Finite interval parameter and state estimation in LTI systems using kernel-based multiple regression
Bibliographic record
Abstract
A recursive version of a generalized least squares for parameter estimation in Reproducing Kernel Hilbert Space (RKHS) is presented in this thesis.It begins with the understanding and derivation of a special construction of a forward-backward kernel representation of linear differential invariants for a third-order linear system.Methods for parameter and state estimation from single noisy realizations of the system output on a time interval [a, b] is discussed.Parameter estimation is solved by the way of stochastic regression.Generalized Least squares with covariance weighting is employed to deal with high noise.Once the recursive approach estimates the parameters, the output and time derivatives are reconstructed by projection onto the span of fundamental solutions. PrefaceThis is to declare that the work presented in this document was completed and carried out by Surya Kumar Devarajan under the guidance of Professor Hannah Michalska.It builds on the efforts of Debarshi Patanjali Ghoshal, the Ph.D. scholar in the research group who carried out the parameter estimation for linear systems by least-squares and recursive least-squares.The forward-backward kernel-based state and parameter estimation using multiple regression equations, which are very efficient in the presence of heteroskedasticity for a third-order system, were verified and coded.The theoretical background for the RKHS approaches is based on the research notes by Professor Hannah Michalska, which is duly acknowledged.i List of Figures 1.1 Block diagram of closed-loop control systems . . . . . . . . . . . . . . . .5.1 True and noisy system output with AWGN of µ = 0 and σ = 1 and N=3000 5.2 True and reconstructed output trajectories of the system with AWGN of µ = 0 and σ = 1 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . .5.3 True and reconstructed first derivative of the system with AWGN of µ = 0 and σ = 1 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4 True and reconstructed second derivative of the system with AWGN of µ = 0 and σ = 1 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.5 True and noisy system output with AWGN of µ = 0 and σ = 1.5 and N=3000 5.6 True and reconstructed output trajectories of the system with AWGN of µ = 0 and σ = 1.5 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . .5.7 True and reconstructed first derivative of the system with AWGN of µ = 0 and σ = 1.5 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.8 True and reconstructed second derivative of the system with AWGN of µ = 0 and σ = 1.5 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.9 True and noisy system output with AWGN of µ = 0 and σ = 2 and N=3000 5.10 True and reconstructed output trajectories of the system with AWGN of µ = 0 and σ = 2 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . .5.11 True and reconstructed first derivative of the system with AWGN of µ = 0 and σ = 2 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.12 True and reconstructed second derivative of the system with AWGN of µ = 0 and σ = 2 and N=3000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.13 True and noisy system output with AWGN of µ = 0 and σ = 3 and N=3000 List of Tables 5.1 Noise levels and the signal-to-noise ratio in decibel scale . . . . . . . . . . .5.2 True and estimated parameter values from a true output with AWGN µ = 0 and σ = 1.5, N=3000 using third order kernels . . . . . . . . . . . . . . . .5.3 Estimates of parameter values and RM SD for various noise levels and sample size N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4 True and estimated parameter values from a true output with AWGN µ = 0 and σ = 1.5, N=3000 using third order kernels . . . . . . . . . . . . . . . .
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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".