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  • 1.
    Agüero, Juan C.
    et al.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Goodwin, Graham C.
    The University of Newcastle, Australia.
    Fundamental Limitations on the Accuracy of MIMO Linear Models Obtained by PEM for Systems Operating in Open Loop2009In: Proceedings of the Joint 48th IEEE Conference on Decision and Control (CDC’09) and 28th Chinese Control Conference (CCC’09), 2009, p. 482-487Conference paper (Refereed)
    Abstract [en]

    In this paper we show that the variance of estimated parametric models for open loopMultiple-Input Multiple-Output (MIMO) systems obtained by the prediction error method (PEM) satisfies a fundamental integral limitation. The fundamental limitation gives rise to a multivariable 'water-bed' effect.

  • 2.
    Agüero, Juan C.
    et al.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Goodwin, Graham C.
    The University of Newcastle, Australia.
    Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation2012In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 48, no 4, p. 632-637Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation. We present a frequency-domain representation for the information matrix for general linear MIMO models. We show that the variance of estimated parametric models for linear MIMO systems satisfies a fundamental integral trade-off. This trade-off is expressed as a multivariable 'water-bed' effect. An extension to spectral estimation is also discussed.

  • 3.
    Blomberg, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Approximate regularization path for nuclear norm based H2 model reduction2014In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, p. 3637-3641Conference paper (Refereed)
    Abstract [en]

    This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this tradeoff is determined by one crucial design parameter. The main contribution is a methodology to approximately calculate all solutions up to a certain tolerance to the model reduction problem as a function of the design parameter. This is called the regularization path in sparse estimation and is a very important tool in order to find the appropriate balance between fit and complexity. We extend this to the more complicated nuclear norm case. The key idea is to determine when to exactly calculate the optimal solution using an upper bound based on the so-called duality gap. Hence, by solving a fixed number of optimization problems the whole regularization path up to a given tolerance can be efficiently computed. We illustrate this approach on some numerical examples.

  • 4.
    Blomberg, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Regularization Paths for Re-Weighted Nuclear Norm Minimization2015In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 11, p. 1980-1984Article in journal (Refereed)
    Abstract [en]

    We consider a class of weighted nuclear norm optimization problems with important applications in signal processing, system identification, and model order reduction. The nuclear norm is commonly used as a convex heuristic for matrix rank constraints. Our objective is to minimize a quadratic cost subject to a nuclear norm constraint on a linear function of the decision variables, where the trade-off between the fit and the constraint is governed by a regularization parameter. The main contribution is an algorithm to determine the so-called approximate regularization path, which is the optimal solution up to a given error tolerance as a function of the regularization parameter. The advantage is that we only have to solve the optimization problem for a fixed number of values of the regularization parameter, with guaranteed error tolerance. The algorithm is exemplified on a weighted Hankel matrix model order reduction problem.

  • 5.
    Blomberg, Niclas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Approximate Regularization Paths for Nuclear Norm Minimization using Singular Value Bounds: with Implementation and Extended Appendix2015Conference paper (Refereed)
    Abstract [en]

    The widely used nuclear norm heuristic for rank minimizationproblems introduces a regularization parameter which isdifficult to tune. We have recently proposed a method to approximatethe regularization path, i.e., the optimal solution asa function of the parameter, which requires solving the problemonly for a sparse set of points. In this paper, we extendthe algorithm to provide error bounds for the singular valuesof the approximation. We exemplify the algorithms on largescale benchmark examples in model order reduction. Here,the order of a dynamical system is reduced by means of constrainedminimization of the nuclear norm of a Hankel matrix.

  • 6. Bombois, Xavier
    et al.
    den Dekker, Arjan J.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Van den Hof, Paul M. J.
    Optimal experiment design for hypothesis testing applied to functional magnetic resonance imaging2011In: Proceedings of the 18th IFAC World Congress, 2011, p. 9953-9958Conference paper (Refereed)
    Abstract [en]

    Hypothesis testing is a classical methodology of making decisions using experimental data. In hypothesis testing one seeks to discover evidence that either accepts or rejects a given null hypothesis H0. The alternative hypothesis H1 is the hypothesis that is accepted when H0 is rejected. In hypothesis testing, the probability of deciding H1 when in fact H0 is true is known as the false alarm rate, whereas the probability of deciding H1when in fact H1is true is known as the detection rate (or power) of the test. It is not possible to optimize both rates simultaneously. In this paper, we consider the problem of determining the data to be used for hypothesis testing that maximize the detection rate for a given false alarm rate. We consider in particular a hypothesis test which is relevant in functional magnetic resonance imaging (fMRI).

