Fredrik Gustafsson

Linköping University, Linköping, Östergötland, Sweden

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Publications (353)323.75 Total impact

  • Clas Veibäck, Gustaf Hendeby, Fredrik Gustafsson
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    ABSTRACT: Visual animal tracking is a challenging problem generally requiring extended target models, group tracking and handling of clutter and missed detections. Furthermore, the dolphin tracking problem we consider includes basin constraints, shadows, limited field of view and rapidly changing light conditions. We describe the whole pipeline of a solution based on a ceiling-mounted fisheye camera that includes foreground segmentation and observation extraction in each image, followed by a target tracking framework. A novel contribution is a potential field model of the basin edges as a part of the motion model, that provides a robust prediction of the dolphin trajectories in phases with long segments of missed detections. The overall performance on real data is quite promising.
    18th International Conference on Information Fusion, Washington, DC; 07/2015
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    ABSTRACT: A local series expansion of a received signal is proposed for computing direction of arrival (DOA) in sensor arrays. The advantages compared to classical DOA estimation methods include general sensor configurations, ultra-slow sampling, small dimension of the arrays, and that it applies for both narrowband and 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 to also include the near-field, which enables target tracking using a network of sensor arrays in one framework.
    18th International Conference of Information Fusion, Washington, DC; 07/2015
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    ABSTRACT: 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.
    IEEE Signal Processing Letters 05/2015; DOI:10.1109/LSP.2015.2437456 · 1.64 Impact Factor
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    Saikat Saha, Gustaf Hendeby, Fredrik Gustafsson
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    ABSTRACT: The discrete time general state-space model is a flexible framework to deal with the nonlinear and/or non-Gaussian time series problems. However, the associated (Bayesian) inference problems are often intractable. Additionally, for many applications of interest, the inference solutions are required to be recursive over time. The particle filter (PF) is a popular class of Monte Carlo based numerical methods to deal with such problems in real time. However, PF is known to be computationally expensive and does not scale well with the problem dimensions. If a part of the state space is analytically tractable conditioned on the remaining part, the Monte Carlo based estimation is then confined to a space of lower dimension, resulting in an estimation method known as the Rao-Blackwellized particle filter (RBPF). In this chapter, we present a brief review of Rao-Blackwellized particle filtering. Especially, we outline a set of popular conditional tractable structures admitting such Rao-Blackwellization in practice. For some special and/or relatively new cases, we also provide reasonably detailed descriptions.We confine our presentation mostly to the practitioners’ point of view.
    Current Trends in Bayesian Methodology with Applications, Edited by Satyanshu K. Upadhyay, Umesh Singh, Dipak K. Dey, Appaia Loganathan, 05/2015: chapter Mixture Kalman Filters and Beyond: pages 537-562; Chapman and Hall/CRC., ISBN: 9781482235111
  • Patrik Axelsson, Fredrik Gustafsson
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    ABSTRACT: Prediction and filtering of continuous-time stochastic processes often require a solver of a continuous-time differential Lyapunov equation (CDLE), for example the time update in the Kalman filter. Even though this can be recast into an ordinary differential equation (ODE), where standard solvers can be applied, the dominating approach in Kalman filter applications is to discretize the system and then apply the discrete-time difference Lyapunov equation (DDLE). To avoid problems with stability and poor accuracy, oversampling is often used. This contribution analyzes over-sampling strategies, and proposes a novel low-complexity analytical solution that does not involve oversampling. The results are illustrated on Kalman filtering problems in both linear and nonlinear systems.
