On convergence properties of subspace trackers based on orthogonal iteration
Bibliographic record
Abstract
This paper studies convergence properties of subspace trackers using orthogonal iteration. In the context of blind estimation of a time-varying channel, orthogonal iteration and its variants have been widely considered for tracking the channel parameters by updating the eigendecomposition of an exponentially weighted correlation matrix. While it is well known that orthogonal iteration converges exponentially with arbitrary initial conditions, orthogonal-iteration-based subspace trackers can only inherit these merits when the channels considered undergo extremely slow time-variations. In this paper, we generalize the traditional (i.e. fixed subspace) convergence analysis of the orthogonal iteration to include non-stationary situations as well. We use the results to investigate the convergence behavior of subspace trackers based on orthogonal iteration under slow, moderate and rapid time-variations of the underlying subspace. In the latter case, we expose a fundamental limitation of the orthogonal iteration, i.e. practical limit on subspace variations to ensure effective tracking.
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How this classification was reachedexpand
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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".