Articles | Volume 7, issue 5
https://doi.org/10.5194/amt-7-1475-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue:
https://doi.org/10.5194/amt-7-1475-2014
© Author(s) 2014. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
27 May 2014
Research article |
| 27 May 2014
Limited constraint, robust Kalman filtering for GNSS troposphere tomography
W. Rohm
Institute of Geodesy and Geoinformatics, Wroclaw University of Environmental and Life Sciences, Wroclaw, Poland
Satellite Positioning for Atmosphere, Climate and Environment (SPACE) Research Centre, RMIT University, Melbourne, VIC, Australia
Satellite Positioning for Atmosphere, Climate and Environment (SPACE) Research Centre, RMIT University, Melbourne, VIC, Australia
J. Bosy
Institute of Geodesy and Geoinformatics, Wroclaw University of Environmental and Life Sciences, Wroclaw, Poland
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Cited
63 citations as recorded by crossref.
- Detecting Water Vapor Variability during Heavy Precipitation Events in Hong Kong Using the GPS Tomographic Technique B. Chen et al. https://doi.org/10.1175/JTECH-D-16-0115.1
- Reconstruction of Wet Refractivity Field Using an Improved Parameterized Tropospheric Tomographic Technique B. Chen et al. https://doi.org/10.3390/rs12183034
- A GPS water vapour tomography method based on a genetic algorithm F. Yang et al. https://doi.org/10.5194/amt-13-355-2020
- Assessment of tomographic window and sampling rate effects on GNSS water vapor tomography F. Yang et al. https://doi.org/10.1186/s43020-023-00096-4
- Spatiotemporal Analysis of GNSS-Derived Water Vapor Variations and Moisture Convergence Mechanism During Extreme Rainfall Events: A Hong Kong Case Study H. Qiu et al. https://doi.org/10.1109/JSTARS.2025.3605166
- Enhancing GNSS water vapor tomography using machine learning-generated virtual tropospheric delays N. Huang et al. https://doi.org/10.1016/j.asr.2026.04.084
- Statistical significance of trends in Zenith Wet Delay from re-processed GPS solutions A. Klos et al. https://doi.org/10.1007/s10291-018-0717-y
- An optimal method for GNSS water vapor tomography based on parameter adaptation F. Yang et al. https://doi.org/10.1007/s10291-025-02006-4
- Review of the state of the art and future prospects of the ground-based GNSS meteorology in Europe G. Guerova et al. https://doi.org/10.5194/amt-9-5385-2016
- Modeling the Slant Wet Delays From One GPS Receiver as a Series Expansion With Respect to Time and Space: Theory and an Example of Application for the Tahiti Island F. Zhang et al. https://doi.org/10.1109/TGRS.2020.2975458
- LDBF-IART: A hybrid framework combining an LSTM-driven background field and an improved algebraic reconstruction technique for GNSS tropospheric tomography K. Yu et al. https://doi.org/10.1016/j.atmosres.2026.109384
- Pre-analysis of GNSS tomography solution using the concept of spread of model resolution matrix Z. Adavi et al. https://doi.org/10.1007/s00190-022-01620-1
- Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication: Progress, Insights and Trends W. Song et al. https://doi.org/10.1109/JAS.2023.123588
- An Improved Tomography Approach Based on Adaptive Smoothing and Ground Meteorological Observations B. Zhang et al. https://doi.org/10.3390/rs9090886
- Cross-Comparison and Methodological Improvement in GPS Tomography H. Brenot et al. https://doi.org/10.3390/rs12010030
- Retrieval of refractivity fields from GNSS tropospheric delays: theoretical and data-based evaluation of collocation methods and comparisons with GNSS tomography E. Shehaj et al. https://doi.org/10.1007/s00190-024-01903-9
- Estimation of 3D wet refractivity by tomography, combining GNSS and NWP data: First results from assimilation of wet refractivity into NWP E. Trzcina & W. Rohm https://doi.org/10.1002/qj.3475
- B-spline function-based approach for GPS tropospheric tomography S. Haji-Aghajany et al. https://doi.org/10.1007/s10291-020-01005-x
- An overview of GNSS remote sensing K. Yu et al. https://doi.org/10.1186/1687-6180-2014-134
- Application of the GPS reflected signals in tomographic reconstruction of the wet refractivity in Italy M. Shafei & M. Hossainali https://doi.org/10.1016/j.jastp.2020.105348
