![Fig. 2: Schematic of a consistent feedback loop: Z [r]](https://www.researchgate.net/publication/389947062/figure/fig1/AS:11431281317253454@1742356125886/Schematic-of-a-consistent-feedback-loop-Z-r_Q320.jpg)
March 2025
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Estimating the parameters of nonlinear block-oriented state-space models from input-output data typically involves solving a highly non-convex optimization problem, making it susceptible to poor local minima and slow convergence. This paper presents a computationally efficient initialization method for fully parametrizing nonlinear linear fractional representation (NL-LFR) models using periodic data. The approach first infers the latent variables and then estimates the model parameters, yielding initial estimates that serve as a starting point for further nonlinear optimization. The proposed method shows robustness against poor local minima, and achieves a twofold error reduction compared to the state-of-the-art on a challenging benchmark dataset.
![a Circular target glued on the COST F3 beam. The nominal value of the internal and external diameters are D¯int\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{D}_{int}$$\end{document} = 1,5 mm and D¯ext=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{D}_{ext}=$$\end{document}10,5 mm, respectively [35]. b Target detected and extracted with the MSER algorithm, feature points and surrounding box [25, 36]](https://www.researchgate.net/publication/371222341/figure/fig1/AS:11431281172338199@1688523328393/a-Circular-target-glued-on-the-COST-F3-beam-The-nominal-value-of-the-internal-and_Q320.jpg)
![Flowchart for feature detection and tracking in a video sequence. The bonded targets are extracted with a MSER feature detector from a binary version of the first frame. Each feature is described by an ellipse and a surrounding bounding box. Then, some feature points are detected inside each region. For every next frame, feature points are tracked and the position of the surrounding boxes is updated by applying a geometric transformation estimated by matching point pairs at the frame i and i+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i+1$$\end{document}. The output consists in the coordinates of the centroid of each box for all frames. imax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i_{\max }$$\end{document} is the last frame of the video sequence and jmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j_{\max }$$\end{document} the maximum number of detected targets, respectively](https://www.researchgate.net/publication/371222341/figure/fig2/AS:11431281172338201@1688523328537/Flowchart-for-feature-detection-and-tracking-in-a-video-sequence-The-bonded-targets-are_Q320.jpg){kind=tracking}
![a Experimental setup of the COST F3 beam [32], b picture (4096 x 500 pixels) of the beam taken by the Vieworks VC-12MX-M/C 180 digital camera and c detected targets, labels and surrounding boxes](https://www.researchgate.net/publication/371222341/figure/fig4/AS:11431281172338202@1688523328735/a-Experimental-setup-of-the-COST-F3-beam-32-b-picture-4096-x-500-pixels-of-the-beam_Q320.jpg){kind=tracking}
