Approximate maximum likelihood estimators for array processing in multiplicative noise environments
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Bibliographic record
Abstract
We consider the problem of localizing a source by means of a sensor array when the received signal is corrupted by multiplicative noise. This scenario is encountered, for example, in communications, owing to the presence of local scatterers in the vicinity of the mobile or due to wavefronts that propagate through random inhomogeneous media. Since the exact maximum likelihood (ML) estimator is computationally intensive, two approximate solutions are proposed, originating from the analysis of the high and low signal to-noise ratio (SNR) cases, respectively. First, starting with the no additive noise case, a very simple approximate ML (AML/sub 1/) estimator is derived. The performance of the AML/sub 1/ estimator in the presence of additive noise is studied, and a theoretical expression for its asymptotic variance is derived. Its performance is shown to be close to the Cramer-Rao bound (CRB) for moderate to high SNR. Next, the low SNR case is considered, and the corresponding AML/sub 2/ solution is derived. It is shown that the approximate ML criterion can be concentrated with respect to both the multiplicative and additive noise powers, leaving out a two-dimensional (2-D) minimization problem instead of a four-dimensional (4-D) problem required by the exact ML. Numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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