  • 7. Brighenti, C.
    et al.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Input design using Markov chains for system identification2009In: Proceedings of the 48th IEEE Conference on  Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009, IEEE conference proceedings, 2009, p. 1557-1562Conference paper (Refereed)
    Abstract [en]

    This paper studies the input design problem for system identification where time domain constraints have to be considered. A finite Markov chain is used to model the input of the system. This allows to directly include input amplitude constraints in the input model by properly choosing the state space of the Markov chain, which is defined so that the Markov chain generates a multi-level sequence. The probability distribution of the Markov chain is shaped in order to minimize the cost function considered in the input design problem. Stochastic approximation is used to minimize that cost function. With this approach, the input signal to apply to the system can be easily generated by extracting samples from the optimal distribution. A numerical example shows how this method can improve estimation with respect to other input realization techniques.

  • 8.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Annergren, Mariette
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian A.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Molander, Mats
    Sjöberg, Johan
    Application Set Approximation in Optimal Input Design for Model Predictive Control2014In: 2014 European Control Conference (ECC), 2014, p. 744-749Conference paper (Refereed)
    Abstract [en]

    This contribution considers one central aspect of experiment design in system identification, namely application set approximation. When a control design is based on an estimated model, the achievable performance is related to the quality of the estimate. The degradation in control performance due to plant-modeling missmatch is quantified by an application cost function. A convex approximation of the set of models that satisfy the control specification is typically required in optimal input design. The standard approach is to use a quadratic approximation of the application cost function, where the main computational effort is to find the corresponding Hessian matrix. Our main contribution is an alternative approach for this problem, which uses the structure of the underlying optimal control problem to considerably reduce the computations needed to find the application set. This technique allows the use of applications oriented input design for MPC on much more complex plants. The approach is numerically evaluated on a distillation control problem.

  • 9.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Valenzuela, Patricio E
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Applications oriented input design for closed-loop system identification: a graph-theory approach2014In: Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, IEEE conference proceedings, 2014, p. 4125-4130Conference paper (Refereed)
    Abstract [en]

    A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification.

  • 10.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Valenzuela, Patricio Esteban
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Model Predictive Control oriented experiment design for system identification: A graph theoretical approach2017In: Journal of Process Control, ISSN 0959-1524, E-ISSN 1873-2771, Vol. 52, p. 75-84Article in journal (Refereed)
    Abstract [en]

    We present a new approach to Model Predictive Control (MPC) oriented experiment design for the identification of systems operating in closed-loop. The method considers the design of an experiment by minimizing the experimental cost, subject to probabilistic bounds on the input and output signals due to physical limitations of actuators, and quality constraints on the identified model. The excitation is done by intentionally adding a disturbance to the loop. We then design the external excitation to achieve the minimum experimental effort while we are also taking care of the tracking performance of MPC. The stability of the closed-loop system is guaranteed by employing robust MPC during the experiment. The problem is then defined as an optimization problem. However, the aforementioned constraints result in a non-convex optimization which is relaxed by using results from graph theory. The proposed technique is evaluated through a numerical example showing that it is an attractive alternative for closed-loop experiment design.

  • 11.
    Ebadat, Afrooz
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Larsson, Christian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Applications Oriented Input Design in Time-Domain Through Cyclic Methods2014Conference paper (Refereed)
    Abstract [en]

    In this paper we propose a method for applications oriented input design for linear systems in open-loop under time-domain constraints on the amplitude of input and output signals. The method guarantees a desired control performance for the estimated model in minimum time, by imposing some lower bound on the information matrix. The problem is formulated as a time-domain optimization problem, which is non-convex. This is addressed through an alternating method, where we separate the problem into two steps and at each step we optimize the cost function with respect to one of two variables. We alternate between these two steps until convergence. A time recursive input design algorithm is performed, which enables us to use the algorithm with control. Therefore, a receding horizon framework is used to solve each optimization problem. Finally, we illustrate the method with a numerical example which shows the good ability of the proposed approach in generating an optimal input signal.

  • 12. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Cost function shaping of the output error criterion2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 76, p. 53-60Article in journal (Refereed)
    Abstract [en]

    Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because in most cases both the corresponding objective function and the search space are nonconvex. The difficulty in solving the optimization problem depends mainly on the experimental conditions, more specifically on the spectra of the input/output data collected from the system. It is therefore possible to improve the convergence of the algorithms by properly choosing the data prefilters; in this paper we show how to perform this choice. We present the application of the proposed approach to case studies where the standard algorithms tend to fail to converge to the global minimum.

  • 13. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cost function shaping of the output error criterion2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 76, p. 53-60Article in journal (Refereed)
    Abstract [en]

    Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because in most cases both the corresponding objective function and the search space are nonconvex. The difficulty in solving the optimization problem depends mainly on the experimental conditions, more specifically on the spectra of the input/output data collected from the system. It is therefore possible to improve the convergence of the algorithms by properly choosing the data prefilters; in this paper we show how to perform this choice. We present the application of the proposed approach to case studies where the standard algorithms tend to fail to converge to the global minimum.

