Equivalence analysis of two-domain combined adjustment solutions of pseudo-range single point positioning
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摘要: 针线性观测模型观测值域联合平差解和平差值域联合平差解完全等价，但实际中联合平差的观测模型多为非线性模型，参数估计时常常需要进行线性化处理，存在线性化引起的模型误差，该误差对两域平差解的等价性影响值得探讨. 以伪距单点定位(SPP)为例，论文推导了其平差值域联合平差求解公式，分析了两域联合平差不能完全等价的原因，并用实例进行了数值对比. 研究表明：在配置相同的情况下，不同全球卫星导航系统(GNSS)组合SPP的两域平差位置解在毫米量级上数值相同，就SPP应用而言，两域平差解可认为相同. 论文内容对于一些GNSS其他应用也具有一定的参考意义.
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关键词:
- 非线性观测模型 /
- 观测值域联合平差 /
- 平差值域联合平差 /
- 全球卫星导航系统(GNSS) /
- 伪距单点定位(SPP)
Abstract: The combined adjustment solutions of the linear observation model in the observation domain and in the adjustment range are completely equivalent. However, in practice, the observation models of the combined adjustment are mostly nonlinear, which always need to be linearized in parameter estimation, resulting in linearized model error. The influence of this error on the equivalence of the two-domain adjustment solutions remains to be discussed. Thus, taking pseudo-range single point positioning (SPP) as an example, the solution formulas of the combined adjustment in the adjustment range of the observation model are deduced in this paper, on which the reason why the two-domain combined adjustment cannot be completely equivalent under the SPP model is presented and a numerical analysis is carried out with the example data. Research shows, the two-domain adjustment solution of SPP cannot be equivalent because it is assumed that the initial value of each iteration solution of a single system is the same as that of the combined adjustment of the observation range. And under the same configuration, the two-domain adjustment position solutions of different Global Navigation Satellites System (GNSS) combined SPP are the same value on the order of millimeter, that is, for the application of SPP, the two-domain adjustment solutions can be considered the same. The content of this paper also has certain reference significance for some other GNSS applications. -
表 1 GPS、BDS两域平差结果
m 参数 符号 观测值域解(G+C) G解 C解 平差值域解(G+C) 位置解 x −106941.7802 −106 941.8318 −106941.6682 −106941.7802 y 5549269.0604 5549268.4557 5549269.1410 5549269.0603 z 3139215.3791 3139214.4693 3139215.6265 3139215.379 1 精
度sdx 1.243 2 2.227 1 1.566 8 1.243 2 sdy 3.262 2 5.220 4 4.365 6 3.262 2 sdz 1.614 3 3.385 4 1.8632 1.614 2 sdxy 0.267 4 1.505 0 −0.967 7 0.267 4 sdyz 1.674 1 2.968 2 2.118 5 1.674 1 sdzx −0.647 2 −1.492 1 −0.788 6 −0.647 2 
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表 2 GPS、BDS、GLONASS两域平差结果
m 参数 符号 观测值域解(G+C+R) G解 C解 R解 平差值域解(G+C+R) 位置解 x −106 941.724 6 −106 941.831 8 −106 941.668 2 −106 942.853 8 −106 941.724 4 y 5549268.8020 5549268.4557 5549269.1410 5549260.0306 5549268.8018 z 3139215.0532 3139214.4693 3139215.6265 3139208.7432 3139215.0531 精
度sdx 1.159 8 2.227 1 1.566 8 3.638 8 1.159 8 sdy 3.116 0 5.220 4 4.365 6 12.818 2 3.115 9 sdz 1.554 6 3.385 4 1.863 2 7.227 6 1.554 6 sdxy 0.323 8 1.505 0 −0.967 7 4.033 7 0.323 8 sdyz 1.655 3 2.968 2 2.118 5 8.806 1 1.655 3 sdzx −0.540 6 −1.492 1 −0.788 6 3.064 4 −0.540 6
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表 3 GPS、BDS、GLONASS、Galileo两域平差结果
m 参数 符号 观测值域解(G+C+R+E) G解 C解 R解 E解 平差值域解(G+C+R+E) 位置解 x −106 941.732 6 −106 941.831 8 −106 941.668 2 −106 942.853 8 −106 941.108 1 −106 941.732 5 y 5549268.8676 5549268.4557 5549269.1410 5549260.0306 5549271.9139 5549268.8676 z 3139215.0770 3139214.4693 3139215.6265 3139208.7432 3139215.1082 3139215.0770 精
度sdx 1.068 9 2.227 1 1.566 8 3.638 8 6.498 8 1.068 9 sdy 3.021 9 5.220 4 4.365 6 12.818 2 25.272 3 3.021 9 sdz 1.509 5 3.385 4 1.863 2 7.227 6 7.725 1 1.509 4 sdxy 0.591 0 1.505 0 −0.967 7 4.033 7 12.106 8 0.590 9 sdyz 1.578 8 2.968 2 2.118 5 8.806 1 −5.706 5 1.578 8 sdzx −0.465 7 −1.492 1 −0.788 6 3.064 4 −4.322 1 −0.465 8
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