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摘要: 随着全球卫星导航系统（global navigation satellite system，GNSS）进入多系统时代，空中导航卫星的可见卫星数不断增加，中国北斗卫星导航系统（BeiDou navigation satellite system，BDS）已开始面向用户提供三频导航信号，这都有利于改善单历元实时动态定位（real-time kinematic，RTK）的精度和可靠性。中长基线单历元RTK通常采用电离层无关组合算法，但是该方法将观测噪声进行了放大，模糊度固定成功率随着基线长度的增加而明显降低。提出一种BDS/GPS（global positioning system）中长基线单历元多频RTK定位算法，先以较高成功率快速固定BDS的两个超宽巷模糊度，继而通过简单变换得到BDS宽巷模糊度，然后将其辅助提高GPS宽巷模糊度固定成功率，最后采用将电离层延迟误差参数化的策略以提高BDS/GPS窄巷模糊度固定成功率。结合实测数据进行验证分析，结果表明本文算法是可行的。Abstract: The number of visible satellites is increasing in the age of multiple global navigation systems. The global navigation satellite system (GNSS), and Chinese BeiDou satellite navigation system (BDS) offer three frequencies signals to users, the ambiguity resolution is improved the higher accuracy and reliability of GNSS-RTK positioning.In general, ionosphere-free combinations are used in single-epoch RTK(Real-Time Kinematic)for medium-baseline. But this algorithm amplifies the measurement noise and the ambiguity resolution performance deteriorates as the length of baseline increases. In this paper, a single-epoch and multi-frequency RTK positioning algorithm for medium-baseline is presented, based on the BDS/GPS dual system combination. Two BDS extra-wide lane ambiguities were fixed at a high success rate and the BDS wide-lane ambiguity was sloved through a simple transformation. Ambiguity-fixed WL was used to improve the success rate of GPS WL ambiguity fixing, and parameterization strategy of ionospheric delay error was used to improve the success rate of BDS/GPS NL ambiguity fixing. This algorithm was validated with real-time data. The results show that the proposed algorithm ia feasible for ambiguity resolution and positioning accuracy.
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表 1 不同载波线性组合观测量的特性及总噪声水平(σΔφ=1 cm)
Table 1 Characteristics of Different Combinations and Total Noise Level Under Two Different Error Budgets(σΔφ=1 cm)
(i, j, k) λ/m β(i, j, k) μ(i, j, k) ΔδI1=10 cm
Δδtrop=5 cm
Δδorb=1 cmΔδI1=100 cm
Δδtrop=15 cm
Δδorb=8 cm(0，-1，1) 4.884 2 -1.591 5 28.528 7 0.067 7 0.332 9 (1，4，-5) 6.370 7 0.652 1 172.623 5 0.271 3 0.290 9 (1，-1，0) 0.847 0 -1.293 2 5.575 2 0.176 8 1.540 4 (1，0，-1) 1.024 7 -1.230 6 6.875 1 0.146 3 1.214 3 
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表 2 采用的数据集
Table 2 General Situation of Data Set
数据集 基线长度 观测时长/s GPS平均可见卫星数 BDS平均可见卫星数 A 8 m 9 644 8 9 B 8 km 7 200 6 8 C 17 km 9 726 8 10 D 37 km 7 200 8 10 E 44 km 7 200 8 9 F 50 km 7 200 7 9
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表 3 超宽巷/宽巷模糊度解算效果
Table 3 AR Performance of EWL and WL
数据集 模糊度固定成功率/% ratio≥2.0 ratio≥3.0 ratio≥5.0 EWL
(MCAR)WL
(MCAR)WL
(GPS)EWL
(MCAR)WL
(MCAR)WL
(GPS)EWL
(MCAR)WL
(MCAR)WL
(GPS)A 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 B 100.0 100.0 98.0 100.0 100.0 92.1 100.0 100.0 65.3 C 100.0 99.9 91.2 100.0 94.2 78.6 100.0 69.1 54.5 D 100.0 99.8 73.1 99.9 94.0 61.6 99.5 68.8 37.1 E 99.9 99.6 65.3 99.6 93.7 55.3 99.3 68.6 32.8 F 99.7 99.5 59.9 99.5 93.3 42.2 99.2 68.2 24.9
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表 4 窄巷模糊度解算效果
Table 4 AR Performance of NL
数据集 模糊度固定成功率/% ratio≥2.0 ratio≥3.0 ratio≥5.0 消电离层模型 MCAR 消电离层模型 MCAR 消电离层模型 MCAR A 100.0 100.0 100.0 100.0 100.0 100.0 B 100.0 100.0 100.0 100.0 96.6 94.9 C 99.7 99.9 90.7 91.6 40.0 47.0 D 48.2 96.2 16.3 88.4 0.0 38.7 E 35.7 94.5 11.3 82.6 0.0 34.4 F 30.9 93.4 8.7 78.2 0.0 29.5
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表 5 ratio阈值为2时模糊度解算效果
Table 5 AR Performance with Threshold is 2
数据集 A B C D E F 固定成功率/% 100 100 99.9 96.2 94.5 93.4 未固定但解算正确历元 0 0 10 64 96 135 错误拒绝率/% 0 0 0.01 0.89 1.33 1.87
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表 6 定位精度统计结果(均方根)/cm
Table 6 Statistical Results of RTK Positioning Error(RMS)/cm
数据集 E N U A 0.15 0.17 0.43 B 0.48 0.37 0.56 C 0.51 0.43 1.05 D 0.59 0.61 1.65 E 0.60 0.66 1.74 F 0.63 0.74 1.90
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