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  • 1.
    Deleskog, Viktor
    et al.
    Totalförsvarets forskningsinstitut (FOI).
    Habberstad, Hans
    Totalförsvarets forskningsinstitut (FOI).
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wahlström, Niklas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust NLS Sensor Localization using MDS Initialization2014In: 17th International Conference on Information Fusion (FUSION), 2014, Institute of Electrical and Electronics Engineers (IEEE), 2014, p. 1-7Conference paper (Refereed)
    Abstract [en]

    Before a sensor network can be used for target localization, the locations of the sensors need to be determined. We approach this calibration step by moving a source to distinct positions around the network. At each position, the range to each sensor is measured,and from these range measurements the sensor locations can be estimated by solving a nonlinear least squares (NLS) problem. Here we formulate the NLS problem and describe how to robustly initialize it by the use of multidimensional scaling. The method is evaluated on both simulations and real data from an acoustic sensor network. Withas few as six source positions, a robust calibration is demonstrated that gives a position error about the same size as the range error.  In the acoustic example this RMSE is less than 40 cm.

  • 2.
    Eriksson, Mats
    et al.
    Linköping University, Department of Physics, Chemistry and Biology, Chemical and Optical Sensor Systems. Linköping University, Faculty of Science & Engineering.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bjorklund, Robert
    Linköping University, Department of Physics, Chemistry and Biology.
    Winquist, Fredrik
    Linköping University, Department of Physics, Chemistry and Biology, Biosensors and Bioelectronics. Linköping University, Faculty of Science & Engineering.
    Sundgren, Hans
    Linköping University, Department of Physics, Chemistry and Biology, Chemical and Optical Sensor Systems. Linköping University, Faculty of Science & Engineering.
    Lundström, Ingemar
    Linköping University, Department of Physics, Chemistry and Biology, Biosensors and Bioelectronics. Linköping University, Faculty of Science & Engineering.
    Drinking water monitoring with voltammetric sensors2011In: Procedia Engineering, ISSN 1877-7058, E-ISSN 1877-7058, Vol. 25, p. 1165-1168Article in journal (Refereed)
    Abstract [en]

    Pulsed voltammetry has been applied to drinking water monitoring. This non-selective technique facilitates detection of several different threats to the drinking water. A multivariate algorithm shows that anomaly detection is possible with a minimum of false alarms. Multivariate analysis can also be used to classify different types of substances added to the drinking water. Low concentrations of sewage water contaminating the drinking water can be detected. A network of such sensors is envisaged to facilitate real-time and on-line monitoring of drinking water distribution networks.

  • 3.
    Eriksson, Mats
    et al.
    Linköping University, Department of Physics, Chemistry and Biology, Applied Physics. Linköping University, The Institute of Technology.
    Winquist, Fredrik
    Linköping University, Department of Physics, Chemistry and Biology, Applied Physics. Linköping University, The Institute of Technology.
    Bjorklund, Robert
    Linköping University, Department of Physics, Chemistry and Biology, Applied Physics. Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sundgren, Hans
    Linköping University, Department of Physics, Chemistry and Biology, Applied Physics. Linköping University, The Institute of Technology.
    Lundström, Ingemar
    Linköping University, Department of Physics, Chemistry and Biology, Applied Physics. Linköping University, The Institute of Technology.
    Event Detection in Crisis Management Systems2009In: Procedia Chemistry, ISSN 1876-6196, E-ISSN 1876-6196, Vol. 1, no 1, p. 1055-1058Article in journal (Refereed)
    Abstract [en]

    The EVENT project concerns drinking water surveillance and includes sensors and algorithms that detect anomalies in the drinking water properties, communication of the evaluated sensor data to a crises management system and presentation of information that is relevant for the end users of the crises management system. We have chosen to focus on a sensor technique based on an "electronic tongue", since this robust type of non-selective sensor, can detect a plurality of anomalies without the need of a specific sensor for each type of event. Measurements of natural variations and contamination events are presented and discussed.

  • 4.
    Gustafsson, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Mathai, George
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Habberstad, Hans
    Swedish Defence Research Agency (FOI).
    Direction of Arrival Estimation in Sensor Arrays Using Local Series Expansion of the Received Signal2015In: 18th International Conference of Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)
    Abstract [en]

    A local series expansion of a received signal is pro-posed for computing direction of arrival (DOA) in sensor arrays. The advantages compared to classical DOA estimation methods include general sensor configurations, ultra-slow sampling, smalldimension of the arrays, and that it applies for both narrowbandand wideband signals without prior knowledge of the signals. This makes the method well suited for DOA estimation in sensor networks where size and energy consumption have to be small. We generalize the common far-field assumption of the target toalso include the near-field, which enables target tracking usinga network of sensor arrays in one framework.