  • 14. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Input design as a tool to improve the convergence of PEM2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 11, p. 3282-3291Article in journal (Refereed)
    Abstract [en]

    The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The shape of the cost function, and hence the difficulty in solving the optimization problem, depends directly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. Therefore, it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input; in this paper, we address this problem. We present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design. We present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima.

  • 15. Eckhard, Diego
    et al.
    Bazanella, Alexandre S.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the convergence of the Prediction Error Method to its global minimum2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, p. 698-703Conference paper (Refereed)
    Abstract [en]

    The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The existence of local minima, and hence the difficulty in solving the optimization, depends mainly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. It is therefore possible to avoid the existence of local minima by properly choosing the spectrum of the input; in this paper we show how to perform this choice. We present sufficient conditions for the convergence of PEM to the global minimum and from these conditions we derive two approaches to avoid the existence of nonglobal minima. We present the application of one of these two approaches to a case study where standard identification toolboxes tend to get trapped in nonglobal minima.

  • 16. Eckhard, Diego
    et al.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Gevers, Michel
    Mean-squared error experiment design for linear regression models2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, p. 1629-1634Conference paper (Refereed)
    Abstract [en]

    This work solves an experiment design problem for a linear regression problem using a reduced order model. The quality of the model is assessed using a mean square error measure that depends linearly on the parameters. The designed input signal ensures a predefined quality of the model while minimizing the input energy.

  • 17. Esparza, Alicia
    et al.
    Agüero, Juan C.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Godoy, Boris I.
    The University of Newcastle, Australia.
    Asymptotic statistical analysis for model-based control design strategies2011In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, no 5, p. 1041-1046Article in journal (Refereed)
    Abstract [en]

    In this paper, we generalize existing fundamental limitations on the accuracy of the estimation of dynamic models. In addition, we study the large sample statistical behavior of different estimation-based controller design strategies. In particular, fundamental limitations on the closed-loop performance using a controller obtained by Virtual Reference Feedback Tuning (VRFT) are studied. We also extend our results to more general estimation-based control design strategies. We present numerical examples to show the application of our results.

  • 18.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Effect of Noise Correlation in Parameter Identification of SIMO Systems2015In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 48, no 28, p. 326-331Article in journal (Refereed)
    Abstract [en]

    The accuracy of identified linear time-invariant single-input multi-output (SIMO) models can be improved when the disturbances affecting the output measurements are spatially correlated. Given a linear parametrization of the modules composing the SIMO structure, we show that the correlation structure of the noise sources and the model structure of the othe modules determine the variance of a parameter estimate. In particular we show that increasing the model order only increases the variance of other modules up to a point. We precisely characterize the variance error of the parameter estimates for finite model orders. We quantify the effect of noise correlation structure, model structure and signal spectra.

  • 19.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the Variance Analysis of identified Linear MIMO Models2015In: IEEE Explore, Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)
    Abstract [en]

    We study the accuracy of identified linear time-invariant multi-input multi-output (MIMO) systems. Under a stochastic framework, we quantify the effect of the spatial correlation and choice of model structure on the covariance matrix of the transfer function estimates. In particular, it is shown how the variance of a transfer function estimate depends on signal properties and model orders of other modules composing the MIMO system.

  • 20.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance analysis of linear SIMO models with spatially correlated noise2017In: Automatica, ISSN 0005-1098, Vol. 77, p. 68-81Article in journal (Refereed)
    Abstract [en]

    In this paper we address the identification of linear time-invariant single-input multi-output (SIMO) systems. In particular, we assess the performance of the prediction error method by quantifying the variance of the parameter estimates. Using an orthonormal representation for the modules composing the SIMO structure, we show that the parameter estimate of a module depends on the model structure of the other modules, and on the correlation structure of the output disturbances. We provide novel results which quantify the variance-error of the parameter estimates for finite model orders, where the effects of noise correlation structure, model structure and input spectrum are visible. In particular, we show that a sensor does not increase the accuracy of a module if common dynamics have to be estimated. When a module is identified using less parameters than the other modules, we derive the noise correlation structure that gives the minimum total variance. The implications of our results are illustrated through numerical examples and simulations.

  • 21.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bottegal, Giulio
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance Analysis of Linear SIMO Models with Spatially Correlated NoiseManuscript (preprint) (Other academic)
    Abstract [en]

    Substantial improvement in accuracy of identied linear time-invariant single-input multi-output (SIMO) dynamical models ispossible when the disturbances aecting the output measurements are spatially correlated. Using an orthogonal representation for the modules composing the SIMO structure, in this paper we show that the variance of a parameter estimate of a module is dependent on the model structure of the other modules, and the correlation structure of the disturbances. In addition, we quantify the variance-error for the parameter estimates for finite model orders, where the effect of noise correlation structure, model structure and signal spectra are visible. From these results, we derive the noise correlation structure under which the mentioned model parameterization gives the lowest variance, when one module is identied using less parameters than the other modules.

