Using laguerre filters for system modeling and identification
Bibliographic record
Abstract
When approximating systems with Laguerre Basis Functions it's important to tune the Laguerre pole such that the expansion is parsimonious and accurate.The sum of squared errors has multiple minima with respect to the Laguerre pole, ruling out numerical optimization.Currently there are two alternate methods: an asymptotical method, and the enforced convergence criterion (ECC).A generalization of the ECC will be investigated such that minimizing this generalized ECC and computing the asymptotically optimal Laguerre pole lead to equivalent solutions.It will be proved that the EGG is quasiconvex (it can be solved using numerical optimization techniques).Currently the methods of finding the optimal Laguerre pole are only appropriate in a system modeling framework since they depend on knowledge of the system's poles.It will be shown that the EGO can be formulated in a system identification framework and an algorithm will be proposed to find the minimizing Laguerre pole. TruncatedRamp Weighting Function 4 Conclusion and Future Work A Proof of Linear Independence B Detailed Proof of Theorem 3.1.2B.1 Case 1. B.2 Case 2 B.3 Case 3 C Alternative Proof of Quasiconvexity Bibliography V Wk weighting function for the ECC y(t), Y(z) output of a system in time and frequency domain Z[.] z-transform viii study Laguerre functions, most notably C. Deal and M. Schetzen [56].In his famous 1958 Lecture Series (which has been compiled into a book [64])N. Wiener suggested LBFs were the best basis functions to use for the expansion of Wiener kernels in nonlinear systems.His reasoning was ( 1) that any LTI system can be represented using LBFs, (2) they are orthogonal, (3) they guarantee stability of the nonlinear model (due to the exponential decay of the LBFs), and (4) LBF networks were easy to implement using simple R-C circuits.Some early applications of LBFs included studying hydrological rainfall runoff processes [1] and the eye pupil reflex [61].Since then, Laguerre filters have gained popularity, especially in the modelling and identification of nonlinear systems.Some more recent applications of LBFs include control applications [15], approximation of physiological systems [28][29][30]35,63], RF
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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".