  • 5.
    Johansson, Jimmy
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Cooper, Matthew
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Interactive Analysis of Time-Varying Systems Using Volume Graphics2007Report (Other academic)
    Abstract [en]

    We show how 3-dimensional volume graphics can be used as a tool in system identification. Time-dependent dynamics often leave a significant residual with linear, time-invariant models. The structure of this residual is decisive for the subsequent modelling, and by using advanced visualization techniques, the modeller may gain a deeper insight into this structure than that which can be obtained from standard correlation analysis. We present a development platform that merges a rich variety of estimation programs with state of the art visualization techniques.

  • 6.
    Johansson, Jimmy
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Cooper, Matthew
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Interactive Analysis of Time-Varying Systems Using Volume Graphics2004In: Proceedings of the 43rd IEEE Conference on Decision and Control, 2004, p. 5083-5087Conference paper (Refereed)
    Abstract [en]

    We show how 3-dimensional volume graphics can be used as a tool in system identification. Time-dependent dynamics often leave a significant residual with linear, time-invariant models. The structure of this residual is decisive for the subsequent modelling, and by using advanced visualization techniques, the modeller may gain a deeper insight into this structure than that which can be obtained from standard correlation analysis. We present a development platform that merges a rich variety of estimation programs with state of the art visualization techniques.

  • 7.
    Johansson, Jimmy
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Cooper, Matthew
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Interactive Visualization as a Tool for Analysing Time-Varying and Non-Linear Systems2005In: Proceedings of the 16th IFAC World Congress, 2005, p. 95-95Conference paper (Refereed)
    Abstract [en]

    This paper shows how 3-dimensional interactive visualization can be used as a tool in system identification. Non-linear or time-dependent dynamics often leave a significant residual with linear, time-invariant models. The structure of this residual is decisive for the subsequent modelling, and by using advanced visualization techniques, the modeller may gain a deeper insight into this structure than can be obtained by standard correlation analysis.

  • 8.
    Johansson, Jimmy
    et al.
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Cooper, Matthew
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Interactive Visualization as a Tool for Analysing Time-Varying and Non-Linear Systems2007Report (Other academic)
    Abstract [en]

    This paper shows how 3-dimensional interactive visualization can be used as a tool in system identification. Non-linear or time-dependent dynamics often leave a significant residual with linear, time-invariant models. The structure of this residual is decisive for the subsequent modelling, and by using advanced visualization techniques, the modeller may gain a deeper insight into this structure than can be obtained by standard correlation analysis.

  • 9.
    Johansson, Jimmy
    et al.
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Ljung, Patric
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Cooper, Matthew
    Linköping University, Department of Science and Technology, Media and Information Technology. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Interactive Visualization Approaches to the Analysis of System Identification Data2004In: Information Visualization, 2004. INFOVIS 2004. IEEE Symposium on, 2004Conference paper (Refereed)
    Abstract [en]

    We propose an interactive visualization approach to finding a mathematical model for a real world process, commonly known in the field of control theory as system identification. The use of interactive visualization techniques provides the modeller with instant visual feedback which facilitates the model validation process. When working interactively with such large data sets, as are common in system identification, methods to handle this data efficiently are required. We are developing approaches based on data streaming to´meet this need.

  • 10.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Projection Techniques for Classification and Identification2005Doctoral thesis, monograph (Other academic)
    Abstract [en]

    It is very well understood how to evaluate and find, in different senses, optimal linear projections of measurements on linear systems. The solution to the linear least squares problem, the principal component analysis and partial least squares are all examples of well known techniques that work very well as long as the dependencies in data are fairly linear. When the measurements are due to nonlinear systems or due to measurements on a finite number of objects (classification), it is much more difficult not only to find an optimal projection, but also to asses a general quality measure to a particular projection. The dimension of the measurement is often high, so the search for projections is motivated by the desire to visualize in 2-dimensional diagrams, the need to reduce data with minimal loss (data compression) and to efficiently parameterize nonlinear models.

    For classication of measurements on a finite number of objects, the projection quality is naturally connected to how accurate the classification can be conducted despite the data reduction due to the projection. In this work, methods to estimate this accuracy as well as numerical methods to find the optimal projection with respect to this estimated accuracy are investigated. It is found that the nonlinear conjugate gradient method on the Grassmann manifold is one of the most time efficient numerical optimization methods to use with this type of problems.

