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  • 1. Order onlineBuy this publication >>
    Ardeshiri, Tohid
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Analytical Approximations for Bayesian Inference2015Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Bayesian inference is a statistical inference technique in which Bayes’ theorem is used to update the probability distribution of a random variable using observations. Except for few simple cases, expression of such probability distributions using compact analytical expressions is infeasible. Approximation methods are required to express the a priori knowledge about a random variable in form of prior distributions. Further approximations are needed to compute posterior distributions of the random variables using the observations. When the computational complexity of representation of such posteriors increases over time as in mixture models, approximations are required to reduce the complexity of such representations.

    This thesis further extends existing approximation methods for Bayesian inference, and generalizes the existing approximation methods in three aspects namely; prior selection, posterior evaluation given the observations and maintenance of computation complexity.

    Particularly, the maximum entropy properties of the first-order stable spline kernel for identification of linear time-invariant stable and causal systems are shown. Analytical approximations are used to express the prior knowledge about the properties of the impulse response of a linear time-invariant stable and causal system.

    Variational Bayes (VB) method is used to compute an approximate posterior in two inference problems. In the first problem, an approximate posterior for the state smoothing problem for linear statespace models with unknown and time-varying noise covariances is proposed. In the second problem, the VB method is used for approximate inference in state-space models with skewed measurement noise.

    Moreover, a novel approximation method for Bayesian inference is proposed. The proposed Bayesian inference technique is based on Taylor series approximation of the logarithm of the likelihood function. The proposed approximation is devised for the case where the prior distribution belongs to the exponential family of distributions.

    Finally, two contributions are dedicated to the mixture reduction (MR) problem. The first contribution, generalize the existing MR algorithms for Gaussian mixtures to the exponential family of distributions and compares them in an extended target tracking scenario. The second contribution, proposes a new Gaussian mixture reduction algorithm which minimizes the reverse Kullback-Leibler divergence and has specific peak preserving properties.

    List of papers
    1. Maximum entropy properties of discrete-time first-order stable spline kernel
    Open this publication in new window or tab >>Maximum entropy properties of discrete-time first-order stable spline kernel
    Show others...
    2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 66, p. 34-38Article in journal (Refereed) Published
    Abstract [en]

    The first order stable spline (SS-1) kernel (also known as the tunedcorrelated kernel) is used extensively in regularized system identification, where the impulse response is modeled as a zero-mean Gaussian process whose covariance function is given by well designed and tuned kernels. In this paper, we discuss the maximum entropy properties of this kernel. In particular, we formulate the exact maximum entropy problem solved by the SS-1 kernel without Gaussian and uniform sampling assumptions. Under general sampling assumption, we also derive the special structure of the SS-1 kernel (e.g. its tridiagonal inverse and factorization have closed form expression), also giving to it a maximum entropy covariance completion interpretation.

    Keywords
    System identification;Regularization method;Kernel structure;Maximum entropy
    National Category
    Signal Processing
    Identifiers
    urn:nbn:se:liu:diva-121618 (URN)10.1016/j.automatica.2015.12.009 (DOI)
    Available from: 2015-09-28 Created: 2015-09-28 Last updated: 2017-12-01Bibliographically approved
    2. Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances
    Open this publication in new window or tab >>Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances
    2015 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 12, p. 2450-2454Article in journal (Refereed) Published
    Abstract [en]

    We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.

    Place, publisher, year, edition, pages
    Institute of Electrical and Electronics Engineers (IEEE), 2015
    Keywords
    Adaptive smoothing, Kalman filtering, noise covariance, Rauch-Tung-Striebel smoother, sensor calibration, time-varying noiseco variances, variational Bayes
    National Category
    Signal Processing
    Identifiers
    urn:nbn:se:liu:diva-121617 (URN)10.1109/LSP.2015.2490543 (DOI)000364207300007 ()
    Note

    At the time for thesis presentation publication was in status: Manuscript

    Available from: 2015-09-28 Created: 2015-09-28 Last updated: 2018-03-09Bibliographically approved
    3. Robust Inference for State-Space Models with Skewed Measurement Noise
    Open this publication in new window or tab >>Robust Inference for State-Space Models with Skewed Measurement Noise
    2015 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 11, p. 1898-1902Article in journal (Refereed) Published
    Abstract [en]

    Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-t-distributed measurement noise. The proposed filter and smoother are compared with conventional low-complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.

