不同截止高度角BDS/GPS/Galileo单历元RTK定位性能分析

doi:10.11871/jfdc.issn.2096-742X.2022.04.002

数据与计算发展前沿 ›› 2022, Vol. 4 ›› Issue (4): 13-24.

CSTR: 32002.14.jfdc.CN10-1649/TP.2022.04.002

doi: 10.11871/jfdc.issn.2096-742X.2022.04.002

• 专刊：北斗导航数据处理 • 上一篇下一篇

不同截止高度角BDS/GPS/Galileo单历元RTK定位性能分析

钟海林^1,²(),高睿^1,²,张宝成^1,^*()

1.中国科学院精密测量科学与技术创新研究院,湖北武汉 430071
2.中国科学院大学,北京 100049

收稿日期:2022-03-18 出版日期:2022-08-20 发布日期:2022-08-10
通讯作者: 张宝成
作者简介:钟海林,中国科学院精密测量科学与技术创新研究院,硕士研究生,目前研究方向为GNSS精密导航定位算法研究。
本文承担工作为：数据分析与论文撰写。
ZHONG Hailin is a master's degree candidate at the Innovation Academy for Precision Measurement Science and Technology, CAS. His current research focuses on high-precision GNSS navigation and positioning algorithm.
He undertakes the following tasks in this paper: data analysis and paper writing.
E-mail: zhonghailin@apm.ac.cn|张宝成,中国科学院精密测量科学与技术创新研究院,博士,研究员,博士生导师,研究领域为PPP-RTK技术研究及应用。
本文承担工作为：论文指导。
ZHANG Baocheng, Ph.D., is a full pro-fessor and Ph.D. advisor at the Innovation Academy for Preci-sion Measurement Science and Technology, CAS. His research focuses on modeling multiple global navigation satellite syst-ems for integer ambiguity resolution-enabled precise point positioning (PPP-RTK) applications.
He undertakes the following tasks in this paper: paper super-vision.
E-mail: b.zhang@whigg.ac.cn
基金资助:
国家自然科学基金(41774042);国家自然科学基金(42174034);湖北省重点研发计划(2020BHB014)

Performance Assessment of BDS/GPS/Galileo Single-Epoch RTK under Different Cut-off Elevation Angles

ZHONG Hailin^1,²(),GAO Rui^1,²,ZHANG Baocheng^1,^*()

1. Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan, Hubei 430071, China
2. University of Chinese Academy of Sciences, Beijing 100049, China

Received:2022-03-18 Online:2022-08-20 Published:2022-08-10
Contact: ZHANG Baocheng

摘要/Abstract

摘要：

【目的】为探究北斗卫星导航系统（BeiDou Navigation Satellite System, BDS）、GPS（Global Positioning System）、Galileo单系统及组合系统在中国地区不同截止高度角下单历元双频RTK（Real-Time Kinematic）定位性能,对武汉境内一条短基线进行分析研究。【方法】采用双差RTK模型对短基线数据进行解算,并通过LAMBDA（Least-square AMBiguity Decorrelation Adjustment）法固定模糊度,得到各单系统及组合系统的单历元基线解。【结论】结果表明：在中国地区内的相同截止高度角下,单BDS的综合RTK定位性能明显优于单GPS和单Galileo。在50°大截至高度角下,GPS和Galileo基本丧失独立RTK定位性能,而单BDS仍能保持100%的历元解算率和近乎100%的模糊度固定成功率以实现连续、可靠的高精度单历元RTK定位,在中国境内一些遮挡严重的复杂环境地区（如城市峡谷）,BDS相较于其它两个单系统明显更有优势;且GPS+BDS和GPS+BDS+Galileo组合不仅可以有效改善单BDS的浮点解精度和固定解的垂直精度,同时提高了单BDS在极端高度角下历元解算率和模糊度的固定成功率,进一步增强了单BDS在遮挡环境中的适用性。

关键词: 双差, 北斗卫星导航系统, 实时动态差分, 截止高度角

Abstract:

[Objective] To explore the single-epoch dual-frequency RTK (Real-Time Kinematic) performance of BDS (BeiDou Navigation Satellite System)-only, GPS (Global Positioning System)-only, Galileo-only systems and combined systems under different cut-off elevation angles in China, a short-baseline data collected in Wuhan was analyzed. [Methods] The double-differenced RTK model and the LAMBDA (Least-square AMBiguity Decorrelation Adjustment) method were used for short-baseline resolution and ambiguity resolution respectively to get the single-epoch solution of a single system and combined systems. [Conclusions] The results show that the RTK positioning performance of the BDS-only system is better than GPS-only and Galileo-only systems under the same cut-off elevation angles in China. Under the large cut-off elevation angle of 50°, GPS-only and Galileo-only systems nearly lose their RTK positioning ability, while the BDS-only system can still keep up a 100% epoch solution rate and almost 100% ambiguity success rate to achieve continuous, reliable, and high-precision RTK positioning. In some complex environments (urban canyons) with serious occlusion in China, the BDS-only system has an obvious advantage compared to GPS-only and Galileo-only systems. The combined GPS+BDS and GPS+BDS+Galileo system can not only effectively improve the accuracy of the float solution and the vertical accuracy of the fixed solution, but also improve the epoch solution rate and ambiguity success rate based on the BDS-only system, and further enhances the applicability of BDS-only system in occlusion environment.

Key words: double-differenced, BDS, RTK, cut-off elevation angle

钟海林,高睿,张宝成. 不同截止高度角BDS/GPS/Galileo单历元RTK定位性能分析[J]. 数据与计算发展前沿, 2022, 4(4): 13-24.

ZHONG Hailin,GAO Rui,ZHANG Baocheng. Performance Assessment of BDS/GPS/Galileo Single-Epoch RTK under Different Cut-off Elevation Angles[J]. Frontiers of Data and Computing, 2022, 4(4): 13-24, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2022.04.002.

图/表 13

表1

表2

图1

图2

表3

图3

图4

图5

图6

表4

基线APM8-APM9解算结果统计"

系统	高度角(°)	浮点解RMS(m)			固定解RMS(m)			固定成功率(%)	可用卫星平均数	PDOP均值	解算率(%)
系统	高度角(°)	E	N	U	E	N	U	固定成功率(%)	可用卫星平均数	PDOP均值	解算率(%)
BDS	10	0.1510	0.1596	0.3849	0.0042	0.0067	0.0202	100.0	21.2	1.3	100.0
	20	0.1575	0.1649	0.4376	0.0042	0.0068	0.0200	100.0	19.1	1.6	100.0
	30	0.1854	0.1865	0.6215	0.0040	0.0064	0.0189	100.0	15.4	2.6	100.0
	40	0.2319	0.2161	0.9414	0.0046	0.0065	0.0194	100.0	12.6	3.6	100.0
	50	0.3878	0.2653	1.8866	0.0068	0.0069	0.0300	99.4	8.6	8.2	100.0
	60	0.6255	0.6289	3.5057	0.0091	0.0118	0.0485	67.3	4.9	51.3	85.7
GPS	10	0.1909	0.2185	0.5571	0.0053	0.0102	0.0191	96.5	8.5	2.1	100.0
	20	0.2008	0.2322	0.6244	0.0050	0.0093	0.0199	97.6	7.1	3.1	100.0
	30	0.2491	0.3042	0.9655	0.0061	0.0101	0.0230	93.4	5.5	7.3	97.0
	40	0.4227	0.5109	1.5163	0.0100	0.0129	0.0303	80.3	4.0	30.6	69.0
	50	0.4456	0.5213	1.9732	0.0110	0.0143	0.0378	66.9	2.8	52.6	21.2
	60	-	-	-	-	-	-	-	1.4	-	0.0
Galileo	10	0.1595	0.1510	0.4174	0.0071	0.0112	0.0237	90.0	6.8	2.6	100.0
	20	0.2246	0.1800	0.6290	0.0086	0.0106	0.0278	87.4	5.4	10.8	100.0
	30	0.2392	0.2561	1.1282	0.0085	0.0109	0.0331	80.9	4.2	37.4	85.6
	40	0.2805	0.2774	1.2154	0.0107	0.0131	0.0416	71.1	3.1	95.7	28.0
	50	-	-	-	-	-	-	-	2.0	-	0.0
	60	-	-	-	-	-	-	-	1.2	-	0.0
GPS+BDS	10	0.1185	0.1272	0.3068	0.0037	0.0070	0.0174	100.0	29.8	1.1	100.0
	20	0.1229	0.1304	0.3402	0.0038	0.0070	0.0173	100.0	26.1	1.3	100.0
	30	0.1409	0.1434	0.4577	0.0037	0.0064	0.0164	100.0	20.9	2.0	100.0
	40	0.1772	0.1702	0.7313	0.0040	0.0064	0.0173	100.0	16.6	3.0	100.0
	50	0.2950	0.2186	1.4017	0.0064	0.0068	0.0263	99.5	11.1	6.5	100.0
	60	0.5059	0.4634	3.1979	0.0083	0.0104	0.0470	70.6	6.3	37.7	92.5
GPS+BDS+ Galileo	10	0.0987	0.1067	0.2528	0.0035	0.0072	0.0172	100.0	36.6	0.9	100.0
	20	0.1032	0.1100	0.2840	0.0036	0.0070	0.0172	100.0	31.5	1.2	100.0
	30	0.1175	0.1213	0.3793	0.0035	0.0063	0.0161	100.0	25.0	1.8	100.0
	40	0.1532	0.1459	0.6250	0.0039	0.0065	0.0168	100.0	19.6	2.8	100.0
	50	0.2621	0.2025	1.2547	0.0060	0.0071	0.0251	99.1	13.5	5.9	100.0
	60	0.4908	0.4392	2.8731	0.0088	0.0095	0.0446	76.0	7.5	28.4	94.8