    For nonlinear dynamical systems modeled by nonlinear ARX model structures, the challenge is to find projections of the regression vector that isolate a nonlinear curve or surface. It is not obvious that such low-dimensional projections that well fit the system always exist. When they do exist, for instance when the nonlinearities enter the system additively, we show that the projection can rather efficiently be estimated by using multi-index models fitted by least squares criteria.

    There is also an interesting hybrid case where a continuous system is analyzed by measurements on a nite number of calibration classes. We show how the resulting measurement classes can be used by techniques borrowed from discriminant analysis in order to find good projections where a continuous regression can be performed.

  • 11.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Subspace Optimization Techniques for Classification Problems2003Report (Other academic)
    Abstract [en]

    The nonlinear conjugate gradients method is a very powerful program in the search for Bayes error optimal linear subspaces for classification problems. In this report, techniques to find linear subspaces where the classification error is minimized are surveyed. Summary statistics models of normal populations are used to form smooth, non-convex objective functions of a linear transformation that reduces the dimensionality. Objective functions that are based on the Mahalanobis or Bhattacharyya distances and that are closely related to the probability of misclassification are derived, as well as their subspace gradients. Different approaches to minimize those objective functions are investigated: Householder and Givens parameterizations as well as steepest descent and conjugate gradient methods. The methods are evaluated on experimental data with respect to convergence rate and subspace classification accuracy.

  • 12.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Subspace Selection Techniques for Classification Problems2002Licentiate thesis, monograph (Other academic)
    Abstract [en]

    The main topic of this thesis is linear subspaces for regression - how to find the subspaces and how to evaluate them. The motivation to do regression in a subspace is numerical as well as computational - numerical in the sense that the subspace can filter out the relevant components or features of the problem, computationally in the sense that this filtering can be done quickly and then can nonlinear predictionby artificial neural networks, for instance, be conducted in lower dimensionality.

    The theory is developed in a versatile regression framework into which both discrete (classification) and continuous (quantification) regression can be put. The target is to find good future predictors from past observations. The foundation is the assumption that observations (or measurements) are drawn from a probability distribution, and from there on the theory is developed towards practical results and algorithms. The emphasis is however put on classification problems.

    The applications are many and ranges from identification of dynamical systems to data mining and compression. Particular interest is given processing of sensor data - how to learn something from calibration measurements that in turn can be used to learn something about future unknown samples. In focus are the electronic nose (smell sensor) and the electronic tongue (taste sensor).

    Three new algorithms are introduced and described. The Asymmetric Class Projection is a computationally efficient method to find subspaces for classification between two classes with small mean and large covariance difference. The Optimal Discriminative Projection (ODP) is an algorithm that uses a particular composition of Givens rotations to parameterize all subspaces. The subspaces are optimized for classification. The Clustered Regression Analysis uses the ODP subspace for conditional expectation prediction.

  • 13.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Guldogan, Mehmet B.
    Turgut Ozal University, Turkiet.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Habberstad, Hans
    Totalförsvarets Forskningsinstitut, FOI.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Acoustic Source Localization in a Network of Doppler Shift Sensors2013In: 16th International Conference on Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2013Conference paper (Refereed)
    Abstract [en]

    It is well-known that the motion of an acoustic source can be estimated from Doppler shift observations. It ishowever not obvious how to design a sensor network to efficiently deliver the localization service. In this work a rather simplistic motion model is proposed that is aimed at sensor networks with realistic numbers of sensor nodes. It is also described how to efficiently solve the associated least squares optimization problem by Gauss-Newton variable projection techniques, and how to initiate the numerical search from simple features extracted from the observed frequency series. The methods are demonstrated onreal data by determining the distance to a passing propellerdriven aircraft and by localizing an all-terrain vehicle. It is concluded that the processing components included are fairly mature for practical implementations in sensor networks.

  • 14.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Distributed localization using acoustic Doppler2015In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 107, p. 43-53Article in journal (Refereed)
    Abstract [en]

     It is well-known that the motion of an acoustic source can be estimated from Doppler shift observations. It is however not obvious how to design a sensor network to efficiently deliver the localization service. In this work a rather simplistic motion model is proposed that is aimed at sensor networks with realistic numbersof sensor nodes. It is also described how to efficiently solve the associated least squares optimization problem by Gauss-Newton variable projection techniques, and how to initiate the numerical search from simple features extracted from the observed frequency series. The methods are evaluated by Monte Carlo simulations and demonstrated on real data by localizing an all-terrain vehicle. Itis concluded that the processing components included are fairly mature for practical implementations in sensor networks.

