Information matrix and D-optimal design with Gaussian inputs for Wiener model identification

Mahata, Kaushik; Schoukens, Joannes; Cock, Alexander De

doi:10.1016/j.automatica.2016.02.026

Cited by 24 publications

(14 citation statements)

References 32 publications

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“…Clearly, the uncertainty area is under a given threshold to the value of IFD and target T t can be distinguished from target T 0 when it is outside this area. As shown in Table 2 with T 0 = (20, 30) and T 0 = (25,17), for the selected samples, we can also get the similar property which is given in the last subsection. For example, setting T 1 = (11, 11) and T 8 = (39, 39) with the same Ed = 21.02, the corresponding relationships about D F and IFD are 0.38 < 0.55 and 1.88 > 0.91, respectively.…”

Section: Two-bearings Measurementsupporting

confidence: 57%

“…Fisher information matrix (FIM) is one of important contents in the probability theory and statistics [17,18]. Since a FIM is a symmetric positive-definite matrix, the set of all Fisher information matrices (FIMs) corresponding to a given probability distribution family is a submanifold of PD(n), which is called the information submanifold of PD(n).…”

Section: Introductionmentioning

confidence: 99%

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Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks

Sun

Win

2017

Entropy

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Abstract:In this paper, firstly, manifold PD(n) consisting of all n × n symmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold of PD(n) are presented including metric, geodesic and geodesic distance; Thirdly, the information resolution with sensor networks is presented by three classical measurement models based on information submanifold; Finally, the bearing-only tracking by single sensor is introduced by the Fisher information matrix. The preliminary analysis results introduced in this paper indicate that information submanifold is able to offer consistent and more comprehensive means to understand and solve sensor network problems for targets resolution and tracking, which are not easily handled by some conventional analysis methods.

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Section: Two-bearings Measurementsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks

Sun

Win

2017

Entropy

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“…Input design for structured systems (i.e. the interconnection of linear dynamics with a static nonlinearity) was studied in [6], [7] and [8], with the latter proving that D-optimal inputs can be realized by a mixture of Gaussians for certain Wiener systems. Ideas from input design for impulse response systems were extended to nonlinear systems admitting a nonparametric Volterra series representation in [9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Input Design as Optimal Control of a Hamiltonian System

Umenberger

Schön

2020

IEEE Control Syst. Lett.

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We propose an input design method for a general class of parametric probabilistic models, including nonlinear dynamical systems with process noise. The goal of the procedure is to select inputs such that the parameter posterior distribution concentrates about the true value of the parameters; however, exact computation of the posterior is intractable. By representing (samples from) the posterior as trajectories from a certain Hamiltonian system, we transform the input design task into an optimal control problem. The method is illustrated via numerical examples, including MRI pulse sequence design.

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“…Polynomials (Westwick and Verhaegen, 1996;Janczak, 2005;Stanisławski et al, 2014;Tiels and Schoukens, 2014;Ding et al, 2015;Jansson and Medvedev, 2015;Xiong et al, 2015;Mahataa et al, 2016;Bottegal et al, 2017;Kazemi and Arefi, 2017;Schoukens and Tiels, 2017;Janczak, 2018), Legendre polynomials (Ase and Katayama, 2015), piecewise-linear functions (Dong et al, 2009;Fan and Lo, 2009), cubic splines (Aljamaan et al, 2016), least-squares support vector machine models (Ławryńczuk, 2016), sets of basis functions (Gómez and Baeyens, 2002;2005;Schoukens and Tiels, 2011;Yang et al, 2017), multilayer perceptrons (Al-Duwaish et al, 1996;Janczak, 2005;Ławryńczuk, 2013), kernel expansions (Van Vaerenbergh et al, 2013), or nonparametric representations (Greblicki, 1997;2001) are commonly used for modeling the static nonlinear element or its inverse. The linear dynamic subsystem is usually represented by a transfer function (Janczak, 2005;Dong et al, 2009;Schoukens and Tiels, 2011;Ławryńczuk, 2013;2016;Ding et al, 2015;Xiong et al, 2015;Mahataa et al, 2016;Bottegal et al, 2017;Kazemi and Arefi, 2017;Yang et al, 2001)…”

Section: Introductionmentioning

confidence: 99%

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

Janczak

Korbicz

2019

International Journal of Applied Mathematics and Computer Science

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A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.

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Information matrix and D-optimal design with Gaussian inputs for Wiener model identification

Cited by 24 publications

References 32 publications

Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks

Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks

Nonlinear Input Design as Optimal Control of a Hamiltonian System

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

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