  • 22.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Geometric Approach to Variance Analysis of Cascaded Systems2013In: Proceedings of the 52nd Conference On Decision And Control, IEEE conference proceedings, 2013, p. 6496-6501Conference paper (Refereed)
    Abstract [en]

    Modeling complex and interconnected systems is a key issue in system identification. When estimating individual subsystems of a network of interconnected system, it is of interest to know the improvement of model-accuracy in using different sensors and actuators. In this paper, using a geometric approach, we quantify the accuracy improvement from additional sensors when estimating the first of a set of subsystems connected in a cascade structure. We present results on how the zeros of the first subsystem affect the accuracy of the corresponding model. Additionally we shed some light on how structural properties and experimental conditions determine the accuracy. The results are particularized to FIR systems, for which the results are illustrated by numerical simulations. A surprising special case occurs when the first subsystem contains a zero on the unit circle; as the model orders grows large, thevariance of the frequency function estimate, evaluated at thecorresponding frequency of the unit-circle zero, is shown to be the same as if the other subsystems were completely known.

  • 23.
    Everitt, Niklas
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Variance Results for Parallel Cascade Serial Systems2014In: Proceedings of 19th IFAC World Congress, 2014Conference paper (Refereed)
    Abstract [en]

    Modelling dynamic networks is important in different fields of science. At present, little is known about how different inputs and sensors contribute to the statistical properties concerning an estimate of a specific dynamic system in a network. We consider two forms of parallel serial structures, one multiple-input-multiple-output structure and one single-input multiple-output structure. The quality of the estimated models is analysed by means of the asymptotic covariance matrix, with respect to input signal characteristics, noise characteristics, sensor locations and previous knowledge about the remaining systems in the network. It is shown that an additive property applies to the information matrix for the considered structures. The impact of input signal selection, sensor locations and incorporation of previous knowledge isillustrated by simple examples.

  • 24.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Least Squares Method for Identification of Feedback Cascade Systems2015In: 17th IFAC Symposium on System Identification SYSID 2015 — Beijing, China, 19–21 October 2015, IFAC Papers Online, 2015, Vol. 48, p. 98-103Conference paper (Refereed)
    Abstract [en]

    The problem of identification of systems in dynamic networks is considered. Although the prediction error method (PEM) can be applied to the overall system, the non-standard model structure requires solving a non-convex optimization problem. Alternative methods have been proposed, such as instrumental variables and indirect PEM. In this paper, we first consider acyclic cascade systems, and argue that these methods have different ranges of applicability. Then, for a network with feedback connection, we propose an approach to deal with the fact that indirect PEM yields a non-convex problem in that case. A numerical simulation may indicate that this approach is competitive with other existing methods.

  • 25.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    On Estimating Initial Conditions in Unstructured Models2015In: 2015 54th IEEE Conference on Decision and Control (CDC), IEEE conference proceedings, 2015, p. 2725-2730Conference paper (Refereed)
    Abstract [en]

    Estimation of structured models is an importantproblem in system identification. Some methods, as an intermediatestep to obtain the model of interest, estimate theimpulse response parameters of the system. This approachdates back to the beginning of subspace identification and isstill used in recently proposed methods. A limitation of thisprocedure is that, when obtaining these parameters from ahigh-order unstructured model, the initial conditions of thesystem are typically unknown, which imposes a truncation ofthe measured output data for the estimation. For finite samplesizes, discarding part of the data limits the performance ofthe method. To deal with this issue, we propose an approachthat uses all the available data, and estimates also the initialconditions of the system. Then, as examples, we show how thisapproach can be applied to two methods in a beneficial manner.Finally, we use a simulation study to exemplify the potential ofthe approach.

  • 26.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A weighted least-squares method for parameter estimation in structured models2014In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, p. 3322-3327Conference paper (Refereed)
    Abstract [en]

    Parameter estimation in structured models is generally considered a difficult problem. For example, the prediction error method (PEM) typically gives a non-convex optimization problem, while it is difficult to incorporate structural information in subspace identification. In this contribution, we revisit the idea of iteratively using the weighted least-squares method to cope with the problem of non-convex optimization. The method is, essentially, a three-step method. First, a high order least-squares estimate is computed. Next, this model is reduced to a structured estimate using the least-squares method. Finally, the structured estimate is re-estimated, using weighted least-squares, with weights obtained from the first structured estimate. This methodology has a long history, and has been applied to a range of signal processing problems. In particular, it forms the basis of iterative quadratic maximum likelihood (IQML) and the Steiglitz-McBride method. Our contributions are as follows. Firstly, for output-error models, we provide statistically optimal weights. We conjecture that the method is asymptotically efficient under mild assumptions and support this claim by simulations. Secondly, we point to a wide range of structured estimation problems where this technique can be applied. Finally, we relate this type of technique to classical prediction error and subspace methods by showing that it can be interpreted as a link between the two, sharing favorable properties with both domains.

