Multi-window joint robust estimation for marine acoustic navigation

doi:10.11947/j.AGCS.2026.20250356

Abstract

Abstract:

Marine acoustic navigation typically employs active sonar to obtain the round-trip signal propagation time between the carrier and the navigation beacon. However, it cannot simultaneously acquire multi-beacon acoustic observations, and it is difficult to implement acoustic observation quality control solely relying on single-epoch acoustic observations. To address this issue, this paper proposes a windowed robust least squares estimation algorithm. By implementing a multi-window joint robustness strategy, the algorithm dynamically constructs robust equivalent weights using observation quality information within historical windows during the window sliding process. Specifically, the initial weights for observations in the new window are determined by taking the mean of the robust equivalent weights across multiple historical windows, and the quality of newly added observations within the window is evaluated using the carrier trajectory model prediction information. Experimental results show that: ① under Huber, IGG Ⅱ, and IGG Ⅲ robustness strategies, the proposed algorithm can effectively resist the impact of gross errors, especially significantly enhancing the robustness performance of lever observations at the edge of the window; ② the proposed algorithm can significantly improve the accuracy and reliability of navigation and positioning results, resulting in smoother and more stable robust navigation trajectory estimation.

Key words: acoustic navigation, sliding-window, outlier detection, robust estimation, IGG Ⅲ

CLC Number:

P229

Jiachao BIAN, Shuqiang XUE, Shuang ZHAO, Jixing ZHU, Jinlai GAO, Baojin LI. Multi-window joint robust estimation for marine acoustic navigation[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(3): 515-524.