    IEEE Transactions on Automatic Control 03/2015; 60(3):632-643. DOI:10.1109/TAC.2014.2353112 · 3.17 Impact Factor
  • Feng Yin, Carsten Fritsche, Di Jin, Fredrik Gustafsson, A.M. Zoubir
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    ABSTRACT: We study cooperative sensor network localization in a realistic scenario where 1) the underlying measurement errors more probably follow a non-Gaussian distribution; 2) the measurement error distribution is unknown without conducting massive offline calibrations; and 3) non-line-of-sight identification is not performed due to the complexity constraint and/or storage limitation. The underlying measurement error distribution is approximated parametrically by a Gaussian mixture with finite number of components, and the expectation–conditional maximization (ECM) criterion is adopted to approximate the maximum-likelihood estimator of the unknown sensor positions and an extra set of Gaussian mixture model parameters. The resulting centralized ECM algorithms lead to easier inference tasks and meanwhile retain several convergence properties with a proof of the “space filling” condition. To meet the scalability requirement, we further develop two distributed ECM algorithms where an average consensus algorithm plays an important role for updating the Gaussian mixture model parameters locally. The proposed algorithms are analyzed systematically in terms of computational complexity and communication overhead. Various computer based tests are also conducted with both simulation and experimental data. The results pin down that the proposed distributed algorithms can provide overall good performance for the assumed scenario even under model mismatch, while the existing competing algorithms either cannot work without the prior knowledge of the measurement error statistics or merely provide degraded localization performance when the measurement error is clearly non-Gaussian.
    IEEE Transactions on Signal Processing 03/2015; 63(6):1448-1463. DOI:10.1109/TSP.2015.2394300 · 3.20 Impact Factor
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    ABSTRACT: This paper presents a data-driven receding horizon fault estimation method for additive actuator and sensor faults in unknown linear time-invariant systems, with enhanced robustness to stochastic identification errors. State-of-the-art methods construct fault estimators with identified state-space models or Markov parameters, but they do not compensate for identification errors. Motivated by this limitation, we first propose a receding horizon fault estimator parameterized by predictor Markov parameters. This estimator provides (asymptotically) unbiased fault estimates as long as the subsystem from faults to outputs has no unstable transmission zeros. When the identified Markov parameters are used to construct the above fault estimator, zero-mean stochastic identification errors appear as model uncertainty multiplied with unknown fault signals and online system inputs/outputs (I/O). Based on this fault estimation error analysis, we formulate a mixed-norm problem for the offline robust design that regards online I/O data as unknown. An alternative online mixed-norm problem is also proposed that can further reduce estimation errors when the online I/O data have large amplitudes, at the cost of increased computational burden. Based on a geometrical interpretation of the two proposed mixed-norm problems, systematic methods to tune the user-defined parameters therein are given to achieve desired performance trade-offs. Simulation examples illustrate the benefits of our proposed methods compared to recent literature.
  • Zoran Sjanic, Fredrik Gustafsson
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    ABSTRACT: Synthetic aperture radar (SAR) equipment is a radar imaging system that can be used to create high-resolution images of a scene by utilizing the movement of a flying platform. Knowledge of the platform???s trajectory is essential to get good and focused images. An emerging application field is real-time SAR imaging using small and cheap platforms where estimation errors in navigation systems imply unfocused images. This contribution investigates a joint estimation of the trajectory and SAR image. Starting with a nominal trajectory, we successively improve the image by optimizing a focus measure and updating the trajectory accordingly. The method is illustrated using simulations using typical navigation performance of an unmanned aerial vehicle. One real data set is used to show feasibility, where the result indicates that, in particular, the azimuth position error is decreased as the image focus is iteratively improved.
    IEEE Transactions on Aerospace and Electronic Systems 01/2015; 51(2):1253-1266. DOI:10.1109/TAES.2015.120820 · 1.39 Impact Factor
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    ABSTRACT: Tracking human body motions using inertial sensors has become a well-accepted method in ambulatory applications since the subject is not confined to a lab-bounded volume. However, a major drawback is the inability to estimate relative body positions over time because inertial sensor information only allows position tracking through strapdown integration, but doesn't provide any information about relative positions. In addition, strapdown integration inherently results in drift of the estimated position over time. We propose a novel method in which a permanent magnet combined with 3D magnetometers and 3D inertial sensors are used to estimate the global trunk orientation and relative pose of the hand with respect to the trunk. An Extended Kalman Filter is presented to fuse estimates obtained from inertial sensors with magnetic updates such that the position and orientation between the human hand and trunk as well as the global trunk orientation can be estimated robustly. This has been demonstrated in multiple experiments in which various hand tasks were performed. The most complex task in which simultaneous movements of both trunk and hand were performed resulted in an average rms position difference with an optical reference system of 19:72:2 mm whereas the relative trunk-hand and global trunk orientation error was 2:3 0:9 and 8:68:7 deg respectively.
