Theoretical Limits of Differential Doppler Positioning Using LEO Satellite Signals
Bibliographic record
Abstract
As the need for more accurate and reliable positioning systems grows, satellite-based navigation techniques are gaining significant attention, particularly those utilizing Doppler shifts from Low Earth Orbit (LEO) satellites. Traditional Doppler positioning systems often suffer from errors induced by atmospheric disturbances, satellite clock biases, and other signal impairments, especially in dynamic environments. This has motivated the exploration of differential Doppler positioning as a promising solution to mitigate these common-mode errors. This paper explores the theoretical limits of differential Doppler positioning, focusing on Doppler-only methods where position and velocity estimates are derived from Doppler measurements without relying on time-of-arrival (TOA) measurements. By leveraging the Cramér-Rao lower bound (CRLB), we provide a theoretical performance benchmark for the accuracy of position, velocity, and frequency bias estimation. Furthermore, we present a correlation model for atmospheric effects to demonstrate the impact of baseline distance on the estimation performance of differential Doppler positioning. The results show that differential Doppler positioning notably outperforms traditional non-differential Doppler positioning, particularly in low-SNR environments, with substantial gains in frequency bias, 3D velocity, and 3D position estimation accuracy.
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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 | 0.004 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.006 | 0.007 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 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".