Figures/Tables 11

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Tab. 1

Tab. 2

References 32

[1]	杨元喜, 徐天河, 薛树强. 我国海洋大地测量基准与海洋导航技术研究进展与展望[J]. 测绘学报, 2017(1): 1-8. DOI: . doi: 10.11947/j.AGCS.2017.20160519
	YANG Yuanxi, XU Tianhe, XUE Shuqiang. Progresses and prospects in developing marine geodetic datum and marine navigation of China[J]. Acta Geodaetica et Cartographica Sinica, 2017(1): 1-8. DOI: . doi: 10.11947/j.AGCS.2017.20160519
[2]	杨元喜. 弹性PNT基本框架[J]. 测绘学报, 2018, 47(7): 893-898. DOI: . doi: 10.11947/j.AGCS.2018.20180149
	YANG Yuanxi. Resilient PNT concept frame[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(7): 893-898. DOI: . doi: 10.11947/j.AGCS.2018.20180149
[3]	阳凡林, 辛明真, 刘经南, 等. 超短基线多信标约束的深海动态定位方法探讨[J]. 武汉大学学报(信息科学版), 2023, 48(11): 1876-1883.
	YANG Fanlin, XIN Mingzhen, LIU Jingnan, et al. Discussion of deep-sea dynamic positioning methods with ultra-short baseline multi-beacon constraint[J]. Geomatics and Information Science of Wuhan University, 2023, 48(11): 1876-1883.
[4]	薛树强, 杨诚, 赵爽, 等. 海底大地控制网无人观测系统研究进展[J]. 导航定位学报, 2023, 11(6): 8-21.
	XUE Shuqiang, YANG Cheng, ZHAO Shuang, et al. Review of unmanned observation systems for seafloor geodetic network[J]. Journal of Navigation and Positioning, 2023, 11(6): 8-21.
[5]	赵爽, 王振杰, 刘慧敏. 顾及声线入射角的水下定位随机模型[J]. 测绘学报, 2018, 47(9): 1280-1289. DOI: . doi: 10.11947/j.AGCS.2018.20170026
	ZHAO Shuang, WANG Zhenjie, LIU Huimin. Investigation on underwater positioning stochastic model based on sound ray incidence angle[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(9): 1280-1289. DOI: . doi: 10.11947/j.AGCS.2018.20170026
[6]	刘焱雄, 李梦昊, 刘杨, 等. 海底大地基准建设技术及其研究进展[J]. 海洋科学进展, 2022, 40(4): 684-700.
	LIU Yanxiong, LI Menghao, LIU Yang, et al. Research progress of seafloor geodetic datum construction technology[J]. Advances in Marine Science, 2022, 40(4): 684-700.
[7]	薛树强, 杨元喜, 肖圳, 等. 全球导航卫星系统-声呐组合观测模型分类体系[J]. 哈尔滨工程大学学报, 2023, 44(11): 1857-1868.
	XUE Shuqiang, YANG Yuanxi, XIAO Zhen, et al. Global navigation satellite system-acoustic combined observation model classification system[J]. Journal of Harbin Engineering University, 2023, 44(11): 1857-1868.
[8]	YOKOTA Y, KANEDA M, HASHIMOTO T, et al. Experimental verification of seafloor crustal deformation observations by UAV-based GNSS-A[J]. Scientific Reports, 2023, 13(1): 4105.
[9]	杨元喜. 条件平差、混合平差模型的抗差最小二乘解[J]. 测绘通报, 1995(1): 44-46.
	YANG Yuanxi. Robust least squares solution of conditional adjustment and mixed adjustment models[J]. Bulletin of Surveying and Mapping, 1995(1): 44-46.
[10]	杨元喜, 徐天河. 基于移动开窗法协方差估计和方差分量估计的自适应滤波[J]. 武汉大学学报(信息科学版), 2003, 28(6): 714-718.
	YANG Yuanxi, XU Tianhe. An adaptive Kalman filter combining variance component estimation with covariance matrix estimation based on moving window[J]. Geomatics and Information Science of Wuhan University, 2003, 28(6): 714-718.
[11]	YANG Yuanxi, ZHANG Xiaodong, XU Junyi. Adaptively constrained Kalman filtering for navigation applications[J]. Survey Review, 2011, 43(322): 370-381.
[12]	周江文. 再论拟合推估[J]. 测绘学报, 2001, 30(4): 283-285.
	ZHOU Jiangwen. Further on collocation[J]. Acta Geodaetica et Cartographica Sinica, 2001, 30(4): 283-285.
[13]	杨元喜. 自适应抗差最小二乘估计[J]. 测绘学报, 1996, 25(3): 206-211.
	YANG Yuanxi. Adaptively robust least squares estimation[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(3): 206-211.
[14]	杨元喜, 宋力杰, 徐天河. 大地测量相关观测抗差估计理论[J]. 测绘学报, 2002, 31(2): 95-99.
	YANG Yuanxi, SONG Lijie, XU Tianhe. Robust parameter estimation for geodetic correlated observations[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(2): 95-99.
[15]	欧吉坤. 一种三步抗差方案的设计[J]. 测绘学报, 1996, 25(3): 173-179.
	OU Jikun. Design of a new scheme of robust estimation by three steps[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(3): 173-179.
[16]	黄声享, 王金岭. 多余观测分量与可靠性度量指标研究[J]. 武汉测绘科技大学学报, 1997, 22(2): 114-118.
	HUANG Shengxiang, WANG Jinling. Research on redundant observation components and reliability measures for correlated observations[J]. Journal of Wuhan Tehcnnical University of Surveying and Mapping, 1997, 22(2): 114-118.
[17]	闫凤池, 王振杰, 赵爽, 等. 顾及双程声径的常梯度声线跟踪水下定位算法[J]. 测绘学报, 2022, 51(1): 31-40. DOI: . doi: 10.11947/j.AGCS.2022.20210234
