Underwater gravity FKF matching enhancement algorithm based on local SCHA modeling

doi:10.11947/j.AGCS.2023.20220609

Abstract

Abstract: An underwater gravity matching navigation method based on federal Kalman filter (FKF) and spherical cap harmonic analysis (SCHA) modeling of local gravity field is proposed. Firstly, based on the well posed boundary value problem, the gravity gradient complex combination observation of FKF subsystem filter is constructed. Then, adjusted spherical harmonic analysis (ASHA) is used to optimize the spherical crown harmonic modeling method of local gravity field, so as to quickly establish a more accurate moving window spherical crown harmonic model between the local ocean gravity field centered on the matching point and the spatial position. Based on this model, the measurement equation of sub-filter is established. Finally, the prediction residual vector is used to design an adaptive information distribution factor to fuse the state estimation and covariance of each sub-filter to obtain the optimal estimator of inertial navigation position error. The experimental results show that the gravity FKF matching algorithm modeled by SCHA keeps the positioning error of 24-hour navigation within 1.1 n miles, and the navigation positioning accuracy is improved by more than 85%; The positioning accuracy of 10 day long navigation has been improved by 88.7%. The algorithm can overcome the defect of the inertial navigation system due to the accumulation of time error to some extent, improve the navigation and positioning accuracy of the system, and increase the robustness of the matching algorithm.

Key words: FKF, SCHA, gravity gradient, complex combination, match navigation, ASHA

CLC Number:

P228

HUANG Yan, LI Shanshan, LI Xinxing, SONG Xingguang, FAN Diao, WAN Hongfa. Underwater gravity FKF matching enhancement algorithm based on local SCHA modeling[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(11): 1844-1857.