    Place, publisher, year, edition, pages
    IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2015
    Keywords
    Kalman filter; robust filtering; RTS smoother; skew t; skewness; t-distribution; variational Bayes
    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering
    Identifiers
    urn:nbn:se:liu:diva-120129 (URN)10.1109/LSP.2015.2437456 (DOI)000356458700003 ()
    Note

    Funding Agencies|Tampere University of Technology Graduate School; Finnish Doctoral Programme in Computational Sciences (FICS); Foundation of Nokia Corporation; Swedish research council (VR), project ETT [621-2010-4301]

    Available from: 2015-07-14 Created: 2015-07-13 Last updated: 2017-12-04
    4. Bayesian Inference via Approximation of Log-likelihood for Priors in Exponential Family
    Open this publication in new window or tab >>Bayesian Inference via Approximation of Log-likelihood for Priors in Exponential Family
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case where the prior distribution belongs to the exponential family of distributions. The logarithm of the likelihood function is linearized with respect to the sufficient statistic of the prior distribution in exponential family such that the posterior obtains the same exponential family form as the prior. Similarities between the proposed method and the extended Kalman filter for nonlinear filtering are illustrated. Further, an extended target measurement update for target models where the target extent is represented by a random matrix having an inverse Wishart distribution is derived. The approximate update covers the important case where the spread of measurement is due to the target extent as well as the measurement noise in the sensor.

    National Category
    Signal Processing
    Identifiers
    urn:nbn:se:liu:diva-121616 (URN)
    Available from: 2015-09-28 Created: 2015-09-28 Last updated: 2015-10-05Bibliographically approved
    5. Greedy Reduction Algorithms for Mixtures of Exponential Family
    Open this publication in new window or tab >>Greedy Reduction Algorithms for Mixtures of Exponential Family
    2015 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 6, p. 676-680Article in journal (Refereed) Published
    Abstract [en]

    In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a Gaussian inverse Wishart probability hypothesis density (PHD) filter.

    Place, publisher, year, edition, pages
    Institute of Electrical and Electronics Engineers (IEEE), 2015
    Keywords
    Exponential family; extended target; integral square error; Kullback-Leibler divergence; mixture density; mixture reduction; target tracking
    National Category
    Electrical Engineering, Electronic Engineering, Information Engineering
    Identifiers
    urn:nbn:se:liu:diva-112990 (URN)10.1109/LSP.2014.2367154 (DOI)000345236400005 ()
    Note

    Funding Agencies|Swedish research council (VR) under ETT [621-2010-4301]; SSF, project CUAS

    Available from: 2015-01-12 Created: 2015-01-08 Last updated: 2017-12-05
    6. Gaussian Mixture Reduction Using Reverse Kullback-Leibler Divergence
    Open this publication in new window or tab >>Gaussian Mixture Reduction Using Reverse Kullback-Leibler Divergence
    (English)Manuscript (preprint) (Other academic)
    National Category
    Signal Processing
    Identifiers
    urn:nbn:se:liu:diva-121615 (URN)
    Available from: 2015-09-28 Created: 2015-09-28 Last updated: 2015-10-05
  • 2.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Chen, Tianshi
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    MAXIMUM ENTROPY PROPERTY OF DISCRETE-TIME STABLE SPLINE KERNEL2015In: 2015 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING (ICASSP), IEEE , 2015, p. 3676-3680Conference paper (Refereed)
    Abstract [en]

    In this paper, the maximum entropy property of the discrete-time first-order stable spline kernel is studied. The advantages of studying this property in discrete-time domain instead of continuous-time domain are outlined. One of such advantages is that the differential entropy rate is well-defined for discrete-time stochastic processes. By formulating the maximum entropy problem for discrete-time stochastic processes we provide a simple and self-contained proof to show what maximum entropy property the discrete-time first-order stable spline kernel has.

  • 3.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Granström, Karl
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Orguner, Umut
    Middle E Technical University, Turkey.
    Greedy Reduction Algorithms for Mixtures of Exponential Family2015In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 6, p. 676-680Article in journal (Refereed)
    Abstract [en]

    In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a Gaussian inverse Wishart probability hypothesis density (PHD) filter.