	YAN Fengchi, WANG Zhenjie, ZHAO Shuang, et al. A layered constant gradient acoustic ray tracing underwater positioning algorithm considering round-trip acoustic path[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(1): 31-40. DOI: . doi: 10.11947/j.AGCS.2022.20210234
[18]	杨元喜, 刘焱雄, 孙大军, 等. 海底大地基准网建设及其关键技术[J]. 中国科学：地球科学, 2020, 50(7): 936-945.
	YANG Yuanxi, LIU Yanxiong, SUN Dajun, et al. Seafloor geodetic network establishment and key technologies[J]. Scientia Sinica (Terrae), 2020, 50(7): 936-945.
[19]	XUE Shuqiang, YANG Yuanxi, YANG Wenlong, et al. GNSS-a network solution with zenith acoustic delay estimation[J]. Marine Geodesy, 2024, 47(3): 237-268.
[20]	LARSEN M B. Synthetic long baseline navigation of underwater vehicles[C]//Proceedings of OCEANS 2000 MTS/IEEE Conference and Exhibition. New York: IEEE, 2002: 2043-2050.
[21]	宋丽君, 赵万良, 成宇翔, 等. 基于滑动窗因子图优化的多源导航信息融合[J]. 飞控与探测, 2024, 7(5): 20-29.
	SONG Lijun, ZHAO Wanliang, CHENG Yuxiang, et al. Multi-source navigation information fusion based on sliding window factor graph optimization[J]. Flight Control & Detection, 2024, 7(5): 20-29.
[22]	徐天河, 王森, 代培培. UWB/INS紧组合变分贝叶斯自适应滤波算法[J]. 导航定位学报, 2025, 13(2): 1-8.
	XU Tianhe, WANG Sen, DAI Peipei. UWB/INS tightly coupled integration algorithm based on variational Bayesian adaptive Kalman filter[J]. Journal of Navigation and Positioning, 2025, 13(2): 1-8.
[23]	黄紫如, 柴洪洲, 向民志, 等. 基于抗差因子图的AUV多源信息融合定位方法[J]. 测绘学报, 2023, 52(8): 1278-1285. DOI: . doi: 10.11947/j.AGCS.2023.20210735
	HUANG Ziru, CHAI Hongzhou, XIANG Minzhi, et al. AUV multi-source information fusion localization method based on robust factor graph[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(8): 1278-1285. DOI: . doi: 10.11947/j.AGCS.2023.20210735
[24]	段楚峰, 张昊楠, 匡翠林, 等. 应用曲线积分的地震勘探多缆定位算法[J]. 石油地球物理勘探, 2022, 57(6): 1317-1324.
	DUAN Chufeng, ZHANG Haonan, KUANG Cuilin, et al. Multi-streamer positioning algorithm based on curvilinear integral for seismic exploration[J]. Oil Geophysical Prospecting, 2022, 57(6): 1317-1324.
[25]	薛树强, 杨诚, 卞加超, 等. 无外部信息辅助的主动式声呐时间开窗导航定位模型[J]. 武汉大学学报(信息科学版), 2026, 51(2): 296-305.
	XUE Shuqiang, YANG Cheng, BIAN Jiachao, et al. Active sonar time-window navigation and positioning model without appending external navigation information[J]. Geomatics and Information Science of Wuhan University, 2026, 51(2): 296-305.
[26]	闫志闯, 徐新强, 赵德军, 等. 低轨卫星约化动力法定轨参数变换的高效算法[J]. 测绘学报, 2018, 47(S0): 28-37. DOI: . doi: 10.11947/j.AGCS.2018.20180307
	YAN Zhichuang, XU Xinqiang, ZHAO Dejun, et al. An efficient algorithm with reduced dynamic orbit determination for LEOs based on parameter transforming[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(S0): 28-37. DOI: . doi: 10.11947/j.AGCS.2018.20180307
[27]	余文坤, 吴佩达, 张昊楠, 等. 基于多项式曲线拟合的海上地震勘探拖缆定位[J]. 测绘学报, 2022, 51(5): 772-780. DOI: . doi: 10.11947/j.AGCS.2022.20200588
	YU Wenkun, WU Peida, ZHANG Haonan, et al. Offshore towed-streamer seismic positioning based on polynomial curve fitting[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(5): 772-780. DOI: . doi: 10.11947/j.AGCS.2022.20200588
[28]	宋力杰, 杨元喜. 均值漂移模型粗差探测法与LEGE法的比较[J]. 测绘学报, 1999, 28(4): 295-300.
	SONG Lijie, YANG Yuanxi. Comparison between data snooping and LEGE[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(4): 295-300.
[29]	薛树强, 杨文龙, 赵爽. 主动式定位的椭球交会原理及其2种解法[J]. 导航定位学报, 2024, 12(3): 1-7.
	XUE Shuqiang, YANG Wenlong, ZHAO Shuang. The ellipsoid intersection principle of active positioning and its two solutions[J]. Journal of Navigation and Positioning, 2024, 12(3): 1-7.
[30]	WATANABE S I, ISHIKAWA T, YOKOTA Y, et al. GARPOS: analysis software for the GNSS-a seafloor positioning with simultaneous estimation of sound speed structure[J]. Frontiers in Earth Science, 2020, 8: 597532.
[31]	YANG Yuanxi, SONG Lijie, XU Tianhe. Robust estimator for correlated observations based on bifactor equivalent weights[J/OL]. Journal of Geodesy, 2002, 76(6): 353-358.
[32]	YANG Wenlong, XUE Shuqiang, LIU Yixu. P-order secant method for rapidly solving the ray inverse problem of underwater acoustic positioning[J]. Marine Geodesy, 2023, 46(1): 3-15.

