极区惯导编排中地球近似模型的适用性分析
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摘要
极区基于地球第二近似椭球模型横向坐标系编排复杂,编排本身存在原理性误差,而地球第一近似球体模型虽然存在几何误差,但在极区惯导编排简单,且相对于中低纬度地区,第一近似几何误差较小。惯导极区编排地球模型的选用问题随着极区惯导的深入研究逐渐凸显。针对这一问题,在定义适用于极区的地球近似模型的基础上,推导建立了基于地球第一近似模型几何误差引起的惯导系统误差方程,通过仿真分析对比地球近似模型的惯导误差,分析地球近似模型的适用性。仿真结果表明,地球第一近似模型几何误差会随惯导运行时间发散,而第二近似模型的编排误差随时间变化不大,当惯导运行时间长则地球第一近似模型不再适用。
The arrangement of horizontal coordinate system based on the Earth's second approximate ellipsoid model is complicated in polar region, the arrangement itself has the principle error, While the first approximate sphere model has geometric errors, it has simple arrangement in polar regions, and the geometric error is smaller than that in the middle and low latitudes. The selection of the Earth model is becoming more and more prominent with the intensive study of the inertial navigation in polar region. To solve this problem, based on the definition of the Earth approximate model, the system error equations of SINS based on the first approximate model of the Earth is derived. Then comparing the inertial error of the Earth approximate model with the simulation and analyzing the applicability of the Earth approximate model. The simulation results show that the geometric errors of the first approximate model will accumulate with time, while the errors of the second approximate model change little with time. When the inertial navigation run in a long time, the first approximate model of the Earth is no longer suitable for polar area.
The arrangement of horizontal coordinate system based on the Earth's second approximate ellipsoid model is complicated in polar region, the arrangement itself has the principle error, While the first approximate sphere model has geometric errors, it has simple arrangement in polar regions, and the geometric error is smaller than that in the middle and low latitudes. The selection of the Earth model is becoming more and more prominent with the intensive study of the inertial navigation in polar region. To solve this problem, based on the definition of the Earth approximate model, the system error equations of SINS based on the first approximate model of the Earth is derived. Then comparing the inertial error of the Earth approximate model with the simulation and analyzing the applicability of the Earth approximate model. The simulation results show that the geometric errors of the first approximate model will accumulate with time, while the errors of the second approximate model change little with time. When the inertial navigation run in a long time, the first approximate model of the Earth is no longer suitable for polar area.
引文
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[18] CHIRCOP A. Regulatory challenges for international arctic navigation and shipping in an evolving governance environment[J]. Ocean Yearbook, 2014, 28(1): 269-290.
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[22] CLYNCH J R, ALTENBURG R A. Ionospheric residual range error model[C]//Proceedings of International Geodetic Symposium on Satellite Doppler Positioning. Salt Lake City, UT: [s.n.], 1979: 1579-1587.
[23] 李倩. 横坐标系捷联惯导系统极区导航及其误差抑制技术研究[D]. 哈尔滨: 哈尔滨工程大学, 2014. LI Qian. Research on transversal strapdown INS and error depression technology in polar region[D]. Harbin: Harbin Engineering University, 2014.
[24] 李倩, 孙枫, 奔粤阳, 等. 横坐标系捷联惯导系统极区导航及阻尼设计[J]. 系统工程与电子技术, 2014, 36(12): 2496-2503. LI Qian, SUN Feng, BEN Yueyang, et al. Transversal strapdown INS and damping design in polar region[J]. Systems Engineering and Electronics, 2014, 36(12): 2496-2503.
[25] LI Qian, BEN Yueyang, YU Fei, et al. System reset of transversal strapdown INS for ship in polar region[J]. Measurement, 2015, 60: 247-257.
[2] 孙达, 蒲英霞. 地图投影[M]. 2版. 南京: 南京大学出版社, 2012. SUN Da, PU Yingxia. Map projection[M]. 2nd ed. Nanjing: Nanjing University Press, 2012.
[3] 刘文超. 基于地球椭球的极区惯导格网导航与横向坐标导航技术研究[D]. 武汉:海军工程大学, 2016.LIU Wenchao. Research on inertial grid navigation and transverse coordinate navigation based on earth ellipsoid in polar regions[D]. Wuhan: Naval University of Engineering,2016.
[4] YAO Yiqing, XU Xiaosu, YAO Li. Transverse navigation under the ellipsoidal earth model and its performance in both polar and non-polar areas[J]. Journal of Navigation, 2016, 69(2): 335-352.
[5] LI Qian, BEN Yueyang, YU Fei, et al. Transversal strapdown ins based on reference ellipsoid for vehicle in the polar region[J]. IEEE Transactions on Vehicular Technology, 2016, 65(9): 7791-7795.
[6] LI Qian, BEN Yueyang, SUN Feng, et al. Transversal strapdown INS and damping technology for marine in polar region[C]// Proceedings of 2014 IEEE/ION Position, Location and Navigation Symposium. Monterey, CA: IEEE, 2014: 1365-1370.