  • 27. Godoy, B. I.
    et al.
    Valenzuela, Patricio E.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Aguero, J. C.
    Ninness, B.
    A novel input design approach for systems with quantized output data2014In: 2014 European Control Conference, ECC, IEEE , 2014, p. 1049-1054Conference paper (Refereed)
    Abstract [en]

    In this paper, we explore the problem of input design for systems with quantized measurements. For the input design problem, we calculate and optimize a function of the Fisher Information Matrix (FIM). The calculation of the FIM is greatly simplified by using known relationships of the derivative of the likelihood function, and the auxiliary function arising from the Expectation Maximization (EM) algorithm. To optimize the FIM, we design an experiment using a recently published method based on graph theory. A numerical example shows that the proposed experiment can be successfully used in quantized systems.

  • 28.
    Goodwin, Graham C.
    et al.
    The University of Newcastle, Australia.
    Agüero, Juan C.
    The University of Newcastle, Australia.
    Welsh, James S.
    The University of Newcastle, Australia.
    Yuz, Juan I.
    Universidad Técnica Federico Santa María.
    Adams, Greg J.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    Robust Identification of Process Models from Plant Data2008In: Journal of Process Control, ISSN 0959-1524, Vol. 18, no 9, p. 810-820Article in journal (Refereed)
    Abstract [en]

    A precursor to any advanced control solution is the step of obtaining an accurate model of the process. Suitable models can be obtained from phenomenological reasoning, analysis of plant data or a combination of both. Here, we will focus on the problem of estimating (or calibrating) models from plant data. A key goal is to achieve robust identification. By robust we mean that small errors in the hypotheses should lead to small errors in the estimated models. We argue that, in some circumstances, it is essential that special precautions, including discarding some part of the data, be taken to ensure that robustness is preserved. We present several practical case studies to illustrate the results.

  • 29.
    Goodwin, Graham C.
    et al.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    Welsh, James S.
    The University of Newcastle, Australia.
    Good, Bad and Optimal Experiments for Identification2006In: Forever Ljung in System Identification - Workshop on the occasion of Lennart Ljung’s 60th birthday / [ed] Torkel Glad and Gustaf Hendeby, Lund, Sweden: Studentlitteratur, 2006Chapter in book (Other academic)
  • 30. Ha, H.
    et al.
    Welsh, J. S.
    Blomberg, Niclas
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Reweighted nuclear norm regularization: A SPARSEVA approach2015In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 48, no 28, p. 1172-1177Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is computationally expensive, hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework to overcome this problem. Furthermore, we suggest the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. Numerical examples demonstrate the veracity of this method which has close ties with the traditional technique of cross validation, but using much less computations.

  • 31.
    Hjalmarsson, Håkan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Mårtensson, Jonas
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Söderström, Torsten
    Uppsala University.
    On the accuracy in errors-in-variables identification compared to prediction-error identification2011In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, ISSN 0005-1098, Vol. 47, no 12, p. 2704-2712Article in journal (Refereed)
    Abstract [en]

    Errors-in-variables estimation problems for single-inputsingle-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle's formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.

  • 32.
    Hjalmarsson, Håkan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Model Structure Selection - An Update2014In: 2014 European Control Conference (ECC), IEEE , 2014, p. 2382-2385Conference paper (Refereed)
    Abstract [en]

    While the topic has a long history in research, model structure selection is still one of the more challenging problems in system identification. In this tutorial we focus on impulse response modelling, and link classical techniques such as hypothesis testing and information criteria (e.g. AIC) to recent model estimation approaches, including regularisation. We discuss the problem from minimum mean-square error and maximum-likelihood perspectives.

  • 33.
    Hjalmarsson, Håkan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rivera, D. E.
    System identification: A Wiener-Hammerstein benchmark2012In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 20, no 11, p. 1095-1096Article in journal (Other academic)
  • 34.
    Hjalmarsson, Håkan
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Welsh, James S.
    The University of Newcastle, Australia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Identification of box-jenkins models using structured ARX models and nuclear norm relaxation2012In: 16th IFAC Symposium on System Identification, IFAC , 2012, p. 322-327Conference paper (Refereed)
    Abstract [en]

    In this contribution we present a method to estimate structured high order ARX models. By this we mean that the estimated model, despite its high order is close to a low order model. This is achieved by adding two terms to the least-squares cost function. These two terms correspond to nuclear norms of two Hankel matrices. These Hankel matrices are constructed from the impulse response coefficients of the inverse noise model, and the numerator polynomial of the model dynamics, respectively. In a simulation study the method is shown to be competitive as compared to the prediction error method. In particular, in the study the performance degrades more gracefully than for the Prediction Error Method when the signal to noise ratio decreases.

