552
[6]赵琳, 李亮, 孙明, 等. 基于SVD的SINS多位置对准可观测性分析[J]. 中国惯性技术学报, 2008, 16(5): 523ZHAO Lin, LI Liang, SUN Ming, et al. Analysis on observability of SINS multi-position alignment based on singular value decomposition[J]. Journal of Chinese Inertial Technology, 2008, 16(5): 523. DOI:10.13695/j.cnki.12-1222/o3.2008. 05.009
[7]张庆, 高延滨, 张勤拓. 机载战术武器传递对准可观测性分析[J]. 华中科技大学学报(自然科学版), 2010, 38(11): 68ZHANG Qing, GAO Yanbin, ZHANG Qintuo. Analyzing the observability of transfer alignment of airborne tactical weapons[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2010, 38(11): 68. DOI:10.13245/j.hust. 2010.11.005
[8]周卫东, 蔡佳楠, 孙龙, 等. GPS/SINS超紧组合导航系统可观测性分析[J]. 北京航空航天大学学报, 2013, 39(9): 1157ZHOU Weidong, CAI Jianian, SUN Long, et al. Observability analysis of GPS/SINS ultra-tightly coupled system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(9): 1157. DOI:10.13700/j.bh.1001-5965.2013.09.006
[9]程建华, 陈岱岱, 王冰玉, 等. 基于可观测度分析的传递对准精度评估方法[J]. 系统工程与电子技术, 2015, 37(4): 895CHENG Jianhua, CHEN Daidai, WANG Bingyu, et al. Approach of transfer alignment accuracy evaluation based on observability degree analysis[J]. Systems Engineering and Electronics, 2015, 37(4): 895. DOI:10.3969/j.issn.1001-506X.2015.04.26
[10]王丹力, 张洪钺. 几种可观测性分析方法及在惯导中的应用[J]. 北京航空航天大学学报, 1999, 25(3): 342WANG Danli, ZHANG Hongyue. Methods for the analysis of observability and their application to INS initial alignment[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(3): 342. DOI:10.13700/j.bh.1001-5965.1999.03.057
[11]HERMANN R, ARTHUR J K. Nonliner controllability and observability[J]. IEEE Transactions on Automatic Control, 1977, 22(5): 728. DOI:10.1109/TAC.1977.1101601
[12]YIM J R, CRASSIDIS J L, JUNKINS J L. Autonomous orbit navigation of interplanetary spacecraft[D]. Texas: Texas A&M University, 2002. DOI:10.2514/6.2000-3936
[13]崔平远, 常晓华, 崔祜涛. 基于可观测性分析的深空自主导航方法研究[J]. 宇航学报, 2011, 32(10): 2115CUI Pingyuan, CHANG Xiaohua, CUI Hutao. Research on observability analysis-based autonomous navigation method for deep space[J]. Journal of Astronautics, 2011, 32(10): 2115. DOI:10.3873/j.issn.1000-1328.2011.10.004
[14]梅春波, 秦永元, 游金川. SINS 基于非线性量测的大失准角初始对准算法[J]. 宇航学报, 2016, 37(3): 291MEI Chunbo, QIN Yongyuan, YOU Jinchuan. Nonlinear measurement based SINS initial alignment algorithm under large misalignment angle[J]. Journal of Astronautics, 2016, 37(3): 291. DOI:10.3873/j.issn. 1000-1328.2016.03.007
[15]严恭敏, 严卫生, 许德民. 简化UKF滤波在SINS大失准角初始对准中的应用[J]. 中国惯性技术学报, 2008, 16(3): 253YAN Gongmin, YAN Weisheng, XU Demin. Application of simplified UKF in SINS initial alignment for large misalignment angles[J]. Journal of Chinese Inertial Technology, 2008, 16(3): 253. DOI:10.13695/j.cnki.12-1222/o3.2008.03.006