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  • 151.
    Valenzuela, P. E.
    et al.
    Dept. of Automatic Control, KTH, Royal Institute of Technology, Stockholm, Sweden.
    Dahlin, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Rojas, C. R.
    Dept. of Automatic Control, KTH, Royal Institute of Technology, Stockholm, Sweden.
    Schön, Thomas
    Dept. of Information Technology, Uppsala University, Uppsala, Sweden.
    A graph/particle-based method for experiment design in nonlinear systems2014Ingår i: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Edward Boje and Xiaohua Xia, International Federation of Automatic Control , 2014, s. 1404-1409Konferensbidrag (Refereegranskat)
    Abstract [en]

    We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass function (pmf) from which an input sequence is sampled. The feasible set of the stationary pmf is a polytope, allowing it to be expressed as a convex combination of its extreme points. The extreme points in the feasible set of pmf’s can be computed using graph theory. Therefore, the final information matrix can be approximated as a convex combination of the information matrices associated with each extreme point. For nonlinear systems, the information matrices for each extreme point can be computed by using particle methods. Numerical examples show that the proposed techniquecan be successfully employed for experiment design in nonlinear systems.

  • 152.
    Wahlström, Niklas
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Kok, Manon
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Modeling Magnetic Fields using Gaussian Processes2013Ingår i: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013, IEEE conference proceedings, 2013, s. 3522-3526Konferensbidrag (Refereegranskat)
    Abstract [en]

    Starting from the electromagnetic theory, we derive a Bayesian nonparametric model allowing for joint estimation of the magnetic field and the magnetic sources in complex environments. The model is a Gaussian process which exploits the divergence- and curl-free properties of the magnetic field by combining well-known model components in a novel manner. The model is estimated using magnetometer measurements and spatial information implicitly provided by the sensor. The model and the associated estimator are validated on both simulated and real world experimental data producing Bayesian nonparametric maps of magnetized objects.

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  • 153.
    Wills, Adrian
    et al.
    University of Newcastle, Australia.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ninness, Brett
    University of Newcastle, Australia.
    Parameter Estimation for Discrete-Time Nonlinear Systems Using EM2008Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we consider parameter estimation of general stochastic nonlinear statespace models using the Maximum Likelihood method. This is accomplished via the employment of an Expectation Maximisation algorithm, where the essential components involve a particle smoother for the expectation step, and a gradient-based search for the maximisation step. The utility of this method is illustrated with several nonlinear and non-Gaussian examples.  

  • 154.
    Wills, Adrian
    et al.
    University of Newcastle, Australia.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Lindsten, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ninness, Brett
    University of Newcastle, Australia.
    Estimation of Linear Systems using a Gibbs Sampler2012Ingår i: Proceedings of the 16th IFAC Symposium on System Identification, 2012, s. 203-208Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper considers a Bayesian approach to linear system identification. One motivation is the advantage of the minimum mean square error of the associated conditional mean estimate. A further motivation is the error quantifications afforded by the posterior density which are not reliant on asymptotic in data length derivations. To compute these posterior quantities, this paper derives and illustrates a Gibbs sampling approach, which is a randomized algorithm in the family of Markov chain Monte Carlo methods. We provide details on a numerically robust implementation of the Gibbs sampler. In a numerical example, the proposed method is illustrated to give good convergence properties without requiring any user tuning.

  • 155.
    Wills, Adrian
    et al.
    University of Newcastle, Australia.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ninness, Brett
    University of Newcastle, Australia.
    Blind Identification of Wiener Models2011Ingår i: Proceedings of the 18th IFAC World Congress, 2011, s. 5597-5602Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper develops and illustrates methods for the identification of Wiener model structures. These techniques are capable of accommodating the “blind” situation where the input excitation to the linear block is not observed. Furthermore, the algorithm developed here can accommodate a nonlinearity which need not be invertible, and may also be multivariable. Central to these developments is the employment of the Expectation Maximisation (EM) method for computing maximum likelihood estimates, and the use of a new approach to particle smoothing to efficiently compute stochastic expectations in the presence of nonlinearities.

  • 156.
    Wills, Adrian
    et al.
    University of Newcastle, Australia .
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ninness, Brett
    University of Newcastle, Australia .
    Identification of Hammerstein-Wiener Models2013Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, nr 1, s. 70-81Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and colored stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case.

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  • 157.
    Wills, Adrian
    et al.
    University of Newcastle, Australia.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ninness, Brett
    University of Newcastle, Australia.
    Estimating State-Space Models in Innovations Form using the Expectation Maximisation Algorithm2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The expectation maximisation (EM) algorithm has proven to be effective for a range of identification problems. Unfortunately, the way in which the EM algorithm has previously been applied has proven unsuitable for the commonly employed innovations form model structure. This paper addresses this problem, and presents a previously unexamined method of EM algorithm employment. The results are profiled, which indicate that a hybrid EM/gradient-search technique may in some cases outperform either a pure EM or a pure gradient-based search approach.

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  • 158.
    Wills, Adrian
    et al.
    University of Newcastle, Australia.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ninness, Brett
    University of Newcastle, Australia.
    Estimating State-Space Models in Innovations Form using the Expectation Maximisation Algorithm2010Ingår i: Proceedings of the 49th IEEE Conference on Decision and Control, 2010, s. 5524-5529Konferensbidrag (Refereegranskat)
    Abstract [en]

    The expectation maximisation (EM) algorithm has proven to be effective for a range of identification problems. Unfortunately, the way in which the EM algorithm has previously been applied has proven unsuitable for the commonly employed innovations form model structure. This paper addresses this problem, and presents a previously unexamined method of EM algorithm employment. The results are profiled, which indicate that a hybrid EM/gradient-search technique may in some cases outperform either a pure EM or a pure gradient-based search approach.

  • 159.
    Wills, Adrian
    et al.
    University of Newcastle, Australia.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ninness, Brett
    University of Newcastle, Australia.
    Parameter Estimation for Discrete-Time Nonlinear Systems Using EM2008Ingår i: Proceedings of the 17th IFAC World Congress, 2008, s. 4012-4017Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper we consider parameter estimation of general stochastic nonlinear statespace models using the Maximum Likelihood method. This is accomplished via the employment of an Expectation Maximisation algorithm, where the essential components involve a particle smoother for the expectation step, and a gradient-based search for the maximisation step. The utility of this method is illustrated with several nonlinear and non-Gaussian examples.  

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