  • 35.
    Huang, Lirong
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On consistent estimation of farthest NMP zeros of stable LTI systems2011In: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC11), 2011, p. 5094-5099Conference paper (Refereed)
    Abstract [en]

    Recently, identification of real-valued NMP zerosof discrete-time LTI systems has been studied in a few works. Among the key results, an adaptive input design approach is presented for consistent estimation of NMP zeros of stable LTI systems. However, this result is not applicable if the sign of the first impulse response coefficient is unknown. This paper studies the problem of estimation of the farthest NMP zeros without such prior knowledge.

  • 36. Katselis, D.
    et al.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Godoy, B. I.
    Aguero, J. C.
    On experiment design for single carrier and multicarrier systems2015In: 2015 European Control Conference, ECC 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 1772-1777Conference paper (Refereed)
    Abstract [en]

    In this paper, the problem of experiment design in single input single output (SISO) single carrier (SC) systems under a deterministic channel assumption is investigated and several connections with optimal preamble designs in multicarrier (MC) systems are established. In the context of SC systems, we derive optimal input sequences for the least-squares (LS) channel estimator under an input energy constraint. We then establish certain connections to optimal input designs for LS frequency domain channel estimation in MC systems. These connections reflect similarities between SC and MC systems both quantitative, i.e., in the achievable mean square error (MSE) performance, as well as qualitative, i.e., in the actual optimal input sequences. Simulations are provided to support the derived results.

  • 37.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kofidis, Eleftherios
    On Preamble-Based Channel Estimation in OFDM/OQAM Systems2011In: Proceedings of the 19th European Signal Processing Conference (EUSIPCO 2011), EURASIP , 2011Conference paper (Refereed)
  • 38. Katselis, Dimitrios
    et al.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Application-Oriented Estimator Selection2015In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 4, p. 489-493Article in journal (Refereed)
    Abstract [en]

    Designing the optimal experiment for the recovery of an unknown system with respect to the end performance metric of interest is a recently established practice in the system identification literature. This practice leads to superior end performance to designing the experiment with respect to some generic metric quantifying the distance of the estimated model from the true one. This is usually done by choosing and fixing the estimation method to either a standard maximum likelihood (ML) or a Bayesian estimator. In this paper, we pose the intuitive question: Can we design better estimators than the usual ones with respect to an end performance metric of interest? Based on a simple linear regression example we affirmatively answer this question.

  • 39. Katselis, Dimitrios
    et al.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Beck, Carolyn L.
    Estimator selection: End-performance metric aspects2015In: Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers , 2015, p. 4430-4435Conference paper (Refereed)
    Abstract [en]

    Recently, a framework for application-oriented optimal experiment design has been introduced. In this context, the distance of the estimated system from the true one is measured in terms of a particular end-performance metric. This treatment leads to superior unknown system estimates to classical experiment designs based on usual pointwise functional distances of the estimated system from the true one. The separation of the system estimator from the experiment design is done within this new framework by choosing and fixing the estimation method to either a maximum likelihood (ML) approach or a Bayesian estimator such as the minimum mean square error (MMSE). Since the MMSE estimator delivers a system estimate with lower mean square error (MSE) than the ML estimator for finite-length experiments, it is usually considered the best choice in practice in signal processing and control applications. Within the application-oriented framework a related meaningful question is: Are there endperformance metrics for which the ML estimator outperforms the MMSE when the experiment is finite-length? In this paper, we affirmatively answer this question based on a simple linear Gaussian regression example.

  • 40.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Björnson, Emil
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bombois, Xavier
    Delft University of Technology.
    Shariati, Nafiseh
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Training sequence design for MIMO channels: an application-oriented approach2013In: EURASIP Journal on Wireless Communications and Networking, ISSN 1687-1472, E-ISSN 1687-1499, Vol. 2013, p. 245-Article in journal (Refereed)
    Abstract [en]

    In this paper, the problem of training optimization for estimating a multiple-input multiple-output (MIMO) flat fading channel in the presence of spatially and temporally correlated Gaussian noise is studied in an application-oriented setup. So far, the problem of MIMO channel estimation has mostly been treated within the context of minimizing the mean square error (MSE) of the channel estimate subject to various constraints, such as an upper bound on the available training energy. We introduce a more general framework for the task of training sequence design in MIMO systems, which can treat not only the minimization of channel estimator's MSE but also the optimization of a final performance metric of interest related to the use of the channel estimate in the communication system. First, we show that the proposed framework can be used to minimize the training energy budget subject to a quality constraint on the MSE of the channel estimator. A deterministic version of the 'dual' problem is also provided. We then focus on four specific applications, where the training sequence can be optimized with respect to the classical channel estimation MSE, a weighted channel estimation MSE and the MSE of the equalization error due to the use of an equalizer at the receiver or an appropriate linear precoder at the transmitter. In this way, the intended use of the channel estimate is explicitly accounted for. The superiority of the proposed designs over existing methods is demonstrated via numerical simulations.