    IEEE Transactions on Neural Systems and Rehabilitation Engineering 09/2014; DOI:10.1109/TNSRE.2014.2357579 · 2.82 Impact Factor
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    Gustaf Hendeby, Fredrik Gustafsson, Niklas Wahlström
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    ABSTRACT: The Kalman filter has been the work horse in model based filtering for five decades, and basic knowledge and understanding of it is an important part of the curriculum in many Master of Science programs. It is therefore important to combine theoretical studies with practical experience to allow the students to deepen their understanding of the filter. We have developed a lab where the students implement a Kalman filter in a real-time MATLAB framework, to which data are streamed from the smartphone over WiFi. The goal of the lab is to estimate the orientation of the smartphone, which can be nicely visualized graphically and also be compared to the built-in filters in the smartphone. The filter can accept any combination of sensor data from accelerometers, gyroscopes, and magnetometer, with different performance. Different tunings and tricks in the Kalman filter are easily evaluated on-line. The smartphone app is also a stand-alone tool to visualize the sensor data graphically. So far the lab seems to have been successful in reaching the pedagogic goals and to engage the students.
    The 19th World Congress of the International Federation of Automatic Control (IFAC), Cape Town, South Africa; 08/2014
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    ABSTRACT: Traffic monitoring using low-cost two-axis magnetometers is considered. Although detection of metallic vehicles is rather easy, detecting the driving direction is more challenging. We propose a simple algorithm based on a nonlinear transformation of the measurements, which is simple to implement in embedded hardware. A theoretical justification is provided, and the statistical properties of the test statistic are presented in closed form. The method is compared with the standard likelihood ratio test on both simulated data and real data from field tests, where very high detection rates are reported, despite the presence of sensor saturation, measurement noise, and near-field effects of the magnetic field.
    IEEE Transactions on Intelligent Transportation Systems 08/2014; 15(4):1405-1418. DOI:10.1109/TITS.2014.2298199 · 2.47 Impact Factor
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    Michael Roth, Gustaf Hendeby, Fredrik Gustafsson
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    ABSTRACT: Nonlinear Kalman filter adaptations such as extended Kalman filters (EKF) or unscented Kalman filters (UKF) provide approximate solutions to state estimation problems in nonlinear models. The algorithms utilize mean values and covariance matrices to represent the probability densities in the otherwise intractable Bayesian filtering equations. As a consequence, their estimation performance can show significant dependence on the choice of state coordinates. The here considered problem of tracking maneuvering targets using coordinated turn (CT) models is one practically relevant example: The velocity in the target state can either be formulated in Cartesian or polar coordinates. We extend a previous study to a broader range of CT models that allow for changes in target speed and turn rate, and investigate UKF as well as EKF variants in terms of their performance and sensitivity to noise parameters. The results advocate for the use of polar CT models.
    17th International Conference on Information Fusion, Salamanca, Spain; 07/2014
  • David Lindgren, Gustaf Hendeby, Fredrik Gustafsson
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    ABSTRACT: 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 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 evaluated by Monte Carlo simulations and demonstrated on real data by localizing an all-terrain vehicle. It is concluded that the processing components included are fairly mature for practical implementations in sensor networks.
    Signal Processing 07/2014; 107. DOI:10.1016/j.sigpro.2014.06.031 · 2.24 Impact Factor
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    ABSTRACT: Random set-based methods have provided a rigorous Bayesian framework and have been used extensively in the last decade for point object estimation. In this article, we emphasize that the same methodology offers an equally powerful approach to estimation of so-called extended objects, i.e., objects that result in multiple detections on the sensor side. Building upon the analogy between Bayesian state estimation of a single object and random finite set (RFS) estimation for multiple objects, we give a tutorial on random set methods with an emphasis on multiple-extended-object estimation. The capabilities are illustrated on a simple yet insightful real-life example with laser range data containing several occlusions.