  • 4.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Larsson, Fredrik
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Schön, Thomas B.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Felsberg, Michael
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Bicycle Tracking Using Ellipse Extraction2011In: Proceedings of the 14thInternational Conference on Information Fusion, 2011, IEEE , 2011, p. 1-8Conference paper (Refereed)
    Abstract [en]

    A new approach to track bicycles from imagery sensor data is proposed. It is based on detecting ellipsoids in the images, and treat these pair-wise using a dynamic bicycle model. One important application area is in automotive collision avoidance systems, where no dedicated systems for bicyclists yet exist and where very few theoretical studies have been published.

    Possible conflicts can be predicted from the position and velocity state in the model, but also from the steering wheel articulation and roll angle that indicate yaw changes before the velocity vector changes. An algorithm is proposed which consists of an ellipsoid detection and estimation algorithm and a particle filter.

    A simulation study of three critical single target scenarios is presented, and the algorithm is shown to produce excellent state estimates. An experiment using a stationary camera and the particle filter for state estimation is performed and has shown encouraging results.

  • 5.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Löfberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Convex Optimization Approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints2010Report (Other academic)
    Abstract [en]

    The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive system. It is shown how the speed dependent constraints should be added in order to keep the convexity of the overall problem. A method to, conservatively, approximate the linear speed dependent constraints by a convex constraint is also proposed. A numerical example proves versatility of the extension proposed in this paper.

  • 6.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Norrlöf, Mikael
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Löfberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Convex Optimization Approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints2011In: Proceedings of the 18th IFAC World Congress, IFAC , 2011, p. 14648-14653Conference paper (Refereed)
    Abstract [en]

    The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive system. It is shown how the speed dependent constraints should be added in order to keep the convexity of the overall problem. A method to, conservatively, approximate the linear speed dependent constraints by a convex constraint is also proposed. A numerical example proves versatility of the extension proposed in this paper.

  • 7.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nurminen, Henri
    Department of Automation Science and Engineering, Tampere University of Technology, Finland.
    Pichè, Robert
    Department of Automation Science and Engineering, Tampere University of Technology, Finland.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Variational Iterations for Filtering and Smoothing with skew-t measurement noise2015Report (Other academic)
    Abstract [en]

    In this technical report, some derivations for the filter and smoother proposed in [1] are presented. More specifically, the derivations for the cyclic iteration needed to solve the variational Bayes filter and smoother for state space models with skew t likelihood proposed in [1] are presented.

  • 8.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Department of Electrical and Electronics Engineering, Middle East Technical University, Ankara, Turkey.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bayesian Inference via Approximation of Log-likelihood for Priors in Exponential FamilyManuscript (preprint) (Other academic)
    Abstract [en]

    In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case where the prior distribution belongs to the exponential family of distributions. The logarithm of the likelihood function is linearized with respect to the sufficient statistic of the prior distribution in exponential family such that the posterior obtains the same exponential family form as the prior. Similarities between the proposed method and the extended Kalman filter for nonlinear filtering are illustrated. Further, an extended target measurement update for target models where the target extent is represented by a random matrix having an inverse Wishart distribution is derived. The approximate update covers the important case where the spread of measurement is due to the target extent as well as the measurement noise in the sensor.

  • 9.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Orguner, Umut
    Middle East Technical University.
    Lundquist, Christian
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On mixture reduction for multiple target tracking2012Conference paper (Refereed)
  • 10.
    Ardeshiri, Tohid
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    An adaptive PHD filter for tracking with unknown sensor characteristics2013Conference paper (Refereed)
    Abstract [en]

    In multi-target tracking, the discrepancy between the nominal and the true values of the model parameters might result in poor performance. In this paper, an adaptive Probability Hypothesis Density (PHD) filter is proposed which accounts for sensor parameter uncertainty. Variational Bayes technique is used for approximate inference which provides analytic expressions for the PHD recursions analogous to the Gaussian mixture implementation of the PHD filter. The proposed method is evaluated in a multi-target tracking scenario. The improvement in the performance is shown in simulations.

  • 11.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Orguner, Umut
    Middle East Technical University.
    On Reduction of Mixtures of the Exponential Family Distributions2013Report (Other academic)
    Abstract [en]

    Many estimation problems require a mixture reduction algorithm with which an increasing number of mixture components are reduced to a tractable level. In this technical report a discussion on dierent aspects of mixture reduction is given followed by a presentation of numerical simulation on reduction of mixture densities where the component density belongs to the exponential family of distributions.