  • 41.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Frequency smoothing gains in preamble-based channel estimation for multicarrier systems2013In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 93, no 9, p. 2777-2782Article in journal (Refereed)
    Abstract [en]

    In this paper, the problem of least-squares (LS) preamble-based channel estimation in multicarrier systems under a deterministic channel assumption is revisited. The analysis is presented for the filterbank multicarrier offset quadrature amplitude modulation (FBMC/OQAM) system, although the derived results hold unchanged for the cyclic prefixed orthogonal frequency division multiplexing (CP-OFDM) system, as well. Assuming independent noise disturbances per subcarrier, we show that frequency-domain smoothing techniques can be used to improve the mean square error (MSE) performance. Depending on the number of subcarriers, the choice of smoothing may be different. We also present the time-domain formulation of the frequency-domain smoothing. Based on this formulation, we show that frequency-domain smoothing techniques can minimize the variance of the LS channel estimator, while they can further reduce its MSE by trading bias for variance. Simulations are given to support the derived results.

  • 42. Katselis, Dimitrios
    et al.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Godoy, Boris I.
    Agueero, Juan C.
    Beck, Carolyn L.
    On the end-performance metric estimator selection2015In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 58, p. 22-27Article in journal (Refereed)
    Abstract [en]

    It is well known that appropriately biasing an estimator can potentially lead to a lower mean square error (MSE) than the achievable MSE within the class of unbiased estimators. Nevertheless, the choice of an appropriate bias is generally unclear and only recently there have been attempts to systematize such a selection. These systematic approaches aim at introducing MSE bounds that are lower than the unbiased Cramer-Rao bound (CRB) for all values of the unknown parameters and at choosing biased estimators that beat the standard maximum-likelihood (ML) and/or least squares (LS) estimators in the finite sample case. In this paper, we take these approaches one step further and investigate the same problem from the aspect of an end-performance metric different than the classical MSE. This study is motivated by recent advances in the area of system identification indicating that the optimal experiment design Should be done by taking into account the end-performance metric of interest and not by quantifying a quadratic distance of the unknown model from the true one.

  • 43.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Applications-oriented least squares experiment design in multicarrier communication systems2013In: Proceedings of the 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing (ALCOSP 2013), 2013, p. 74-79Conference paper (Refereed)
    Abstract [en]

    Recently, the application-oriented framework for pilot design in communication systems has been introduced. This framework is mostly appropriate for such a design since the training sequences are selected to optimize a final performance metric of interest and not some of the classical metrics quantifying the distance between the estimated model and the true one, e.g., the mean square error (MSE). In this perspective, the known pilot sequences that are optimal for any communication system and for any estimation task have to be reexamined. In this paper, the problem of training pilot design for the task of channel estimation in cyclic prefixed orthogonal frequency division multiplexing (CP-OFDM) systems is revisited. So far, the optimal training sequences for least squares (LS) channel estimation with respect to minimizing the channel MSE under a training energy constraint have been derived. Here, we investigate the same problem for the LS channel estimator, but when the design takes into account an end performance metric of interest, namely, the symbol estimate MSE due to the use of per subcarrier zero forcing (ZF) symbol estimators/equalizers at the receiver side. Based on some convex approximations, we verify that the optimal full preamble, i.e, the preamble employing pilots on all subcarriers, for LS channel estimation in its classical context are near optimal in the aforementioned application-oriented context for the ZF symbol estimate MSE in certain target signal-to-noise ratio (SNR) operating intervals.

  • 44.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Least Squares End Performance Experiment Design in Multicarrier Systems: The Sparse Preamble Case2014In: 2014 European Control Conference (ECC), IEEE , 2014, p. 13-18Conference paper (Refereed)
    Abstract [en]

    In this paper, the problem of experiment design for the task of channel identification in cyclic prefixed orthogonal frequency division multiplexing (CP-OFDM) systems is revisited. So far, the optimal input sequences for least squares (LS) channel identification with respect to minimizing the channel mean square error (MSE) under an input energy constraint have been derived. Here, we investigate the same problem for the LS channel estimator, but when the design takes into account an end performance metric of interest, namely, the symbol estimate MSE. Based on some convex approximations, we verify that optimal sparse preambles, i.e, input vectors employing as many pilots as the channel length, for LS channel estimation in its classical context are near optimal in the aforementioned application-oriented context for the symbol estimate MSE.

  • 45.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Chernoff convexification for chance constrained MIMO training sequence design2012In: Signal Processing Advances in Wireless Communications (SPAWC), 2012 IEEE 13th International Workshop on, IEEE , 2012, p. 40-44Conference paper (Refereed)
    Abstract [en]

    In this paper, multiple input multiple output (MIMO) channel estimation formulated as a chance constrained problem is investigated. The chance constraint is based on the presumption that the estimated channel can be used in an application to achieve a given performance level with a prescribed probability. The aforementioned performance level is dictated by the particular application of interest. The resulting optimization problem is known to be nonconvex in most cases. To this end, convexification is attempted by employing a Chernoff inequality. As an application, we focus on the estimation of MIMO wireless channels based on a general L-optimality type of performance measure.