表4

图7

图8

表5

参考文献 18

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符号和解释	参数含义
$\Phi_{j r, i}^{S}=\Phi_{j, i}^{S}-\Phi_{r, i}^{S}$	单差相位观测值
$N_{j r, i}^{s}=N_{j, i}^{s}-N_{r, i}^{s} $	单差模糊度
$p_{j r, i}^{S}=p_{j, i}^{s}-p_{r, i}^{s} $	单差伪距观测值
$\rho_{j r}^{S}=\rho_{j}^{S}-\rho_{r}^{S} $	单差站星距
$d t_{j r}=d t_{j}-d t_{r} $	单差接收机钟差
$\delta_{j r, i}=\delta_{j, i}-\delta_{r, i} $	单差接收机相位硬件延迟
$\tau_{j r, i}=\tau_{j, i}-\tau_{r, i} $	单差接收机伪距硬件延迟

符号和解释	参数含义
$\Phi_{j r, i}^{q s}=\Phi_{j, i}^{q}-\Phi_{r, i}^{q}-\Phi_{j, i}^{s}+\Phi_{r, i}^{s}$	双差相位观测值
$N_{j r, i}^{q s}=N_{j, i}^{q}-N_{r, i}^{q}-N_{j, i}^{s}+N_{r, i}^{s} $	双差模糊度
$p_{j r, i}^{q s}=p_{j, i}^{q}-p_{r, i}^{q}-p_{j, i}^{s}+p_{r, i}^{s} $	双差伪距观测值
$\rho_{j r}^{q s}=\rho_{j}^{q}-\rho_{r}^{q}-\rho_{j}^{s}+\rho_{r}^{s}$	双差站星距

基线评估指标	计算方式
RMS	$\sqrt{\sum_{i=1}^{n}\left(X_{i}-\widetilde{X}\right) / n}$ (n为数据个数, $\widetilde{X}$为真值,X_i为第i个解算结果)
解算率	(有效历元数/总观测历元数) ×100%
固定成功率	(模糊度固定正确的历元数/有效历元数) ×100%
可用卫星平均数	所有历元可用卫星总数/总观测历元数
PDOP均值	有效历元PDOP总数/有效历元数

组合系统	浮点解精度提升效果(%)			固定解精度提升效果(%)
组合系统	E	N	U	E	N	U
GPS+BDS	21.5	20.3	20.3	11.9	-4.5	13.9
	22.0	20.9	22.3	9.5	-2.9	13.5
	24.0	23.1	26.4	7.5	0.0	43.3
	23.6	21.2	22.3	13.0	1.5	41.2
	23.9	17.6	25.7	5.9	1.4	12.3
	19.1	26.3	8.8	8.8	11.9	3.1
GPS+BDS+Galileo	34.6	33.1	34.3	16.7	-7.5	14.9
	34.5	33.3	35.1	14.3	-2.9	14.0
	36.6	35.0	39.0	12.5	1.6	44.3
	33.9	32.5	33.6	15.2	0.0	42.9
	32.4	23.7	33.5	11.8	-2.9	16.3
	21.5	30.2	18.0	3.3	19.5	8.0

不同截止高度角BDS/GPS/Galileo单历元RTK定位性能分析

Performance Assessment of BDS/GPS/Galileo Single-Epoch RTK under Different Cut-off Elevation Angles

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