GNSS modulation: a unified statistical description with application to tracking bounds
Bibliographic record
Abstract
A unifying framework for all signals belonging to the Global Positioning System (GPS) and Galileo system is presented and applied to assess the potential code tracking performance of modernized satellite radionavigation signals. The framework reconciles, under a single analytical formulation, subcarrier signaling schemes, including the Binary Offset Carrier (BOC), Multiplexed Binary Offset Carrier (MBOC), and Alternative Binary Offset Carrier (ALTBOC). The new formulation allows for the derivation of closed form equations for the Auto-Correlation Function (ACF) and Power Spectral Density (PSD) containing, as special cases, the corresponding functions for GPS and Galileo signals. The analytical expressions are used to obtain new bounds on code tracking accuracy based on the Ziv-Zakai Bound (ZZB). Although the code tracking performance of GPS and Galileo signals is typically investigated using the Cramér-Rao Bound (CRB), the approach is heuristic. The CRB does not adequately describe the potential code tracking performance of weak or wideband signals and does not account for tracking biases. On the other hand, there are no such restrictions for Bayesian bounds such as the ZZB. However, because the CRB is easier to evaluate, it is advantageous to quantitatively identify when the CRB is a meaningful benchmark before having to resort to the ZZB. Therefore, thresholds on signal energy are provided to indicate necessary conditions for the use of the CRB. In agreement with information-theoretic developments, the thresholds reveal that a large signal bandwidth cannot reliably compensate for low signal energy in order to sustain code tracking performance.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".