Conventional Real-Time Kinematic(RTK)and Network RTK(NRTK)functional models for medium-to-long baselines typically parameterize Double-Differenced(DD)slant ionospheric delays for individual satellite pairs to mitigate...Conventional Real-Time Kinematic(RTK)and Network RTK(NRTK)functional models for medium-to-long baselines typically parameterize Double-Differenced(DD)slant ionospheric delays for individual satellite pairs to mitigate iono spheric effects.When multi-constellation observations are integrated,this strategy introduces severe over-parameter ization,which weakens the model strength and degrades ambiguity resolution performance.To address this problem,we propose an ionospheric gradient modeling method that replaces the conventional DD slant-ionosphere param eterization in RTK and NRTK functional models while maintaining effective ionospheric mitigation.Specifically,all DD slant ionospheric parameters in the RTK/NRTK functional models are replaced by an ionospheric gradient model con structed from ionospheric pierce points.The gradient model coefficients are estimated simultaneously with ambigui ties,tropospheric delays,and position parameters.Experimental results show that the ionospheric gradient model can effectively represent DD ionospheric delays for all tracked satellites.The modeling residuals exhibit a clear elevation dependent behavior,with larger residuals at low satellite elevations and an average standard deviation of less than 4 cm.For NRTK positioning,the float ambiguity precision and ambiguity-fixing success rate are increased by 12.1%and 2.6%,respectively,when the ionospheric gradient model is applied.Compared with the conventional Iono sphere-Weighted(IW)model,the proposed functional model reduces the average RTK convergence time from 10.4 to 7.4 s.Meanwhile,the positioning accuracy is improved from 2.8,3.2,and 4.3 cm to 2.4,2.8,and 3.9 cm in the north,east,and up components,respectively,and the ambiguity-fixing success rate increases from 96.2 to 98.6%.展开更多
With the rapid development of multi-frequency Global Navigation Satellite Systems(GNSS),Geometry-Free(GF)Three-Carrier Ambiguity Resolution(TCAR)has become an increasingly viable solution for high-precision positionin...With the rapid development of multi-frequency Global Navigation Satellite Systems(GNSS),Geometry-Free(GF)Three-Carrier Ambiguity Resolution(TCAR)has become an increasingly viable solution for high-precision positioning.The GF TCAR model enables satellite-by-satellite ambiguity resolution,offering robustness independent of satellite geometry.However,its performance in network Real-Time Kinematic(RTK)applications is highly sensitive to residual atmospheric errors.To accurately quantify these impacts and optimize ambiguity resolution strategies,this study proposes an enhanced analysis framework and presents a comprehensive sensitivity analysis of the GF TCAR model under different atmospheric and noise conditions.Theoretical derivations and simulations confirm that non-dis persive errors,such as tropospheric delays,are effectively mitigated within the GF framework.In addition,the study establishes quantitative accuracy thresholds for ionospheric modeling across constellations.While Extra-Wide-Lane(EWL)and Wide-Lane(WL)ambiguities remain robust against ionospheric errors of up to dozens of Total Electron Content Units(TECU)and several TECU,respectively,Narrow-Lane(NL)ambiguity resolution is the most challenging step,requiring residual errors to remain about within±0.2 TECU.Furthermore,the analysis shows that EWL ambi guity resolution is relatively insensitive to measurement noise,whereas WL ambiguity resolution is predominantly noise-limited,especially as the EWL wavelength increases.These findings provide valuable error-tolerance references for the quality control of ionospheric corrections in network RTK services.展开更多
实时动态差分(real time kinematic,RTK)定位技术因其成本低、实时性强等优点,已成为实时位移监测领域的重要技术手段.然而,随着跨海大桥、海上平台等远距离基础设施对高精度实时位移监测需求不断增长,常规RTK技术在长距离作业中,因测...实时动态差分(real time kinematic,RTK)定位技术因其成本低、实时性强等优点,已成为实时位移监测领域的重要技术手段.然而,随着跨海大桥、海上平台等远距离基础设施对高精度实时位移监测需求不断增长,常规RTK技术在长距离作业中,因测站间距离增加导致大气误差(对流层和电离层延迟)的空间相关性降低,差分后残余大气误差难以充分消除,严重影响模糊度的收敛从而影响定位精度.针对这一问题,提出一种大气误差附加约束的长距离RTK定位方法:1)将经先验模型改正并进行差分后残余的对流层和电离层延迟参数化并纳入估计模型,针对残余误差分别建立先验约束:对流层残差基于台站间高差和测站距离构建先验方差,更全面地刻画长距离条件下对流层残差的不确定性;电离层残差结合纬度相关性构建先验方差,实现对定位参数解算过程的稳健约束;2)考虑大气误差的时变特性,采用随机游走过程对对流层和电离层参数进行动态估计,电离层活动变化大,随机游走噪声建模考虑基线长度和卫星高度角变化,使动态估计更符合实际情况.基于国际GNSS服务组织(International GNSS Service,IGS)测站和海上平台实测数据开展试验,结果表明:相较于常规RTK方法,所提方法在不同的观测环境下均有效缩短了收敛时间和模糊度首次固定时间,显著提升了模糊度固定率,同时在水平和垂向定位精度上取得明显改善.展开更多
基金The National Natural Science Funds of China(42225401,42504031 and 42430109)Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China(JYB2025XDXM111)+2 种基金the Yangtze River Delta Technology Innovation Community Joint Research Program(2025CSJZN01900)the China Postdoctoral Science Foundation under Grant Number 2025M780216the industrial Collaborative Innovation Project(Technology)of Shanghai Municipality(XTCX-KJ-2024-03).