- An Optimal Troposphere Tomography Technique Using the WRF Model Outputs and Topography of the Area S. Haji-Aghajany et al. https://doi.org/10.3390/rs12091442
- TOMOREF Operator for Assimilation of GNSS Tomography Wet Refractivity Fields in WRF DA System E. Trzcina et al. https://doi.org/10.1029/2020JD032451
- Assimilation of GNSS tomography products into the Weather Research and Forecasting model using radio occultation data assimilation operator N. Hanna et al. https://doi.org/10.5194/amt-12-4829-2019
- Development of an adaptive 4-D water vapour density model for the vertical constraints in GNSS tropospheric tomography M. Zhang et al. https://doi.org/10.1007/s10291-024-01700-z
- Tomographic Reconstruction of Water Vapor Density Fields From the Integration of GNSS Observations and Fengyun-4A Products B. Chen et al. https://doi.org/10.1109/TGRS.2023.3239392
- A novel, optimized approach of voxel division for water vapor tomography Y. Yao & Q. Zhao https://doi.org/10.1007/s00703-016-0450-4
- Application of integrated GNSS tomography in observation study over the area of southern Poland A. Cegla et al. https://doi.org/10.1016/j.asr.2024.07.059
- Detecting Signatures of Giant Hail Events With Integrated GNSS Tomography: A Case Study Over Southern Poland A. Cegla et al. https://doi.org/10.1109/TGRS.2026.3659018
- LEO satellites simulation for GNSS tomography S. Makuch & W. Rohm https://doi.org/10.1016/j.asr.2025.11.008
- Adaptive Voxel-Based Model for the Dynamic Determination of Tomographic Region N. Ding et al. https://doi.org/10.3390/rs15020492
- Real-Time Precise Point Positioning Using Tomographic Wet Refractivity Fields W. Yu et al. https://doi.org/10.3390/rs10060928
- INTOMO operator for GNSS multi-source tomography based on 3D ray tracing technique A. Cegla et al. https://doi.org/10.1007/s00190-024-01915-5
- An improved pixel-based water vapor tomography model Y. Yao et al. https://doi.org/10.5194/angeo-37-89-2019
- An Investigation of Near Real-Time Water Vapor Tomography Modeling Using Multi-Source Data L. Tong et al. https://doi.org/10.3390/atmos13050752
- A troposphere tomography method considering the weighting of input information Q. Zhao et al. https://doi.org/10.5194/angeo-35-1327-2017
- Zenith total delay short-term statistical forecasts for GNSS Precise Point Positioning K. Wilgan https://doi.org/10.13168/AGG.2015.0035
- Enhanced Troposphere Tomography: Integration of GNSS and Remote Sensing Data With Optimal Vertical Constraints S. Izanlou et al. https://doi.org/10.1109/JSTARS.2024.3354884
- GNSS water vapor tomography based on Kalman filter with optimized noise covariance F. Yang et al. https://doi.org/10.1007/s10291-023-01517-2
- A virtual-signal method for enhancing the efficacy of GNSS tropospheric tomography using artificial neural network technique M. Zhang et al. https://doi.org/10.1007/s10291-025-01935-4
- Retrieving the 3-D Tropospheric Wet Refractivity Field From a Standalone Ground-Based GNSS Station With A Priori Information: Theory and Simulation X. Li et al. https://doi.org/10.1109/TGRS.2024.3412689
- Assessing the performance of troposphere tomographic modeling using multi-source water vapor data during Hong Kong's rainy season from May to October 2013 B. Chen & Z. Liu https://doi.org/10.5194/amt-9-5249-2016
- A novel CNN-based method using GNSS tomography and WRF data for regional rainfall prediction L. Li et al. https://doi.org/10.1016/j.asr.2025.12.067
- An optimal tropospheric tomography approach with the support of an auxiliary area Q. Zhao et al. https://doi.org/10.5194/angeo-36-1037-2018
- Approach to leveraging real-time GNSS tomography usage A. Sá et al. https://doi.org/10.1007/s00190-020-01464-7
- Use of Tropospheric Delay in GNSS-Based Climate Monitoring—A Review A. Maciejewska https://doi.org/10.3390/rs17091501
- A New Method of GPS Water Vapor Tomography for Maximizing the Use of Signal Rays F. Yang et al. https://doi.org/10.3390/app9071446
- A New Approach of the Global Navigation Satellite System Tomography for Any Size of GNSS Network Y. Wang et al. https://doi.org/10.3390/rs12040617