  • 15.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Johansson, Jimmy
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Ljung, Patric
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Cooper, Matthew
    Linköping University, Department of Science and Technology, Visual Information Technology and Applications (VITA). Linköping University, The Institute of Technology.
    Interactive Visualization Approaches to the Analysis of System Identification Data2004In: Proceedings of the 10th IEEE Symposium on Information Visualization, 2004, p. 23-Conference paper (Refereed)
    Abstract [en]

    We propose an interactive visualization approach to finding a mathematical model for a real world process, commonly known in the field of control theory as system identification. The use of interactive visualization techniques provides the modeller with instant visual feedback which facilitates the model validation process. When working interactively with such large data sets, as are common in system identification, methods to handle this data efficiently are required. We are developing approaches based on data streaming to meet this need.

  • 16.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Clustered Regression Analysis2002In: Proceedings of the 41st IEEE Conference on Decision and Control, 2002, p. 1838-1844 vol.2Conference paper (Refereed)
    Abstract [en]

    Cluster structure in (multicollinear) data can be utilized by pattern recognition methods in order to find adequate subspaces for nonlinear regression. When regressing a particular severely nonlinear function, it is demonstrated that this approach is superior to polynomial PLS. It is also demonstrated that for nonlinear functions, the choice of regressing explained variables onto the explaining variables, or vice-versa, is not arbitrary. Numerical experiments indicate that the classical statistical model is more powerful than the inverse regression approach.

  • 17.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Clustered Regression Analysis2002Report (Other academic)
    Abstract [en]

    Cluster structure in (multicollinear) data can be utilized by pattern recognition methods in order to find adequate subspaces for nonlinear regression. When regressing a particular severely nonlinear function, it is demonstrated that this approach is superior to polynomial PLS. It is also demonstrated that for nonlinear functions, the choice of regressing explained variables onto the explaining variables, or vice-versa, is not arbitrary. Numerical experiments indicate that the classical statistical model is more powerful than the inverse regression approach.

  • 18.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nonlinear Dynamics Identified by Multi-Index Models2007Report (Other academic)
    Abstract [en]

    For a class of nonlinear systems, the residual of a well fitted model has low intrinsic dimensionality. For these systems, a particular low-dimensional linear projection of the regressor will facilitate both visualization of the nonlinearities and subsequent nonlinear modeling. The least squares fit of polynomial and piecewise affine functions are used as criterion by which numerical programs search for the linear projection that gives the best low-dimensional description of the residual. For a simulated water tank and for real life data sampled from an electronic circuit, the regressor can be projected down to 2 dimensions and still yield a model simulation fit of about 99%. The electronic circuit data can be described by a model structure with far less parameters than conventional, nonlinear black-box models.

  • 19.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nonlinear Dynamics Isolated by Delaunay Triangulation Criteria2004In: Proceedings of the 43rd IEEE Conference on Decision and Control, 2004, p. 3862-3867 Vol.4Conference paper (Refereed)
    Abstract [en]

    Inspired by an idea by Q. Zhang, we show that Delaunay triangulation of data points sampled from a system with an additive nonlinearity gives a criterion by which a linear projection can be found that isolates the nonlinear dependence, leaving out the linear one. This isolation means the nonlinear modeling can be confined to a regressor space of lower dimensionality, which in turn means over-parameterization can be avoided. Monte Carlo simulations indicate that a particular criterion built on triangle asymmetries has a minimum that coincides with the sampled system nonlinear part. The criterion is however complex to compute and non-convex, which makes it difficult to optimize globally.

  • 20.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nonlinear Dynamics Isolated by Delaunay Triangulation Criteria2004Report (Other academic)
    Abstract [en]

    Inspired by an idea by Q. Zhang, we show that Delaunay triangulation of data points sampled from a system with an additive nonlinearity gives a criterion by which a linear projection can be found that isolates the nonlinear dependence, leaving out the linear one. This isolation means the nonlinear modeling can be confined to a regressor space of lower dimensionality, which in turn means over-parameterization can be avoided. Monte Carlo simulations indicate that a particular criterion built on triangle asymmetries has a minimum that coincides with the sampled system nonlinear part. The criterion is however complex to compute and non-convex, which makes it difficult to optimize globally.

  • 21.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Savas, Berkant
    Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.
    Rank Reduction and Volume Minimization Approach to State-Space Subspace System Identification2006In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 86, no 11, p. 3275-3285Article in journal (Refereed)
    Abstract [en]

    In this paper we consider the reduced rank regression problem

    solved by maximum-likelihood-inspired state-space subspace system identification algorithms. We conclude that the determinant criterion is, due to potential rank-deficiencies, not general enough to handle all problem instances. The main part of the paper analyzes the structure of the reduced rank minimization problem and identifies signal properties in terms of geometrical concepts. A more general minimization criterion is considered, rank reduction followed by volume minimization. A numerically sound algorithm for minimizing this criterion is presented and validated on both simulated and experimental data.