数据集	解算方案	抗差方案	E绝对误差		N绝对误差		定位绝对误差
数据集	解算方案	抗差方案	均值	标准差	均值	标准差	均值	标准差
MYGI-1306	逐窗抗差估计	Huber	3.16	2.23	3.77	4.61	5.45	4.54
		IG Ⅱ	3.08	2.26	3.65	4.68	5.31	4.64
		IG Ⅲ	2.72	2.19	3.48	4.69	4.96	4.56
	多窗联合抗差	Huber	3.14	2.25	3.76	4.60	5.41	4.29
		IG Ⅱ	2.41	3.10	1.93	3.37	3.25	4.47
		IG Ⅲ	2.08	1.07	0.87	0.77	2.38	1.07
CHOS-1808	逐窗抗差估计	Huber	2.48	2.17	2.56	3.51	3.98	3.72
		IG Ⅱ	2.24	2.09	2.51	3.52	3.72	3.77
		IG Ⅲ	1.88	1.70	2.40	4.05	3.46	4.07
	多窗联合抗差	Huber	2.42	2.09	2.51	3.49	3.89	3.69
		IG Ⅱ	1.79	1.58	0.99	0.97	2.18	1.70
		IG Ⅲ	1.64	1.32	0.91	0.96	1.99	1.49
KAMS-1906	逐窗抗差估计	Huber	2.34	2.01	2.72	3.37	4.02	3.48
		IG Ⅱ	2.30	2.04	2.66	3.38	3.94	3.52
		IG Ⅲ	2.23	2.21	2.27	3.29	3.51	3.68
	多窗联合抗差	Huber	2.33	2.02	2.50	3.44	3.86	3.56
		IG Ⅱ	1.47	0.92	2.11	2.90	2.86	2.77
		IG Ⅲ	1.19	0.45	0.66	0.64	1.44	0.51

数据集	窗口大小	解算方案	E绝对误差		N绝对误差		定位绝对误差
数据集	窗口大小	解算方案	均值	标准差	均值	标准差	均值	标准差
MYGI-1306	16历元	最小二乘估计	3.28	2.56	4.01	5.05	5.66	5.17
		逐窗抗差估计	2.92	2.60	3.55	5.15	5.11	5.31
		多窗联合抗差	2.22	0.91	0.76	0.82	2.47	0.95
	20历元	最小二乘估计	3.21	2.25	3.84	4.58	5.54	4.51
		逐窗抗差估计	2.72	2.19	3.48	4.69	4.96	4.56
		多窗联合抗差	2.08	1.07	0.87	0.77	2.38	1.07
	24历元	最小二乘估计	3.14	1.90	4.06	4.21	5.61	4.01
		逐窗抗差估计	2.77	1.86	3.52	4.33	4.93	4.25
		多窗联合抗差	2.14	1.17	1.01	0.96	2.57	1.15