Site Characterization and Multipath Maps Using Zernike Polynomials
Bibliographic record
Abstract
Receiver antenna calibration plays an important role in precise point positioning (PPP). The correct management of the phase center offset and variations (PCV) and multipath effects can drastically improve the estimation of tropospheric parameters and the stability of the position over short measurement sessions. Correction parameters, to compensate for PCV, are usually computed in laboratory on all the geodetic grade antennas, but they are not available for low-cost apparatus; multipath can be partially mitigated by a robot calibration on site but this is an expensive procedure that is rarely adopted. Multipath staking maps (MPS) using carrier phase observation residuals are a cheap and powerful tool to generate site-specific corrections, effective for reducing both near-field and far-field effects. These maps can be generated by gridding multiple residuals falling in a cell of a pre-determined size. In this work, we propose to compute a set of polynomial coefficients of a Zernike expansion from the residuals of a PPP uncombined least-squares adjustment performed by the open-source goGPS processing software; these coefficients can be later used to synthesize corrections of the observations for the next processing of the target station. In contrast with gridding techniques, this approach allows a to generate smoother corrections and allows a limited automatic extrapolation of the correction values in areas of the sky that were not covered by observations in the set of data used in the calibration phase. The results show that the technique is effective in the modelling of multipath and residual phase center variations allowing a drastic reduction of the undifferenced residuals. Zernike polynomials are a sequence of polynomials orthogonal on the unit disk, vastly used in optics but, to our knowledge, never considered for GNSS applications, their symmetric properties and the circular support area makes them an interesting object of investigation for other possible usages in GNSS processing.
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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 | 0.001 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".