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

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

Abstract

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

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.

Figures/Tables 13

Table 1

Table 2

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Table 3

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Table 4

Statistical results for baseline APM8-APM9"

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

Table 4

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Fig.8

Table 5

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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