644 research outputs found

    Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models

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    Standard multiparameter eigenvalue problems (MEPs) are systems of k2k\ge 2 linear kk-parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems has emerged: a rectangular MEP (RMEP) with only one multivariate rectangular matrix pencil, where we are looking for combinations of the parameters for which the rank of the pencil is not full. Applications include finding the optimal least squares autoregressive moving average (ARMA) model and the optimal least squares realization of autonomous linear time-invariant (LTI) dynamical system. For linear and polynomial RMEPs, we give the number of solutions and show how these problems can be solved numerically by a transformation into a standard MEP. For the transformation we provide new linearizations for quadratic multivariate matrix polynomials with a specific structure of monomials and consider mixed systems of rectangular and square multivariate matrix polynomials. This numerical approach seems computationally considerably more attractive than the block Macaulay method, the only other currently available numerical method for polynomial RMEPs.Comment: 26 page

    A globally convergent matricial algorithm for multivariate spectral estimation

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    In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate spectral estimation, and test its effectiveness through simulation. Simulation shows that, in the case of short observation records, this method may provide a valid alternative to standard multivariable identification techniques such as MATLAB's PEM and MATLAB's N4SID

    Ambient Response Analysis Modal Analysis for Large Structures

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    Bibliographic Review on Distributed Kalman Filtering

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    In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

    Comparison of System Identification Methods using Ambient Bridge Test Data

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    Document Version Publisher's PDF, also known as Version of record Link to publication from Aalborg University Citation for published version (APA)

    The R-package phtt: Panel Data Analysis with Heterogeneous Time Trends

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    The R-package phtt provides estimation procedures for panel data with large dimensions n, T, and general forms of unobservable heterogeneous effects. Particularly, the estimation procedures are those of Bai (2009) and Kneip, Sickles, and Song (2012), which complement one another very well: both models assume the unobservable heterogeneous effects to have a factor structure. Kneip et al. (2012) considers the case in which the time varying common factors have relatively smooth patterns including strongly positive auto-correlated stationary as well as non-stationary factors, whereas the method of Bai (2009) focuses on stochastic bounded factors such as ARMA processes. Additionally, the phtt package provides a wide range of dimensionality criteria in order to estimate the number of the unobserved factors simultaneously with the remaining model parameters
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