Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data
Bibliographic record
Abstract
This paper on performance analysis of parameter estimation is motivated by a practical consideration that the data length is finite. In particular, for time-varying systems, we study the properties of the well-known forgetting factor least-squares (FFLS) algorithm in detail in the stochastic framework, and derive upperbounds and lowerbounds of the parameter estimation errors (PEE), using directly the finite input-output data. The analysis indicates that the mean square PEE upperbounds and lowerbounds of the FFLS algorithm approach two finite positive constants, respectively, as the data length increases, and that these PEE upperbounds can be minimized by choosing appropriate forgetting factors. We further show that for time-invariant systems, the PEE upperbounds and lowerbounds of the ordinary least-squares algorithm both tend to zero as the data length increases. Finally, we illustrate and verify the theoretical findings with several example systems, including an experimental water-level system.
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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 | 0.012 | 0.077 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".