Analysis of Propagation Delay Effects on Bearings-Only Fusion of Heterogeneous Sensors
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Bibliographic record
Abstract
In bearings-only tracking applications, the standard bearing model ignores the propagation delay of signal, except in cases where the target speed is comparable to the signal speed. This paper provides a theoretical analysis of the performance degradation suffered by a maximum likelihood estimator (MLE) that neglects the signal propagation delay in the bearings-only fusion of heterogeneous sensors: one with negligible propagation delay and the other with non-negligible delay. By using a higher order Taylor-series based analysis, we derive approximate expressions for the bias and mean square error (MSE) of the MLE. The analysis shows that neglecting the propagation delay of a sensor (with non-negligible delay) in such bearings-only fusion problems leads to severe degradation in performance even when the signal speed is orders of magnitude higher than that of target. Simulation results confirm the validity of the theoretical predictions. Finally, a bias-compensated MLE is proposed that not only takes into account the propagation delay, but also compensates for the estimation bias. This bias-compensated MLE is nearly unbiased and exhibits an RMS error performance close to the Cramer Rao lower bound.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it