An Orthogonal Transformation Algorithm for GPS Positioning
Bibliographic record
Abstract
The Global Positioning System (GPS) is a satellite based navigation system. GPS satellites transmit signals that allow one to determine the location of GPS receivers. In GPS, a typical technique for kinematic position estimation is differential positioning where two receivers are used: one receiver is stationary and its exact position is known, and the other is roving and its position is to be estimated. We describe the physical situation and derive the mathematical model based on the difference of the so-called carrier phase measurements at the stationary and roving receivers. We then present a recursive least squares approach for position estimation. We take full account of the structure of the problem to make our algorithm efficient, and use orthogonal transformations to ensure numerical reliability of the algorithm. Simulation results are presented to demonstrate the performance of the algorithm. A comparison with the van Graas and Lee positioning algorithm [Navigation, Journal of the Institute of Navigation, 42 (1995), pp. 605--618] is given. Our algorithm is seen to be both efficient and accurate, but an additional contribution of this approach is that some of the drawbacks of double differencing are avoided, and yet the vector of double differenced integer ambiguities is still available and can be used to fix the integer ambiguities and handle satellite rising and setting.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.005 |
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".