  • 22.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Spångeus, Per
    Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
    A Novel Feature Extraction Algorithm for Asymmetric Classification2004In: IEEE Sensors Journal, ISSN 1530-437X, E-ISSN 1558-1748, Vol. 4, p. 643-650Article in journal (Refereed)
    Abstract [en]

    A linear feature extraction technique for asymmetric distributions is introduced, the asymmetric class projection (ACP). By emph {asymmetric classification} is understood discrimination among distributions with different covariance matrices. Two distributions with unequal covariance matrices do not in general have a symmetry plane, a fact that makes the analysis more difficult compared to the symmetric case. The ACP is similar to linear discriminant analysis (LDA) in the respect that both aim at extracting discriminating features (linear combinations or projections) from many variables. However, the drawback of the well known LDA is the assumption of symmetric classes with separated centroids. The ACP, incontrast, works on (two) possibly concentric distributions with unequal covariance matrices. The ACP is tested on data from anarray of semiconductor gas sensors with the purpose of distinguish bad grain from good.

  • 23.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Spångéus, Per
    Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
    A Novel Feature Extraction Algorithm for Asymmetric Classification2002Report (Other academic)
    Abstract [en]

    A linear feature extraction technique for asymmetric distributions is introduced, the asymmetric class projection (ACP). By emph {asymmetric classification} is understood discrimination among distributions with different covariance matrices. Two distributions with unequal covariance matrices do not in general have a symmetry plane, a fact that makes the analysis more difficult compared to the symmetric case. The ACP is similar to linear discriminant analysis (LDA) in the respect that both aim at extracting discriminating features (linear combinations or projections) from many variables. However, the drawback of the well known LDA is the assumption of symmetric classes with separated centroids. The ACP, incontrast, works on (two) possibly concentric distributions with unequal covariance matrices. The ACP is tested on data from anarray of semiconductor gas sensors with the purpose of distinguish bad grain from good.

  • 24.
    Lindgren, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Spångéus, Per
    Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
    A Novel Feature Extraction Algorithm for Asymmetric Classification II2003Report (Other academic)
    Abstract [en]

    A linear feature extraction technique for asymmetric distributions is introduced, the asymmetric class projection (ACP). By asymmetric classification is understood discrimination among distributions with different covariance matrices. Two distributions with unequal covariance matrices do not in general have a symmetry plane, a fact that makes the analysis more difficult compared to the symmetric case. The ACP is similar to linear discriminant analysis (LDA) in the respect that both aim at extracting discriminating features (linear combinations or projections) from many variables. However, the drawback of the well known LDA is the assumption of symmetric classes with separated centroids. The ACP, incontrast, works on (two) possibly concentric distributions with unequal covariance matrices. The ACP is tested on data from anarray of semiconductor gas sensors with the purpose of distinguish bad grain from good.

  • 25.
    Ljung, Lennart
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nonlinear Dynamics Identified by Multi-Index Models2005In: Proceedings of the 16th IFAC World Congress, 2005, p. 32-32Conference paper (Refereed)
    Abstract [en]

    For a class of nonlinear systems, the residual of a well fitted model has low intrinsic dimensionality. For these systems, a particular low-dimensional linear projection of the regressor will facilitate both visualization of the nonlinearities and subsequent nonlinear modeling. The least squares fit of polynomial and piecewise affine functions are used as criterion by which numerical programs search for the linear projection that gives the best low-dimensional description of the residual. For a simulated water tank and for real life data sampled from an electronic circuit, the regressor can be projected down to 2 dimensions and still yield a model simulation fit of about 99%. The electronic circuit data can be described by a model structure with far less parameters than conventional, nonlinear black-box models.

  • 26.
    Spångéus, Per
    et al.
    Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Efficient Parameterization for the Dimensional Reduction Problem2003Report (Other academic)
    Abstract [en]

    A new method to optimize with orthonormal constraints is described, where a particular composition of plane (Givens) rotations is used to parameterize decision variables in terms of angles. It is showed that this parameterization is complete and that any orthonormal k-by-nmatrix can be derived to a set of no more than kn-k(k+1) angles. The technique is applied to the emph {feature extraction problem} where a linear subspace is optimized with respect to non-linear objective functions. The Optimal Discriminative Projection (ODP) algorithm is described. ODP is a data compression or feature extraction algorithm that combines powerful model optimization with regularization to avoid over training. The ODP is used primarily for classification problems.

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