基于DBSCAN的多粗差识别RAIM算法

doi:10.11947/j.AGCS.2026.20250033

测绘学报 ›› 2026, Vol. 55 ›› Issue (1): 59-72.doi: 10.11947/j.AGCS.2026.20250033

• 大地测量学与导航 • 上一篇

基于DBSCAN的多粗差识别RAIM算法

余德荧¹(), 李厚朴¹(), 刘一², 武曙光¹, 李得宴¹, 李明超³, 李文魁¹, 边少锋¹

^1.海军工程大学，湖北　武汉　430033
^2.香港理工大学，香港　999077
^3.91656部队，浙江　宁波　315700

收稿日期:2025-01-20 修回日期:2026-01-13 发布日期:2026-02-13
通讯作者: 李厚朴 E-mail:20500601@nue.edu.cn;1210051025@nue.edu.cn
作者简介:余德荧（1998—），男，博士，研究方向为卫星无线电导航技术及应用。E-mail：20500601@nue.edu.cn
基金资助:
国家自然科学基金(42174051; 42430101; 42404017)

A DBSCAN-based RAIM algorithm for multiple gross error identification

Deying YU¹(), Houpu LI¹(), Yi LIU², Shuguang WU¹, Deyan LI¹, Mingchao LI³, Wenkui LI¹, Shaofeng BIAN¹

^1.Naval University of Engineering, Wuhan 430033, China
^2.The Hong Kong Polytechnic University, Hong Kong 999077, China
^3.Troops 91656, Ningbo 315700, China

Received:2025-01-20 Revised:2026-01-13 Published:2026-02-13
Contact: Houpu LI E-mail:20500601@nue.edu.cn;1210051025@nue.edu.cn
About author:YU Deying (1998—), male, PhD, majors in satellite radio navigation technology and its applications. E-mail: 20500601@nue.edu.cn
Supported by:
The National Natural Science Foundation of China(42174051; 42430101; 42404017)

摘要/Abstract

摘要：

随着GNSS在航空、航海等高安全需求领域的广泛应用，接收机自主完好性监测（RAIM）技术对保障导航可靠性至关重要。针对现有RAIM算法在多颗卫星同时发生故障时探测能力不足、计算效率偏低的问题，本文提出一种基于密度空间聚类（DBSCAN）的多粗差识别RAIM算法。该算法首先通过奇偶校验法构建观测样本，进而计算样本间距离以突显异常观测，最后利用DBSCAN聚类，根据数据密度分布自适应识别并隔离多个粗差。仿真与实测试验表明：①在船载仿真场景中，当3颗卫星存在50 m与100 m伪距粗差时，本文算法相比传统最小二乘残差法（LSR），定位精度分别提升约82.8%和92.1%，计算效率分别提升约96.2%和96.1%；②在机载高动态仿真中，算法对5~100 m粗差的识别率从52.9%持续提升至100%，且定位误差保持稳定；③利用IGS站实测数据，算法将水平与三维误差从LSR RAIM的8.61和9.94 m显著降低至0.77和1.08 m；④在城市车载实测场景中，算法在定位精度上与随机样本一致性检验（RANSAC）RAIM算法相当，但计算效率提升超过94.7%。本文算法显著增强了多粗差识别能力，并兼具高效的计算性能，为复杂环境下高可靠性导航定位提供了有效解决方案。

关键词: GNSS, 接收机自主完好性监测, 基于密度的空间聚类算法, 多粗差识别, 计算效率, 导航可靠性

Abstract:

With the widespread application of GNSS in safety-critical fields such as aviation and maritime navigation, receiver autonomous integrity monitoring (RAIM) technology is crucial for ensuring navigation reliability. To address the limitations of existing RAIM algorithms, namely insufficient detection capability and low computational efficiency when multiple satellites fail simultaneously, this paper proposes a novel RAIM algorithm for multiple gross error identification based on density-based spatial clustering of applications with noise (DBSCAN). The algorithm first constructs observation samples via parity checks, calculates inter-sample distances to highlight anomalies, and then employs DBSCAN clustering to adaptively identify and isolate multiple gross errors based on data density distribution. Simulations and real-world experiments demonstrate that: ① In simulated shipborne scenarios with 50 m and 100 m pseudorange gross errors across three satellites, the proposed algorithm improves positioning accuracy by approximately 82.8%and 92.1%, and computational efficiency by about 96.2%and 96.1%, respectively, compared to the traditional least squares residuals (LSR) method；② In simulated high-dynamic airborne scenarios, the algorithm＇s detection rate for gross errors ranging from 5 m to 100 m increases consistently from 52.9%to 100%, while positioning error remains stable；③ Using real data from an IGS station, the algorithm significantly reduces the horizontal and three-dimensional errors from 8.61 and 9.94 m (with LSR RAIM) to 0.77 and 1.08 m；④ In urban vehicular field tests, the algorithm achieves positioning accuracy comparable to the random sample consensus (RANSAC) RAIM algorithm, but with a computational efficiency improvement exceeding 94.7%. The proposed algorithm significantly enhances multiple gross error identification capability while maintaining high computational efficiency, providing an effective solution for high-reliability navigation and positioning in complex environments.

