Development of a 3-D Tomography Approach to Provide Tropospheric Corrections for Use in Network RTK Positioning
Bibliographic record
Abstract
Global Positioning System (GPS) ranging errors attributed to atmospheric effects must be mitigated for precise positioning applications. Atmospheric models with varying degrees of complexity and input parameters are one method of estimating tropospheric range delay. Range delay models based on precise surface pressure observations can effectively remove the hydrostatic component of this delay to within a few millimeters. A second approach uses meteorological parameters from numerical weather predictions to derive tropospheric corrections. Finally, tomography approaches have been developed to estimate atmospheric delay above GPS networks. In this study, a double-difference tomography technique is used to estimate the 3-D wet refractivity fields over a regional GPS network. The model employs double difference (DD) slant wet delay (SWD) observables derived using MultiRef™, an RTK GPS precise positioning software package. The solution of the wetrefractivity values is non-unique so constraints must be added to strengthen the solution. In this paper numerical weather predictions (NWP) from the Canadian Meteorological Centre’s (CMC) regional Global Environmental Model (GEM) are incorporated into the tomography model as constraints in the least-squares adjustment. The University of Calgary has deployed a network of dual-frequency GPS reference stations across Southern Alberta. Data from July 13 and 14, 2004 are processed to derive DD SWD observables to test the tomography approach. The days are selected as case studies representing calm and stormy weather conditions respectively. The tomography model is assessed with and without NWP input. Ionosphere-free (IF) double difference misclosures are used to assess the self consistency of the tomography model performance. DD SWD estimates are re-created by integrating through the estimated model wet refractivity fields. The misclosures are calculated after 1) applying the MultiRef™ default atmospheric delay model (the Modified Hopfield model); 2) the tomography model fields derived with and without NWP constraints; and 3) using the wet refractivity derived from the NWP fields for voxel constraint values. The performance of the tomography model without using the NWP constraints is found to perform marginally better than when the constraints are applied for both the stormy and calm weather conditions. However, the profiles may not result in a physically realistic solution. Incorporating the GPS observation into the tomography model reduces misclosures by 26 – 29 % during the storm event compared with the Modified Hopfield model.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".