Estimation for SISO LTI systems using differential invariance
Bibliographic record
Abstract
A two-step non-asymptotic approach for parameter and state estimation in Reproducing Kernel Hilbert Space (RKHS) is presented in this thesis.It begins with the understanding and derivation of double sided kernel representation for a fourth order linear system and proceeds into discussing and developing methods for state and parameter estimation from single noisy realizations of the system output on a time interval [a, b].Once the parameters are estimated the output is reconstructed by projection onto the span of fundamental solutions and this in turn is used to reconstruct the time derivatives of the system output. PrefaceThis is to declare that the work presented in this document was completed and carried out by Anju John and is part of a collaborative work of three member team guided by Professor Hannah Michalska.The theory of representation of n-th order system using kernels in RKHS was derived by Debarshi Patanjali Ghoshal, PhD scholar in the research group and the representation for fourth order system output and its derivatives was verified and coded by me and also used in the implementation of the cost function for this thesis work .The theoretical background for the RKHS approaches for optimization is based on the research notes by Professor Hannah Michalska, which is duly acknowledged.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".