Key words: GNSS, receiver autonomous integrity monitoring, density-based spatial clustering of applications with noise, multiple gross error identification, computational efficiency, navigation reliability

中图分类号:

P228

余德荧, 李厚朴, 刘一, 武曙光, 李得宴, 李明超, 李文魁, 边少锋. 基于DBSCAN的多粗差识别RAIM算法[J]. 测绘学报, 2026, 55(1): 59-72.

Deying YU, Houpu LI, Yi LIU, Shuguang WU, Deyan LI, Mingchao LI, Wenkui LI, Shaofeng BIAN. A DBSCAN-based RAIM algorithm for multiple gross error identification[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(1): 59-72.

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系统	伪距粗差	RAIM算法	X		Y		Z
系统	伪距粗差	RAIM算法	RMS	STD	RMS	STD	RMS	STD
GPS/Galileo	50	LSR	15.52	3.37	13.40	7.48	3.20	2.99
		RANSAC	3.53	3.53	2.46	2.46	2.05	2.05
		DBSCAN	3.56	3.55	2.54	2.53	2.03	2.03
	100	LSR	30.68	3.71	28.63	12.31	5.37	4.23
		RANSAC	3.64	3.64	2.45	2.45	1.92	1.92
		DBSCAN	3.64	3.64	2.45	2.45	1.92	1.92
GPS/Galileo/BDS	50	LSR	14.19	3.64	25.93	2.35	14.49	2.34
		RANSAC	3.55	3.55	2.69	2.69	2.19	2.19
		DBSCAN	4.69	4.63	4.75	4.68	2.65	2.65
	100	LSR	27.33	3.55	51.95	2.28	29.06	2.41
		RANSAC	3.59	3.59	2.70	2.70	2.14	2.14
		DBSCAN	3.59	3.59	2.70	2.70	2.14	2.14

系统	伪距粗差/m	运行耗时/s			DBSCAN RAIM效率提升/（%）
系统	伪距粗差/m	LSR RAIM	RANSAC RAIM	DBSCAN RAIM	LSR RAIM	RANSAC RAIM
GPS/Galileo	50	0.626 9	5.707 3	0.371 4	40.75	93.49
GPS/Galileo	100	0.830 4	7.552 7	0.484 6	41.64	93.58
GPS/Galileo/BDS	50	1.044 1	9.496 3	0.606 5	41.91	93.61
GPS/Galileo/BDS	100	1.248 6	11.354 7	0.720 3	42.32	93.66

伪距粗差/m	RAIM算法	识别率/（%）	误检率/（%）	漏检率/（%）	F₁值
5	LSR	0	0	100	0
5	DBSCAN	52.87	18.17	47.13	0.46
10	LSR	28.21	1.18	71.79	0.42
10	DBSCAN	72.90	8.27	27.10	0.70
50	LSR	33.33	0	66.67	0.50
50	DBSCAN	99.92	0.02	0.08	1
100	LSR	33.33	0	66.67	0.50
100	DBSCAN	100	0	0	1

伪距粗差	RAIM算法	X		Y		Z
伪距粗差	RAIM算法	RMS	STD	RMS	STD	RMS	STD
5	LSR	4.49	3.21	3.35	2.06	2.34	1.96
5	DBSCAN	4.42	4.08	3.20	2.64	2.57	2.38
10	LSR	7.06	3.53	5.70	2.12	3.11	1.84
10	DBSCAN	4.92	4.34	4.14	3.16	2.84	2.46
50	LSR	14.48	3.64	25.74	2.26	15.12	2.08
50	DBSCAN	3.89	3.89	2.86	2.86	2.20	2.21
100	LSR	28.28	3.53	51.21	2.17	30.37	2.05
100	DBSCAN	3.71	3.71	2.63	2.63	2.14	2.14

基于DBSCAN的多粗差识别RAIM算法

A DBSCAN-based RAIM algorithm for multiple gross error identification

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