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摘要:
实时动态定位(RTK)技术具有高精度和实时动态特性，在自动驾驶领域受到广泛关注，如何定量评估RTK定位完好性是否满足安全性能需求成为亟待解决的关键问题。当前针对RTK完好性的研究大多集中在用户端的算法改进与优化上，少有系统层面的风险分析与定量评估。基于此，提出一种基于风险概率分解的RTK完好性评估方法，并选取中高纬和低纬典型地区的多个观测站，使用不同类型接收机组合及不同年份的观测数据进行RTK完好性定量评估。结果显示，在中高纬电离层平静区域，定位完好性随接收机数据质量不同而存在明显差异，而在低纬度电离层活跃地区及活跃年份，电离层异常成为主要因素，完好性风险明显加大。根据评估结果，当前基于单频单星座及中等长度基线进行RTK定位时，其整体完好性风险概率位于10−4～10−2之间。所得结论与相关RTK数据处理的普遍结论一致，验证了所提方法的合理性，完好性的定量评估结果可作为后续各项监测器设计的重要依据。
Abstract:The real-time kinematic (RTK) technique has attracted extensive attention in the field of autonomous driving for its high precision and high dynamic characteristics. As a result, the quantitative assessment of RTK integrity becomes a pressing issue that needs to be resolved in order to ascertain whether it can satisfy the safety standards in this industry. However, most current RTK integrity studies focus on the improvement and optimization of user-end algorithms rather than the analysis and evaluation of overall risks from system perspectives. Therefore, in this paper, an RTK integrity evaluation method based on risk probability decomposition is proposed, offering a theoretical calculation formula of integrity risks. To verify the rationality of this conclusion, observation data from multiple observation stations with different receiver types in typical regions of mid and low latitudes are used for RTK integrity evaluation. The findings demonstrate that, in middle-latitude regions, positioning integrity changes considerably with receiver data quality; nevertheless, in low-latitude regions, ionosphere anomalies become the primary factor influencing integrity. According to the evaluation results in the paper, the integrity risk probability of RTK positioning is between 10−4 and 10−2 based on single frequency, single constellation and medium-length baseline. The results of this paper are consistent with the general conclusion of RTK data processing, which proves that the proposed method is reasonable and can evaluate the quantitative RTK integrity effectively. Furthermore, the results of the quantitative evaluation of RTK integrity can be used as an important basis for the design of an integrity monitoring scheme.
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Key words:
- integrity /
- integrity risk evaluation /
- RTK integrity /
- autonomous driving /
- receiver data quality
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图 2 ALCU/ALDS组合三维定位误差QQ图及分布直方图
Figure 2. QQ plot and histogram of 3D positioning errors for ALCU/ALDS combination
表 1 观测数据信息
Table 1. Observation data sources
数据
来源观测站
名称接收机
类型编号数据
时段美国连续运行参考站 ALCU Model 1 2016-01-01—2016-01-31 ALDS 陆态网 BJFS Model 2 2020-12-01—2020-12-31 BJSH 北京地区商用观测站 BJYZ Model 3 2020-12-01—2020-12-31/
2022-01-01—2022-01-20BJWG 
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表 2 不同接收机组合RTK定位结果
Table 2. RTK positioning results using different receiver combinations
观测站组合
（移动站/基准站）基线
长度/km模糊度
固定率/%历元
总数95%水平定
位误差/m99.999%水平
定位误差/m水平
最大粗差/m方向 95%定位
误差/m99.9%定位
误差/m99.999%定位
误差/m最大
粗差/m比值1 比值2 ALCU/ALDS 53 72 2675838 0.40 1.42 1.43 东 0.36 1.35 1.40 1.40 3.75 3.89 北 0.19 0.63 1.20 1.21 3.32 6.32 天 0.39 1.40 1.80 2.79 3.59 4.62 BJFS/BJSH 77 65 2661914 0.52 2.02 2.03 东 0.46 1.27 1.50 1.50 2.76 3.26 北 0.26 0.92 1.36 1.44 3.54 5.23 天 0.69 1.82 2.71 2.71 2.64 3.93 BJYZ/BJFS 61 77 2643782 0.43 1.53 1.53 东 0.32 1.45 1.51 1.51 4.53 4.72 北 0.18 0.73 0.85 0.93 4.06 4.72 天 0.39 1.58 2.08 2.09 4.05 5.33 BJYZ/BJWG 26 69 1596289 0.84 16.68 46.64 东 0.63 2.13 13.28 17.92 3.38 21.08 北 0.54 2.46 13.67 45.74 4.56 25.31 天 1.10 3.99 29.00 99.45 3.63 26.36
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表 3 不同类型接收机观测数据连续性指标统计
Table 3. Continuity statistics indicators of observation data for different receivers