    IEEE Robotics &amp amp amp Automation Magazine 06/2014; 21(2):73-82. DOI:10.1109/MRA.2013.2283185 · 2.32 Impact Factor
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    ABSTRACT: In this paper, the measurements of individual wheel speeds and the absolute position from a global positioning system are used for high-precision estimation of vehicle tire radii. The radii deviation from its nominal value is modeled as a Gaussian random variable and included as noise components in a simple vehicle motion model. The novelty lies in a Bayesian approach to estimate online both the state vector and the parameters representing the process noise statistics using a marginalized particle filter (MPF). Field tests show that the absolute radius can be estimated with submillimeter accuracy. The approach is tested in accordance with regulation 64 of the United Nations Economic Commission for Europe on a large data set (22 tests, using two vehicles and 12 different tire sets), where tire deflations are successfully detected, with high robustness, i.e., no false alarms. The proposed MPF approach outperforms common Kalman-filter-based methods used for joint state and parameter estimation when compared with respect to accuracy and robustness.
    IEEE Transactions on Intelligent Transportation Systems 04/2014; 15(2):663-672. DOI:10.1109/TITS.2013.2284930 · 2.47 Impact Factor
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    ABSTRACT: In this paper, we address the problem of multi-target detection and tracking over a network of separately located Doppler-shift measuring sensors. For this challenging problem, we propose to use the probability hypothesis density (PHD) filter and present two implementations of the PHD filter, namely the sequential Monte Carlo PHD (SMC-PHD) and the Gaussian mixture PHD (GM-PHD) filters. Performances of both filters are carefully studied and compared for the considered challenging tracking problem. Simulation results show that both PHD filter implementations, successfully tracks multiple targets using only Doppler shift measurements. Moreover, as a proof-of-concept, an experimental setup consisting of a network of microphones and a loudspeaker was prepared. Experimental study results reveal that it is possible to track multiple ground targets using acoustic Doppler shift measurements in a passive multi-static scenario. We observed that the GM-PHD is more effective, efficient and easy to implement than the SMC-PHD filter.
    Digital Signal Processing 04/2014; 27(1). DOI:10.1016/j.dsp.2014.01.009 · 1.50 Impact Factor
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    ABSTRACT: A marginal version of the enumeration Bayesian Cram´er-Rao Bound (EBCRB) for jump Markov systems is proposed. It is shown that the proposed bound is at least as tight as EBCRB and the improvement stems from better handling of the nonlinearities. The new bound is illustrated to yield tighter results than BCRB and EBCRB on a benchmark example.
    IEEE Signal Processing Letters 03/2014; PP(99):1-1. DOI:10.1109/LSP.2014.2305115 · 1.64 Impact Factor
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    ABSTRACT: The dependence of radio signal propagation on the environment is well known, and both statistical and deterministic methods have been presented in the literature. Such methods are either based on randomised or actual reflectors of radio signals. In this work, we instead aim at estimating the location of the reflectors based on geo-localized radio channel impulse response measurements using methods from synthetic aperture radar (SAR). Radio channel measurements from 3GPP E-UTRAN have been used to verify the usefulness of the proposed approach. The obtained images show that the estimated reflectors are well-correlated with the aerial map of the environment. Also, trajectory segment contributions to different reflectors have been estimated with promising results.
    IEEE Transactions on Antennas and Propagation 03/2014; 62(4). DOI:10.1109/TAP.2014.2300531 · 2.46 Impact Factor
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    Niklas Wahlström, Patrix Axelsson, Fredrik Gustafsson
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    ABSTRACT: Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems. Discretization of continuous-time models is hence fundamental. We present a novel algorithm using a combination of Lyapunov equations and analytical solutions, enabling efficient implementation in software. The proposed method circumvents numerical problems exhibited by standard algorithms in the literature. Both theoretical and simulation results are provided.

Publication Stats

5k Citations
323.75 Total Impact Points


  • 1996–2014
    • Linköping University
      • Department of Electrical Engineering (ISY)
      Linköping, Östergötland, Sweden
  • 2011
    • Delft University Of Technology
      • Delft Center for Systems and Control (DCSC)
      Delft, South Holland, Netherlands
  • 2003
    • Swedish Defence Research Agency
      Tukholma, Stockholm, Sweden
  • 2000
    • Boston College, USA
      Boston, Massachusetts, United States
    • Ericsson
      Tukholma, Stockholm, Sweden
  • 1998
    • University of Newcastle
      • Department of Electrical Engineering
      Newcastle, New South Wales, Australia