[7] 张福斌, 马朋, 王智辉. 基于横坐标系的捷联惯性导航系统/多普勒速度仪极区组合导航算法[J]. 兵工学报, 2016, 37(7): 1229-1235. ZHANG Fubin, MA Peng, WANG Zhihui. SINS/DVL integrated navigation algorithm based on transversal coordinate frame in polar region[J]. Acta Armamentarii, 2016, 37(7): 1229-1235.
[8] GAO Yanbin, LIU Meng, LI Guangchun. Initial alignment for SINS based on pseudo-earth frame in polar regions[J]. Sensors, 2017, 17(6): 1416.
[9] 高伟, 叶攀, 奔粤阳, 等. 一种舰船捷联惯导系统极区动基座对准方法: 中国, 103791918A[P]. 2014-05-14.GAO Wei, YE Pan, BEN Yueyang, et al. Polar region moving base alignment method for naval vessel strapdown inertial navigation system: CN, 103791918A[P]. 2014-05-14.
[10] CHENG Jianhua, WANG Tongda, GUAN Dongxue, et al. Polar transfer alignment of shipborne SINS with a large misalignment angle[J]. Measurement Science and Technology, 2016, 27(3): 035101.
[11] ZHAO C L, WU W Q, LIAN J X. Research on rotating modulation inertial navigation system error characteristics simulation method in polar area[C]//Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference. Yantai, China: IEEE, 2015: 2790-2794.
[12] 郝勇帅, 周爱军, 王海波. 地球模型对横坐标惯导极区导航影响的分析[J]. 舰船电子工程, 2017, 37(7): 37-40. HAO Yongshuai, ZHOU Aijun, WANG Haibo. Analysis of the influence of the earth model of the transverse coordinate polar inertial navigation[J]. Ship Electronic Engineering, 2017, 37(7): 37-40.
[13] EARLE M A. Sphere to spheroid comparisons[J]. Journal of Navigation, 2006, 59(3): 491-496.
[14] 秦永元. 惯性导航[M]. 2版. 北京: 科学出版社, 2014. QIN Yongyuan. Inertial navigation[M]. 2nd ed. Beijing: Science Press, 2014.
[15] 李忠美, 李厚朴, 边少锋. 常用纬度差异极值符号表达式[J]. 测绘学报, 2014, 43(2): 214-220. DOI: 10.13485/j.cnki.11-2089.2014.0031.LI Zhongmei, LI Houpu, BIAN Shaofeng. Symbolic expressions of difference extrema between regular latitudes[J]. Acta Geodaetica et Cartographica Sinica, 2012, 43(2): 214-220. DOI: 10.13485/j.cnki.11-2089.2014.0031.
[16] 刘文超, 卞鸿巍, 王荣颖. 惯导系统横向坐标法导航性能研究[J]. 武汉大学学报(信息科学版), 2015, 40(11): 1520-1525. LIU Wenchao, BIAN Hongwei, WANG Rongying. Navigation performance of SINS transverse coordinate method[J]. Geomatics and Information Science of Wuhan University, 2015, 40(11): 1520-1525.
[17] TITTERTON D H, WESTON J L. Strapdown inertial navigation technology[J]. Aerospace & Electronic Systems Magazine, 2004, 20(7): 33-34.
[18] CHIRCOP A. Regulatory challenges for international arctic navigation and shipping in an evolving governance environment[J]. Ocean Yearbook, 2014, 28(1): 269-290.
[19] DEGGIM H. Ensuring safe, secure and reliable shipping in the Arctic ocean[M]//BERKMAN P, VYLEGZHANIN A. Environmental Security in the Arctic Ocean. Dordrecht: Springer, 2013: 241-254.
[20] 余兴光. 中国第四次北极科学考察报告[M]. 北京: 海洋出版社, 2011. YU Xingguang. The report of 2010 Chinese Arctic research expedition[M]. Beijing: Ocean Press, 2011.
[21] 王有隆. 北极地区飞行中的通信与导航特性[J]. 航空维修与工程, 2016(1): 46-48. WANG Youlong. Characteristics of communication and navigation on cross-polar routes[J]. Aviation maintenance and Engineering, 2016(1): 46-48.
[22] CLYNCH J R, ALTENBURG R A. Ionospheric residual range error model[C]//Proceedings of International Geodetic Symposium on Satellite Doppler Positioning. Salt Lake City, UT: [s.n.], 1979: 1579-1587.
[23] 李倩. 横坐标系捷联惯导系统极区导航及其误差抑制技术研究[D]. 哈尔滨: 哈尔滨工程大学, 2014. LI Qian. Research on transversal strapdown INS and error depression technology in polar region[D]. Harbin: Harbin Engineering University, 2014.
[24] 李倩, 孙枫, 奔粤阳, 等. 横坐标系捷联惯导系统极区导航及阻尼设计[J]. 系统工程与电子技术, 2014, 36(12): 2496-2503. LI Qian, SUN Feng, BEN Yueyang, et al. Transversal strapdown INS and damping design in polar region[J]. Systems Engineering and Electronics, 2014, 36(12): 2496-2503.
[25] LI Qian, BEN Yueyang, YU Fei, et al. System reset of transversal strapdown INS for ship in polar region[J]. Measurement, 2015, 60: 247-257.