接收机类型 观测站名称 周跳概率 数据中断概率 $ P\left({F}_{\text{c}}\right) $统计值 Model 1 ALCU 1.37×10−4 3.86×10−7 1.37×10−4 ALDS 9.65×10−5 3.86×10−7 9.69×10−5 Model 2 BJFS 4.29×10−4 2.06×10−5 4.50×10−4 BJSH 2.08×10−4 1.65×10−4 3.73×10−4 Model 3 BJYZ 2.18×10−4 5.02×10−4 7.20×10−4 BJWG 1.25×10−4 3.13×10−3 3.25×10−3
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表 4 不同类型接收机粗差概率统计结果
Table 4. Statistical results of gross error probabilities for different receivers
接收机类型 观测站名称 $ P\left({F}_{\text{g}}\right) $统计值 Model 1 ALCU 3.23×10−6 ALDS 1.33×10−6 Model 2 BJFS 7.42×10−5 BJSH 1.62×10−4 Model 3 BJYZ 1.57×10−5 BJWG 1.10×10−3
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表 5 不同接收机组合定位解风险概率项
Table 5. Probability term relevant to positioning solution risk for different receiver combinations
观测站组合（移动站/基准站） $ P\left(A\right) $ $ P\left({A}_{2}|A\right) $ $ P\left({B}_{2}|B\right) $ $ P\left(D|{A}_{2}\right) $ $ P\left(D|{B}_{2}\right) $ $ P\left(D,{F}_{0}\right) $ ALCU/ALDS 7.22×10−1 6.99×10−3 9.57×10−3 7.41×10−5 1.40×10−5 4.10×10−7 BJFS/BJSH 6.48×10−1 1.96×10−2 1.27×10−1 2.96×10−5 8.40×10−6 7.51×10−7 BJYZ/BJFS 7.67×10−1 1.62×10−2 1.10×10−1 3.05×10−5 1.47×10−5 7.56×10−7 BJYZ/BJWG 6.90×10−1 5.95×10−2 2.77×10−1 1.41×10−2 8.60×10−3 1.33×10−3
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表 6 不同接收机组合RTK整体完好性风险概率范围
Table 6. RTK integrity risk probability range for different receiver combinations
接收机组合 观测站组合（移动站/基准站） 整体完好性风险概率 Model 1/Model 1 ALCU/ALDS 3.49×10−4～4.39×10−4 Model 2/Model 2 BJFS/BJSH 1.17×10−3～1.26×10−3 Model 3/Model 2 BJYZ/BJFS 1.37×10−3～1.46×10−3 Model 3/Model 3 BJYZ/BJWG 6.53×10−3～6.62×10−3
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表 7 低纬度地区观测数据信息
Table 7. Observation data sources in the low-latitude area
观测数据来源 观测站名称 接收机类型编号 数据时段 香港CORS站 HKCL, HKQT Model 2 2015-03-01—2015-03-30
2020-03-01—2020-03-30HKMW 2020-03-01—2020-03-30
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表 8 香港CORS站RTK定位结果
Table 8. RTK positioning results for HK CORS stations
观测站组合
（移动站/基准站）时间 基线长度/
km模糊度
固定率/%历元
总数95%水平
定位误差/m99.999%水平
定位误差/m水平最大
粗差/m方向 95%定位
误差/m99.9%定
位误差/m99.999%
定位误差/m最大
粗差/m比值1 比值2 HKQT/HKCL 2015-03 31 40 2584500 0.8 17.82 17.84 东 0.59 7.58 17.25 17.29 12.85 29.24 北 0.51 7.66 11.10 11.21 15.02 21.76 天 1.13 13.35 39.15 39.21 11.81 34.65 HKQT/HKCL 2020-03 31 72 2591948 0.29 1.61 6.22 东 0.24 0.67 0.72 2.41 2.79 3.00 北 0.13 0.55 1.46 5.73 4.23 11.23 天 0.38 1.67 4.51 6.53 4.39 11.87 HKMW/HKCL 2020-03 11 91 2591981 0.05 1.01 7.26 东 0.03 0.21 0.52 2.83 7.00 17.33 北 0.04 0.20 0.93 6.68 5.00 23.25 天 0.11 0.45 1.39 7.56 4.09 12.64
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表 9 香港CORS站不同年份连续性概率及伪距粗差概率统计结果
Table 9. Statistical results of continuity probability and gross error probability of HK CORS stations across different years
时间 观测站名称 $ P({F}_{\text{c}}) $ $ P\left({F}_{\text{g}}\right) $ 2015-03 HKCL 5.02×10−3 1.79×10−5 HKQT 3.19×10−3 9.86×10−4 2020-03 HKCL 3.75×10−4 4.95×10−5 HKQT 2.19×10−4 5.09×10−4 HKMW 2.22×10−4 7.76×10−4
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表 10 香港CORS站定位解风险概率项
Table 10. Probability term relevant to positioning solution risk of HK CORS stations
观测站组合（移动站/基准站） 时间 $ P\left(A\right) $ $ P\left({A}_{2}|A\right) $ $ P\left({B}_{2}|B\right) $ $ P\left(D|{A}_{2}\right) $ $ P\left(D|{B}_{2}\right) $ $ P\left(D,{F}_{0}\right) $ HKQT/HKCL 2015-03 4.00×10−1 1.38×10−1 2.20×10−1 1.05×10−2 3.37×10−2 5.01×10−3 HKQT/HKCL 2020-03 7.19×10−1 1.09×10−3 3.44×10−2 4.75×10−4 3.91×10−4 7.47×10−7 HKMW/HKCL 2020-03 9.10×10−1 3.19×10−5 3.43×10−3 1.56×10−2 1.44×10−3 8.93×10−7
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表 11 香港CORS站不同年份RTK整体完好性风险概率
Table 11. RTK integrity risk probability of HK CORS stations in different years
时间 观测站组合
（移动站/基准站）整体完好性风险概率 2015-03 HKQT/HLCL 1.43×10−2～1.44×10−2 2020-03 HKQT/HKCL 1.26×10−3～1.35×10−3 2020-03 HKMW/HKCL 1.53×10−3～1.62×10−3
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