- Wide-Area Retrieval of Water Vapor Field Using an Improved Node Parameterization Tomography B. Chen et al. https://doi.org/10.1109/LGRS.2023.3293824
- Enhancing InSAR accuracy: Unveiling more accurate displacement fields through 3-D troposphere tomography S. Maddahi et al. https://doi.org/10.1016/j.jastp.2024.106207
- A new approach for GNSS tomography from a few GNSS stations N. Ding et al. https://doi.org/10.5194/amt-11-3511-2018
- High-resolution GNSS troposphere tomography through explainable deep learning-based downscaling framework S. Haji-Aghajany et al. https://doi.org/10.1186/s43020-025-00177-6
- Optimal Placement of Positioning Service for Multi-Robot System using Relative Angle Measurement K. Lin et al. https://doi.org/10.1016/j.ifacol.2025.11.278
- A New GNSS-Derived Water Vapor Tomography Method Based on Optimized Voxel for Large GNSS Network Y. Yao et al. https://doi.org/10.3390/rs12142306
- TomoNet: a deep learning–based GNSS tomography approach for tropospheric monitoring A. Cegla & B. Soja https://doi.org/10.1016/j.asr.2026.09.045
- Observing geometry effects on a Global Navigation Satellite System (GNSS)-based water vapor tomography solved by least squares and by compressive sensing M. Heublein et al. https://doi.org/10.5194/angeo-38-179-2020
- Capturing the Signature of Severe Weather Events in Australia Using GPS Measurements K. Zhang et al. https://doi.org/10.1109/JSTARS.2015.2406313
- New parameterized model for GPS water vapor tomography N. Ding et al. https://doi.org/10.5194/angeo-35-311-2017
- The effect of function-based and voxel-based tropospheric tomography techniques on the GNSS positioning accuracy S. Haji-Aghajany et al. https://doi.org/10.1007/s00190-021-01528-2
- GNSS ground-based tomography: state-of-the-art and technological challenges S. Saxena & R. Dwivedi https://doi.org/10.1080/01431161.2023.2247526
- Simultaneous troposphere estimation with precise point positioning T. Hadaś et al. https://doi.org/10.1007/s00190-026-02088-z
- Analyzing Different Parameterization Methods in GNSS Tomography Using the COST Benchmark Dataset Z. Adavi et al. https://doi.org/10.1109/JSTARS.2020.3027909
- Key Technologies for GNSS Water Vapor Retrieval and Their Applications in Marine Environmental Monitoring P. Wang et al. https://doi.org/10.1109/JSTARS.2026.3717583
- Node-Based Optimization of GNSS Tomography with a Minimum Bounding Box Algorithm N. Ding et al. https://doi.org/10.3390/rs12172744
63 citations as recorded by crossref.
- Detecting Water Vapor Variability during Heavy Precipitation Events in Hong Kong Using the GPS Tomographic Technique B. Chen et al. https://doi.org/10.1175/JTECH-D-16-0115.1
- Reconstruction of Wet Refractivity Field Using an Improved Parameterized Tropospheric Tomographic Technique B. Chen et al. https://doi.org/10.3390/rs12183034
- A GPS water vapour tomography method based on a genetic algorithm F. Yang et al. https://doi.org/10.5194/amt-13-355-2020
- Assessment of tomographic window and sampling rate effects on GNSS water vapor tomography F. Yang et al. https://doi.org/10.1186/s43020-023-00096-4
- Spatiotemporal Analysis of GNSS-Derived Water Vapor Variations and Moisture Convergence Mechanism During Extreme Rainfall Events: A Hong Kong Case Study H. Qiu et al. https://doi.org/10.1109/JSTARS.2025.3605166
- Enhancing GNSS water vapor tomography using machine learning-generated virtual tropospheric delays N. Huang et al. https://doi.org/10.1016/j.asr.2026.04.084
- Statistical significance of trends in Zenith Wet Delay from re-processed GPS solutions A. Klos et al. https://doi.org/10.1007/s10291-018-0717-y
- An optimal method for GNSS water vapor tomography based on parameter adaptation F. Yang et al. https://doi.org/10.1007/s10291-025-02006-4
- Review of the state of the art and future prospects of the ground-based GNSS meteorology in Europe G. Guerova et al. https://doi.org/10.5194/amt-9-5385-2016
- Modeling the Slant Wet Delays From One GPS Receiver as a Series Expansion With Respect to Time and Space: Theory and an Example of Application for the Tahiti Island F. Zhang et al. https://doi.org/10.1109/TGRS.2020.2975458
