Improved Between-Satellite Single-Difference Precise Point Positioning Model Using Triple GNSS Constellations: GPS, Galileo, and BeiDou
Bibliographic record
Abstract
This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations of three different GNSS constellations, namely GPS, Galileo, and BeiDou. Our model is based on between-satellite single-difference (BSSD) linear combination, which cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. The reference satellite can be selected from any satellite system GPS, Galileo, and BeiDou when forming BSSD linear combinations. Natural Resources Canada’s GPS Pace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets at four IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the IGS-MGEX network are used to correct both of the GPS and Galileo measurements. It is shown that using the BSSD linear combinations improves the precision of the estimated parameters by about 25% compared with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for both BSSD scenarios, which represent about 50% improvement in comparison with the GPS-only PPP solution.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".