摘要Conventional Real-Time Kinematic(RTK)and Network RTK(NRTK)functional models for medium-to-long baselines typically parameterize Double-Differenced(DD)slant ionospheric delays for individual satellite pairs to mitigate iono spheric effects.When multi-constellation observations are integrated,this strategy introduces severe over-parameter ization,which weakens the model strength and degrades ambiguity resolution performance.To address this problem,we propose an ionospheric gradient modeling method that replaces the conventional DD slant-ionosphere param eterization in RTK and NRTK functional models while maintaining effective ionospheric mitigation.Specifically,all DD slant ionospheric parameters in the RTK/NRTK functional models are replaced by an ionospheric gradient model con structed from ionospheric pierce points.The gradient model coefficients are estimated simultaneously with ambigui ties,tropospheric delays,and position parameters.Experimental results show that the ionospheric gradient model can effectively represent DD ionospheric delays for all tracked satellites.The modeling residuals exhibit a clear elevation dependent behavior,with larger residuals at low satellite elevations and an average standard deviation of less than 4 cm.For NRTK positioning,the float ambiguity precision and ambiguity-fixing success rate are increased by 12.1%and 2.6%,respectively,when the ionospheric gradient model is applied.Compared with the conventional Iono sphere-Weighted(IW)model,the proposed functional model reduces the average RTK convergence time from 10.4 to 7.4 s.Meanwhile,the positioning accuracy is improved from 2.8,3.2,and 4.3 cm to 2.4,2.8,and 3.9 cm in the north,east,and up components,respectively,and the ambiguity-fixing success rate increases from 96.2 to 98.6%.
基金National Natural Science Foundation of China(Grant No.42561160140,42404052)GHP/033/22SZ Guangdong-Hong Kong Technology Cooperation Funding Scheme(Shenzhen Science and Technology Program under Grant SGDX20230116092503007)+2 种基金the SpecialProject for Universities Directly Under the Ministry to Serve Jiangsu’s High-Quality Developmentthe Hong Kong General Research Fund(Grant No.15229622)the University Grants Committee of Hong Kong under the General Research Fund 1060(GRF)(Grant No.15212525).
摘要With the rapid development of multi-frequency Global Navigation Satellite Systems(GNSS),Geometry-Free(GF)Three-Carrier Ambiguity Resolution(TCAR)has become an increasingly viable solution for high-precision positioning.The GF TCAR model enables satellite-by-satellite ambiguity resolution,offering robustness independent of satellite geometry.However,its performance in network Real-Time Kinematic(RTK)applications is highly sensitive to residual atmospheric errors.To accurately quantify these impacts and optimize ambiguity resolution strategies,this study proposes an enhanced analysis framework and presents a comprehensive sensitivity analysis of the GF TCAR model under different atmospheric and noise conditions.Theoretical derivations and simulations confirm that non-dis persive errors,such as tropospheric delays,are effectively mitigated within the GF framework.In addition,the study establishes quantitative accuracy thresholds for ionospheric modeling across constellations.While Extra-Wide-Lane(EWL)and Wide-Lane(WL)ambiguities remain robust against ionospheric errors of up to dozens of Total Electron Content Units(TECU)and several TECU,respectively,Narrow-Lane(NL)ambiguity resolution is the most challenging step,requiring residual errors to remain about within±0.2 TECU.Furthermore,the analysis shows that EWL ambi guity resolution is relatively insensitive to measurement noise,whereas WL ambiguity resolution is predominantly noise-limited,especially as the EWL wavelength increases.These findings provide valuable error-tolerance references for the quality control of ionospheric corrections in network RTK services.
摘要实时动态差分(real time kinematic,RTK)定位技术因其成本低、实时性强等优点,已成为实时位移监测领域的重要技术手段.然而,随着跨海大桥、海上平台等远距离基础设施对高精度实时位移监测需求不断增长,常规RTK技术在长距离作业中,因测站间距离增加导致大气误差(对流层和电离层延迟)的空间相关性降低,差分后残余大气误差难以充分消除,严重影响模糊度的收敛从而影响定位精度.针对这一问题,提出一种大气误差附加约束的长距离RTK定位方法:1)将经先验模型改正并进行差分后残余的对流层和电离层延迟参数化并纳入估计模型,针对残余误差分别建立先验约束:对流层残差基于台站间高差和测站距离构建先验方差,更全面地刻画长距离条件下对流层残差的不确定性;电离层残差结合纬度相关性构建先验方差,实现对定位参数解算过程的稳健约束;2)考虑大气误差的时变特性,采用随机游走过程对对流层和电离层参数进行动态估计,电离层活动变化大,随机游走噪声建模考虑基线长度和卫星高度角变化,使动态估计更符合实际情况.基于国际GNSS服务组织(International GNSS Service,IGS)测站和海上平台实测数据开展试验,结果表明:相较于常规RTK方法,所提方法在不同的观测环境下均有效缩短了收敛时间和模糊度首次固定时间,显著提升了模糊度固定率,同时在水平和垂向定位精度上取得明显改善.