- LDBF-IART: A hybrid framework combining an LSTM-driven background field and an improved algebraic reconstruction technique for GNSS tropospheric tomography K. Yu et al. https://doi.org/10.1016/j.atmosres.2026.109384
- Pre-analysis of GNSS tomography solution using the concept of spread of model resolution matrix Z. Adavi et al. https://doi.org/10.1007/s00190-022-01620-1
- Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication: Progress, Insights and Trends W. Song et al. https://doi.org/10.1109/JAS.2023.123588
- An Improved Tomography Approach Based on Adaptive Smoothing and Ground Meteorological Observations B. Zhang et al. https://doi.org/10.3390/rs9090886
- Cross-Comparison and Methodological Improvement in GPS Tomography H. Brenot et al. https://doi.org/10.3390/rs12010030
- Retrieval of refractivity fields from GNSS tropospheric delays: theoretical and data-based evaluation of collocation methods and comparisons with GNSS tomography E. Shehaj et al. https://doi.org/10.1007/s00190-024-01903-9
- Estimation of 3D wet refractivity by tomography, combining GNSS and NWP data: First results from assimilation of wet refractivity into NWP E. Trzcina & W. Rohm https://doi.org/10.1002/qj.3475
- B-spline function-based approach for GPS tropospheric tomography S. Haji-Aghajany et al. https://doi.org/10.1007/s10291-020-01005-x
- An overview of GNSS remote sensing K. Yu et al. https://doi.org/10.1186/1687-6180-2014-134
- Application of the GPS reflected signals in tomographic reconstruction of the wet refractivity in Italy M. Shafei & M. Hossainali https://doi.org/10.1016/j.jastp.2020.105348
- An Optimal Troposphere Tomography Technique Using the WRF Model Outputs and Topography of the Area S. Haji-Aghajany et al. https://doi.org/10.3390/rs12091442
- TOMOREF Operator for Assimilation of GNSS Tomography Wet Refractivity Fields in WRF DA System E. Trzcina et al. https://doi.org/10.1029/2020JD032451
- Assimilation of GNSS tomography products into the Weather Research and Forecasting model using radio occultation data assimilation operator N. Hanna et al. https://doi.org/10.5194/amt-12-4829-2019
- Development of an adaptive 4-D water vapour density model for the vertical constraints in GNSS tropospheric tomography M. Zhang et al. https://doi.org/10.1007/s10291-024-01700-z
- Tomographic Reconstruction of Water Vapor Density Fields From the Integration of GNSS Observations and Fengyun-4A Products B. Chen et al. https://doi.org/10.1109/TGRS.2023.3239392
- A novel, optimized approach of voxel division for water vapor tomography Y. Yao & Q. Zhao https://doi.org/10.1007/s00703-016-0450-4
- Application of integrated GNSS tomography in observation study over the area of southern Poland A. Cegla et al. https://doi.org/10.1016/j.asr.2024.07.059
- Detecting Signatures of Giant Hail Events With Integrated GNSS Tomography: A Case Study Over Southern Poland A. Cegla et al. https://doi.org/10.1109/TGRS.2026.3659018
- LEO satellites simulation for GNSS tomography S. Makuch & W. Rohm https://doi.org/10.1016/j.asr.2025.11.008
- Adaptive Voxel-Based Model for the Dynamic Determination of Tomographic Region N. Ding et al. https://doi.org/10.3390/rs15020492
- Real-Time Precise Point Positioning Using Tomographic Wet Refractivity Fields W. Yu et al. https://doi.org/10.3390/rs10060928
- INTOMO operator for GNSS multi-source tomography based on 3D ray tracing technique A. Cegla et al. https://doi.org/10.1007/s00190-024-01915-5
- An improved pixel-based water vapor tomography model Y. Yao et al. https://doi.org/10.5194/angeo-37-89-2019
- An Investigation of Near Real-Time Water Vapor Tomography Modeling Using Multi-Source Data L. Tong et al. https://doi.org/10.3390/atmos13050752
- A troposphere tomography method considering the weighting of input information Q. Zhao et al. https://doi.org/10.5194/angeo-35-1327-2017
- Zenith total delay short-term statistical forecasts for GNSS Precise Point Positioning K. Wilgan https://doi.org/10.13168/AGG.2015.0035
- Enhanced Troposphere Tomography: Integration of GNSS and Remote Sensing Data With Optimal Vertical Constraints S. Izanlou et al. https://doi.org/10.1109/JSTARS.2024.3354884
