Systematic Bias Compensation Model of Inter-system Bias and Its Performance Analysis for BDS/GPS Fusion Positioning
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摘要: 多系统的融合定位可有效提高用户导航定位的连续性、可靠性及定位精度。针对BDS、GPS观测量间存在系统间偏差的实际情况，建立了顾及系统误差的BDS/GPS融合定位模型，即在函数模型中增加附加参数来吸收系统间偏差，构造了新的顾及先验信息的融合定位模型，分析了这种新融合模型的特点及其对定位结果的影响。利用不同品牌接收机在中国不同地域对新的融合模型进行试验，试验结果表明：BDS、GPS观测量存在系统间偏差，且不同接收机的系统间偏差量值并不一样；增加系统参数的融合定位模型能较好地吸收BDS、GPS观测量的系统间偏差的影响，改善其融合导航定位性能；在观测卫星数不足、单系统不能定位的情况下，考虑先验信息的融合定位模型仍能获得较好的定位结果。Abstract: Navigation users will significantly benefit from BDS and GPS positioning fusion in terms of availability, accuracy and reliability. However, for single point positioning, systematic biases between multi-GNSS systems cannot be eliminated completely, thus the accuracy of positioning and navigation is not always improved with the un-difference measurements of multi-GNSS systems. In this paper, an integrated BDS/GPS positioning model with unknown systematic parameters that compensates for systematic bias is proposed. Furthermore, a Bayesian estimation of fusion positioning model is specifically investigated in which the priori information of the additional parameters is taken into account. Real data collected from different areas with different types of receivers are used to verify those new algorithms. The results show that (a) receiver-dependent inter-system biases are quite evident, while the size of the system bias varies with the receiver type; (b) the precision of fusion positioning is improved significantly by introducing additional parameters into the functional model; and (c) Bayesian estimation of fusion positioning model can still obtain ideal position solution when the number of visible satellites is not enough.
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图 1 不同测站(仪器)系统参数
Figure 1. Inter-System Bias of the Different Stations or Different Type Receivers
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图 3 可见卫星有限条件下GPS/BDS融合定位结果与参考值的位置差
Figure 3. Positioning Discrepancies Using GPS/BDS Fusion Model with Limited Satellite Visibility
表 1 不同测站(仪器)系统间偏差的精度统计
Table 1 Statistics of Estimated Inter-system Bias in Different Stations with Different Type Receivers
测站 站号 仪器 天气 系统间偏差/ns 2014-08-14 2014-08-15 2014-08-16 三亚 C Trimble R9 晴 99.33±2.17 98.14±3.06 97.60±2.99 桂林 D Trimble R9 阴转雨 110.24±3.26 108.76±4.038 105.05±3.12 宜昌 E UR370-CORS 夜雨 26.13±3.17 28.96±7.09 28.96±7.09 呼和浩特 F HC N71 晴 24.39±5.04 18.85±4.69 20.47±5.41 乌兰浩特 G M300U 暴雨 25.53±3.31 21.37±4.99 22.64±5.65 
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表 2 单系统定位精度统计/m
Table 2 Statistical Results of Estimated Position by Using GPS or BDS/m
测站 GPS BDS N E U N E U 三亚 ±1.06 ±1.37 ±3.09 ±1.39 ±1.22 ±3.78 桂林 ±1.06 ±1.28 ±2.88 ±1.53 ±1.31 ±4.15 宜昌 ±1.82 ±1.78 ±4.02 ±1.59 ±1.96 ±4.57 呼和浩特 ±1.62 ±1.55 ±2.83 ±2.28 ±1.45 ±3.52 乌兰浩特 ±1.51 ±1.69 ±2.71 ±2.87 ±2.04 ±4.17 天津 ±2.56 ±2.23 ±4.22 ±2.87 ±1.44 ±6.72
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表 3 考虑系统间偏差前后的融合定位结果精度统计/m
Table 3 Statistical Results of Different Schemes/m
测站 GPS BDS N E U N E U 三亚 ±2.86 ±3.52 ±12.05 ±0.69 ±0.94 ±2.09 桂林 ±3.14 ±3.47 ±12.02 ±0.69 ±0.87 ±2.04 宜昌 ±1.60 ±2.41 ±5.20 ±1.46 ±2.36 ±4.50 呼和浩特 ±1.27 ±1.26 ±3.07 ±1.07 ±1.1 ±1.90 乌兰浩特 ±1.46 ±1.48 ±3.35 ±1.04 ±1.19 ±1.88 天津 ±48.87 ±69.90 ±151.72 ±1.44 ±1.44 ±3.83
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表 4 系统间偏差不同约束的融合定位结果精度统计/m
Table 4 Statistical Results of Different Constraints/m
测站 先验约束为0.1 ns 先验约束为3 ns N E U N E U 三亚 ±0.70 ±0.96 ±1.89 ±0.69 ±0.94 ±2.05 桂林 ±0.74 ±0.96 ±1.96 ±0.69 ±0.88 ±2.02 宜昌 ±1.43 ±2.43 ±3.87 ±1.43 ±2.37 ±4.40 呼和浩特 ±0.99 ±1.13 ±1.91 ±1.02 ±1.10 ±1.89 乌兰浩特 ±1.11 ±1.25 ±1.95 ±1.01 ±1.19 ±1.87 天津 ±1.38 ±1.37 ±3.40 ±1.54 ±1.44 ±3.39
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表 5 可见卫星有限条件下GPS/BDS融合定位结果精度统计/m
Table 5 Statistical Results of BDS/GPS Fusion Positioning with Limited Satellite Visibility/m
卫星数 N E U 均值 标准值 均方根 均值 标准值 均方根 均值 标准值 均方根 6颗 估计 9.50 ±8.24 12.57 -11.07 ±1.95 11.24 -2.01 ±6.54 6.83 强约束 8.31 ±2.99 8.82 -4.48 ±1.84 4.84 -10.09 ±6.67 12.07 松约束 4.27 ±2.83 5.12 -6.11 ±1.67 6.33 -8.16 ±6.52 10.44 5颗 估计 1.08 ±18.73 18.73 -8.46 ±4.32 9.50 -8.91 ±13.06 15.79 强约束 13.21 ±4.07 13.83 -4.10 ±1.89 4.52 -15.82 ±8.05 17.74 松约束 10.86 ±4.76 11.85 -5.10 ±1.81 5.41 14.46 -±8.23 16.63
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