  • 46.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Chernoff relaxation on the problem of application-oriented finite sample experiment design2012In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE , 2012, p. 202-207Conference paper (Refereed)
    Abstract [en]

    In this paper, application-oriented experiment design formulated as a chance constrained problem is investigated. The chance constraint is based on the presumption that the estimated model can be used in an application to achieve a given performance level with a prescribed probability. The aforementioned performance level is dictated by the particular application of interest. The resulting optimization problem is known to be nonconvex in most cases. To this end, convexification is attempted by employing a Chernoff relaxation. As an application, we focus on the identification of multiple input multiple output (MIMO) wireless channel models based on a general L-optimality type of performance measure.

  • 47.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Application-Oriented Finite Sample Experiment Design: A Semidefinite Relaxation Approach2012In: IFAC Proceedings Volumes (IFAC-PapersOnline) v16 nPART 1: System Identification, International Federation of Automatic Control , 2012, p. 1635-1640Conference paper (Refereed)
    Abstract [en]

    In this paper, the problem of input signal design with the property that the estimated model satisfies a given performance level with a prescribed probability is studied. The aforementioned performance level is associated with a particular application. This problem is well-known to fall within the class of chance-constrained optimization problems, which are nonconvex in most cases. Convexification is attempted based on a Markov inequality, leading to semidefinite programming (SDP) relaxation formulations. As applications, we focus on the identification of multiple input multiple output (MIMO) wireless communication channel models for minimum mean square error (MMSE) channel equalization and zero-forcing (ZF) precoding.

  • 48.
    Katselis, Dimitrios
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Welsh, James S.
    The University of Newcastle, Australia.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Robust Experiment Design for System Identification via Semi-Infinite Programming Techniques2012In: Proceedings of the 16th IFAC Symposium on System Identification (SYSID 2012), 2012, p. 680-685Conference paper (Refereed)
    Abstract [en]

    Robust optimal experiment design for dynamic system identification is cast as a minmax optimization problem, which is infinite-dimensional. If the input spectrum is discretized (either by considering a Riemmann approximation, or by restricting it to the span of a finite dimensional linear space), this problem falls within the class of semi-infinite convex programs. One approach to this optimization problem of infinite constraints is the so called "scenario approach", which is based on a probabilistic description of the uncertainty to deliver a finite program that attempts to approximate the optimal solution with a prescribed probability. In this paper, we propose as an alternative an exchange algorithm based on some recent advances in the field of semi-infinite programming to tackle the same problem. This method is compared with the scenario approach both from the aspects of accuracy and computational efficiency. Furthermore, the comparison includes the MATLAB semi-infinite solver fseminf to provide a general palette of methods approximating the robust optimal design problem.

  • 49. Krishnamurthy, Vikram
    et al.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Reduced Complexity HMM Filtering With Stochastic Dominance Bounds: A Convex Optimization Approach2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 23, p. 6309-6322Article in journal (Refereed)
    Abstract [en]

    This paper uses stochastic dominance principles to construct upper and lower sample path bounds for Hidden Markov Model (HMM) filters. We consider an HMM consisting of an X-state Markov chain with transition matrix P. By using convex optimization methods for nuclear norm minimization with copositive constraints, we construct low rank stochastic matrices (P) under bar and (P) over bar so that the optimal filters using (P) under bar, (P) over bar provably lower and upper bound (with respect to a partially ordered set) the true filtered distribution at each time instant. Since (P) under bar and (P) over bar are low rank (say R), the computational cost of evaluating the filtering bounds is O(XR) instead of O(X-2). A Monte-Carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior. Finally, explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds in terms of the Dobrushin coefficient.

  • 50.
    Krishnamurthy, Vikram
    et al.
    The University of British Columbia.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Computing monotone policies for Markov decision processes by exploiting sparsity2013In: 2013 3rd Australian Control Conference, AUCC 2013, IEEE , 2013, p. 6697239-Conference paper (Refereed)
    Abstract [en]

    This paper considers Markov decision processes whose optimal policy is a randomized mixture of monotone increasing policies. Such monotone policies have an inherent sparsity structure. We present a two-stage convex optimization algorithm for computing the optimal policy that exploits the sparsity. It combines an alternating direction method of multipliers (ADMM) to solve a linear programming problem with respect to the joint action state probabilities, together with a sub-gradient step that promotes the monotone sparsity pattern in the conditional probabilities of the action given the state. In the second step, sum-of-norms regularization is used to stress the monotone structure of the optimal policy.

123 1 - 50 of 129
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