- GNSS water vapor tomography based on Kalman filter with optimized noise covariance F. Yang et al. https://doi.org/10.1007/s10291-023-01517-2
- A virtual-signal method for enhancing the efficacy of GNSS tropospheric tomography using artificial neural network technique M. Zhang et al. https://doi.org/10.1007/s10291-025-01935-4
- Retrieving the 3-D Tropospheric Wet Refractivity Field From a Standalone Ground-Based GNSS Station With A Priori Information: Theory and Simulation X. Li et al. https://doi.org/10.1109/TGRS.2024.3412689
- Assessing the performance of troposphere tomographic modeling using multi-source water vapor data during Hong Kong's rainy season from May to October 2013 B. Chen & Z. Liu https://doi.org/10.5194/amt-9-5249-2016
- A novel CNN-based method using GNSS tomography and WRF data for regional rainfall prediction L. Li et al. https://doi.org/10.1016/j.asr.2025.12.067
- An optimal tropospheric tomography approach with the support of an auxiliary area Q. Zhao et al. https://doi.org/10.5194/angeo-36-1037-2018
- Approach to leveraging real-time GNSS tomography usage A. Sá et al. https://doi.org/10.1007/s00190-020-01464-7
- Use of Tropospheric Delay in GNSS-Based Climate Monitoring—A Review A. Maciejewska https://doi.org/10.3390/rs17091501
- A New Method of GPS Water Vapor Tomography for Maximizing the Use of Signal Rays F. Yang et al. https://doi.org/10.3390/app9071446
- A New Approach of the Global Navigation Satellite System Tomography for Any Size of GNSS Network Y. Wang et al. https://doi.org/10.3390/rs12040617
- Wide-Area Retrieval of Water Vapor Field Using an Improved Node Parameterization Tomography B. Chen et al. https://doi.org/10.1109/LGRS.2023.3293824
- Enhancing InSAR accuracy: Unveiling more accurate displacement fields through 3-D troposphere tomography S. Maddahi et al. https://doi.org/10.1016/j.jastp.2024.106207
- A new approach for GNSS tomography from a few GNSS stations N. Ding et al. https://doi.org/10.5194/amt-11-3511-2018
- High-resolution GNSS troposphere tomography through explainable deep learning-based downscaling framework S. Haji-Aghajany et al. https://doi.org/10.1186/s43020-025-00177-6
- Optimal Placement of Positioning Service for Multi-Robot System using Relative Angle Measurement K. Lin et al. https://doi.org/10.1016/j.ifacol.2025.11.278
- A New GNSS-Derived Water Vapor Tomography Method Based on Optimized Voxel for Large GNSS Network Y. Yao et al. https://doi.org/10.3390/rs12142306
- TomoNet: a deep learning–based GNSS tomography approach for tropospheric monitoring A. Cegla & B. Soja https://doi.org/10.1016/j.asr.2026.09.045
- Observing geometry effects on a Global Navigation Satellite System (GNSS)-based water vapor tomography solved by least squares and by compressive sensing M. Heublein et al. https://doi.org/10.5194/angeo-38-179-2020
- Capturing the Signature of Severe Weather Events in Australia Using GPS Measurements K. Zhang et al. https://doi.org/10.1109/JSTARS.2015.2406313
- New parameterized model for GPS water vapor tomography N. Ding et al. https://doi.org/10.5194/angeo-35-311-2017
- The effect of function-based and voxel-based tropospheric tomography techniques on the GNSS positioning accuracy S. Haji-Aghajany et al. https://doi.org/10.1007/s00190-021-01528-2
- GNSS ground-based tomography: state-of-the-art and technological challenges S. Saxena & R. Dwivedi https://doi.org/10.1080/01431161.2023.2247526
- Simultaneous troposphere estimation with precise point positioning T. Hadaś et al. https://doi.org/10.1007/s00190-026-02088-z
- Analyzing Different Parameterization Methods in GNSS Tomography Using the COST Benchmark Dataset Z. Adavi et al. https://doi.org/10.1109/JSTARS.2020.3027909
- Key Technologies for GNSS Water Vapor Retrieval and Their Applications in Marine Environmental Monitoring P. Wang et al. https://doi.org/10.1109/JSTARS.2026.3717583
- Node-Based Optimization of GNSS Tomography with a Minimum Bounding Box Algorithm N. Ding et al. https://doi.org/10.3390/rs12172744
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