A Closed-Form Method With Low Noise Sensitivity for Locating a Moving Source on Earth at a Known Altitude
Bibliographic record
Abstract
This article proposes a closed-form method that does not require an initial guess to determine the geographical location and velocity of a moving source at a known altitude. The primary objective of this method is to overcome the main limitations of the two-step weighted least squares (TWLS) method and its related approaches, by exploiting the prior knowledge that the source is on earth with known altitude such as in geolocation. For this reason, our proposed approach refrains from assuming simplifications or linearizations in the TWLS relationships by utilizing the earth model and known source altitude in locating the source with the measurements. Unlike the TWLS method that does not use any prior knowledge of the source location, which becomes less effective beyond a noise threshold, our method consistently demonstrates improved performance. The main idea of the proposed method is to use a different regressor in the formulation from the measurement models of the localization problem. The regressor matrix in the proposed method is noise-free and depends only on the 2-D coordinates of the receivers. The proposed approach in the formulation not only solves the singularity issue of the regressor caused by factors like noise variance and receiver arrangement (such as being in a line, a plane, or close to each other) but also reduces the required minimum number of receivers from five to three. Finally, for the purpose of evaluating and comparing the proposed method with other recent approaches, the constrained Cramer–Rao lower bound (CCRLB) has been evaluated. The CCRLB is obtained with two constraints, both of which pertain to the World Geodetic System 1984 model assumed for the earth. Simulation results show that the proposed method performs better than other methods in challenging scenarios.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.004 |
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".