References

[1] WANG Bo, ZHU Yuwei, DENG Zhihong, et al. The gravity matching area selection criteria for underwater gravity-aided navigation application based on the comprehensive characteristic parameter[J]. ASME Transactions on Mechatronics, 2016, 21(6):2935-2943.
[2] YOO Y M, LEE W H, LEE S M, et al. Improvement of TERCOM aided inertial navigation system by velocity correction[C]//Proceedings of 2012 IEEE/ION Position, Location and Navigation Symposium. Myrtle Beach:IEEE, 2012:1082-1087.
[3] LI Zhaowei, ZHENG Wei, WU Fan. Improving the reliability of underwater gravity matching navigation based on a priori recursive iterative least squares mismatching correction method[J]. IEEE Access, 2020, 8:8648-8657.
[4] 王伟, 李姗姗, 邢志斌, 等. RAE并行滤波的重力异常匹配算法[J]. 武汉大学学报(信息科学版), 2016, 41(12):1664-1670. WANG Wei, LI Shanshan, XING Zhibin, et al. A matching algorithm using gravity anomaly based on the RAE parallel filtering[J]. Geomatics and Information Science of Wuhan University, 2016, 41(12):1664-1670.
[5] 王志刚, 边少锋, 肖胜红. 基于局部地球重力场模型的水下重力辅助惯性导航[J]. 测绘学报, 2009, 38(5):408-414. WANG Zhigang, BIAN Shaofeng, XIAO Shenghong. Underwater gravity aided inertial navigation based on local gravity field model[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(5):408-414.
[6] 黄炎, 李姗姗, 谭勖立, 等. 基于地球重力场模型的重力匹配数据随机线性化方法[J]. 中国惯性技术学报, 2022, 30(3):328-335. HUANG Yan, LI Shanshan, TAN Xuli, et al. Random linearization method of gravity matching data based on Earth gravity field model[J]. Journal of Chinese Inertial Technology, 2022, 30(3):328-335.
[7] 张强, 吴磊, 杨迪, 等. 基于联邦滤波的多传感器管道定位方法[J]. 导航定位与授时, 2022, 9(1):111-118. ZHANG Qiang, WU Lei, YANG Di, et al. Multi-sensor pipeline location method based on federated filter[J]. Navigation Positioning and Timing, 2022, 9(1):111-118.
[8] 严恭敏, 戴晨杰, 刘璠. 再论联邦滤波在组合导航中的应用可行性[J]. 导航定位与授时, 2022, 9(4):1-6. YAN Gongmin, DAI Chenjie, LIU Fan. Further discussion on the application feasibility of federated Kalman filter in integrated navigation[J]. Navigation Positioning and Timing, 2022, 9(4):1-6.
[9] 杨伟星. 复数在坐标正反算计算中的应用[J]. 西北水电, 2015(3):15-17. YANG Weixing. Application of complex number in coordinate positive and negative calculation[J]. Northwest Hydropower, 2015(3):15-17.
[10] 邓冠铁. 复指数系的完备性[J]. 数学年刊(A辑), 2005, 26(4):537-542. DENG Guantie. Completeness of complex exponential system[J]. Chinese Annals of Mathematics, 2005, 26(4):537-542.
[11] 许大欣. 利用重力异常匹配技术实现潜艇导航[J]. 地球物理学报, 2005, 48(4):812-816. XU Daxin. Using gravity anomaly matching techniques to implement submarine navigation[J]. Chinese Journal of Geophysics, 2005, 48(4):812-816.
[12] ODERA P A, FUKUDA Y, KUROISHI Y. A high-resolution gravimetric geoid model for Japan from EGM2008 and local gravity data[J]. Earth, Planets and Space, 2012, 64(5):361-368.
[13] WU Lin, WANG Hubiao, CHAI Hua, et al. Research on the relative positions-constrained pattern matching method for underwater gravity-aided inertial navigation[J]. Journal of Navigation, 2015, 68(5):937-950.
[14] 邹嘉盛, 肖云, 孟宁, 等. 一种基于约束条件的重力匹配导航算法[J]. 武汉大学学报(信息科学版), 2020, 45(10):1570-1577, 1632. ZOU Jiasheng, XIAO Yun, MENG Ning, et al. A gravity matching navigation algorithm based on constraint[J]. Geomatics and Information Science of Wuhan University, 2020, 45(10):1570-1577, 1632.
[15] 欧阳明达, 孙艺轩, 邝英才, 等. 应用抗差估计SITAN算法的水下重力匹配导航方法[J]. 中国惯性技术学报, 2021, 29(2):214-220. OUYANG Mingda, SUN Yixuan, KUANG Yingcai, et al. Underwater gravity matching navigation method of SITAN algorithm with robust estimation[J]. Journal of Chinese Inertial Technology, 2021, 29(2):214-220.
[16] HAN Yurong, WANG Bo, DENG Zhihong, et al. Point mass filter based matching algorithm in gravity aided underwater navigation[J]. Journal of Systems Engineering and Electronics, 2018, 29(1):152-159.
[17] 李建成,陈俊勇,宁津生,等. 地球重力场逼近理论与中国2000似大地水准面的确定[M]. 武汉:武汉大学出版社, 2003. LI Jiancheng, CHEN Junyong, NING Jinsheng, et al. The theory of approximation of the earth's gravity field and the determination of China's 2000 quasi-geoid[M]. Wuhan:Wuhan University Press, 2003.
[18] HAINES G V. Spherical cap harmonic analysis[J]. Journal of Geophysical Research:Solid Earth, 1985, 90(B3):2583-2591.
[19] HAINES G V. Magsat vertical field anomalies above 40°N from spherical cap harmonic analysis[J]. Journal of Geophysical Research:Solid Earth, 1985, 90(B3):2593-2598.
[20] 彭富清, 于锦海. 球冠谐分析中非整阶Legendre函数的性质及其计算[J]. 测绘学报, 2000, 29(3):204-208. PENG Fuqing, YU Jinhai. The characters and computation of Legendre function with non integral degree in SCHA[J]. Acta Geodaetica et Cartographic Sinica, 2000, 29(3):204-208.
[21] DE SANTIS A, TORTA J M. Spherical cap harmonic analysis:a comment on its proper use for local gravity field representation[J]. Journal of Geodesy, 1997, 71(9):526-532.
[22] 严恭敏, 翁浚. 捷联惯导算法与组合导航原理[M]. 西安:西北工业大学出版社, 2019. YAN Gongmin, WENG Jun. Strapdown inertial navigation algorithm and integrated navigation principle[M]. Xi'an:Northwestern Polytechnical University Press, 2019.
[23] 杨元喜. 自适应动态导航定位[M]. 2版. 北京:测绘出版社, 2017. YANG Yuanxi. Adaptive navigation and kinematic positioning[M]. 2nd ed. Beijing:Surveying and Mapping Press, 2017.
[24] 杨元喜, 任夏, 许艳. 自适应抗差滤波理论及应用的主要进展[J]. 导航定位学报, 2013, 1(1):9-15. YANG Yuanxi, REN Xia, XU Yan. Main progress of adaptively robust filter with applications in navigation[J]. Journal of Navigation and Positioning, 2013, 1(1):9-15.
[25] 陈荣娟, 王海波, 胡宏灿, 等. 船舶惯性导航系统圆概率误差可信度分析[J]. 中国航海, 2015, 38(2):18-20. CHEN Rongjuan, WANG Haibo, HU Hongcan, et al. Simulation analysis on reliability of CEP of ship INS[J]. Navigation of China, 2015, 38(2):18-20.
[26] 胡平华, 赵明, 黄鹤, 等. 航空/海洋重力测量仪器发展综述[J]. 导航定位与授时, 2017, 4(4):10-19. HU Pinghua, ZHAO Ming, HUANG He, et al. Review on the development of airborne/marine gravimetry instruments[J]. Navigation Positioning and Timing, 2017, 4(4):10-19.
[27] 马越原. 重力匹配辅助水下导航的若干问题研究[D]. 郑州:信息工程大学, 2017. MA Yueyuan. Research on problems of underwater gravity aided inertial navigation[D]. Zhengzhou:Information Engineering University, 2017.