  • 12.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Department of Electrical and Electronics Engineering, Middle East Technical University, Ankara, Turkey.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Approximate Bayesian Smoothing with Unknown Process and Measurement Noise Covariances2015In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 12, p. 2450-2454Article in journal (Refereed)
    Abstract [en]

    We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is computationally efficient, easy to implement, and can be applied to high dimensional linear systems. The performance of the algorithm is illustrated on a target tracking example.

  • 13.
    Ardeshiri, Tohid
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Variational Iterations for Smoothing with Unknown Process and Measurement Noise Covariances2015Report (Other academic)
    Abstract [en]

    In this technical report, some derivations for the smoother proposed in [1] are presented. More specifically, the derivations for the cyclic iteration needed to solve the variational Bayes smoother for linear state-space models with unknownprocess and measurement noise covariances in [1] are presented. Further, the variational iterations are compared with iterations of the Expectation Maximization (EM) algorithm for smoothing linear state-space models with unknown noise covariances.

    [1] T. Ardeshiri, E. Özkan, U. Orguner, and F. Gustafsson, ApproximateBayesian smoothing with unknown process and measurement noise covariances, submitted to Signal Processing Letters, 2015.

  • 14.
    Chen, Tianshi
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Ardeshiri, Tohid
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Carli, Francesca P.
    Department of Engineering, University of Cambridge, Cambridge, United Kingdom.
    Chiuso, Alessandro
    Dept. of Information Engineering, University of Padova, Padova, Italy.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Pillonetto, Gianluigi
    Dept. of Information Engineering, University of Padova, Padova, Italy.
    Maximum entropy properties of discrete-time first-order stable spline kernel2016In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 66, p. 34-38Article in journal (Refereed)
    Abstract [en]

    The first order stable spline (SS-1) kernel (also known as the tunedcorrelated kernel) is used extensively in regularized system identification, where the impulse response is modeled as a zero-mean Gaussian process whose covariance function is given by well designed and tuned kernels. In this paper, we discuss the maximum entropy properties of this kernel. In particular, we formulate the exact maximum entropy problem solved by the SS-1 kernel without Gaussian and uniform sampling assumptions. Under general sampling assumption, we also derive the special structure of the SS-1 kernel (e.g. its tridiagonal inverse and factorization have closed form expression), also giving to it a maximum entropy covariance completion interpretation.

  • 15.
    Nurminen, Henri
    et al.
    Tampere University of Technology, Finland.
    Ardeshiri, Tohid
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Piche, Robert
    Tampere University of Technology, Finland.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    A NLOS-robust TOA positioning filter based on a skew-t measurement noise model2015In: 2015 INTERNATIONAL CONFERENCE ON INDOOR POSITIONING AND INDOOR NAVIGATION (IPIN), IEEE , 2015Conference paper (Refereed)
    Abstract [en]

    A skew-t variational Bayes filter (STVBF) is applied to indoor positioning with time-of-arrival (TOA) based distance measurements and pedestrian dead reckoning (PDR). The proposed filter accommodates large positive outliers caused by occasional non-line-of-sight (NLOS) conditions by using a skew-t model of measurement errors. Real-data tests using the fusion of inertial sensors based PDR and ultra-wideband based TOA ranging show that the STVBF clearly outperforms the extended Kalman filter (EKF) in positioning accuracy with the computational complexity about three times that of the EKF.

  • 16.
    Nurminen, Henri
    et al.
    Tampere University of Technology, Finland.
    Ardeshiri, Tohid
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Piche, Robert
    Tampere University of Technology, Finland.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Robust Inference for State-Space Models with Skewed Measurement Noise2015In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 11, p. 1898-1902Article in journal (Refereed)
    Abstract [en]

    Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-t-distributed measurement noise. The proposed filter and smoother are compared with conventional low-complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.

  • 17.
    Nurminen, Henri
    et al.
    Tampere University of Technology, Department of Automation Science and Engineering, Finland.
    Rui, Rafael
    Universidade Federal do Rio Grande do Sul, Brazil.
    Ardeshiri, Tohid
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bazanella, Alexandre
    Universidade Federal do Rio Grande do Sul Porto Alegre, Rio Grande do Sul, Brazil.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Mean and covariance matrix of a multivariate normal distribution with one doubly-truncated component2016Report (Other academic)
    Abstract [en]

    This technical report gives analytical formulas for the mean and covariancematrix of a multivariate normal distribution with one componenttruncated from both below and above.

1 - 17 of 17
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