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  • 551.
    Törnqvist, David
    et al.
    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.
    Klein, Inger
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    GLR Tests for Fault Detection over Sliding Data Windows2005Report (Other academic)
    Abstract [en]

    The Generalized Likelihood Ratio (GLR) test for fault detection as derived by Willsky and Jones is a recursive method to detect additive changes in linear systems in a Kalman filter framework. Here, we evaluate the GLR test on a sliding window and compare it to stochastic parity space approaches. Robust fault detection defined as being insensitive to faults in the signal space is also studied in the GLR framework.

  • 552.
    Törnqvist, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    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.
    Tight Integration Between IMU and GPS for Sounding Rockets2010Report (Other academic)
    Abstract [en]

    This report presents integrity monitoring and integration methods for an Inertial Measurement Unit (IMU) and a gps receiver. The methods are applied to data from a Maxus sounding rocket used for microgravity research. It is crucial to determine the rocket position during launch to ensure a safe landing location. Today, the navigation relies on IMU integration only. Involving a GPS receiver enhances the position accuracy but there is a need for protection against faulty satellite range measurements. Monitoring over a sequence of the measurements gives higher confidence to the tests.

  • 553.
    Törnqvist, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Helmersson, Anders
    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.
    Window Based GPS Integrity Test using Tight GPS/IMU Integration Applied to a Sounding Rocket2010In: Proceedings of the 2010 IEEE Aerospace Conference, 2010Conference paper (Refereed)
    Abstract [en]

    This paper presents an integrity monitoring method for tight integration of an Inertial Measurement Unit (IMU) and a GPS receiver. The method is applied to data from a Maxus sounding rocket used for microgravity research. It is crucial to determine the rocket position during launch to ensure a safe landing location. Today, the navigation relies on IMU integration only. Involving a GPS receiver enhances the position accuracy but there is a need for protection against faulty satellite range measurements. Monitoring over a sequence of the measurements gives higher confidence to the tests.

  • 554.
    Törnqvist, David
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Saha, Saikat
    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.
    Fault Detection using Nonlinear Parameter Estimation2011In: Proceedings of the 2011 IEEE Aerospace Conference, 2011, , p. 6Conference paper (Refereed)
    Abstract [en]

    For linear and Gaussian systems, fault detection over a batch of data is well-studied, and analytical solutions exist in a stochastic framework. The parity space approach handles additive faults and can be shown to be equivalent to estimating the state trajectory and then removing its influence on the output sequence. Multiplicative faults in linear systems can be handled using parameter estimation methods, such as the EM-algorithm in combination with the Kalman smoother. For nonlinear and non-Gaussian systems, we propose to estimate the state trajectory and the faults over the data batch using a particle smoother and the EM-algorithm. The result is a generic fault detection and isolation scheme that applies to arbitrary nonlinear and non-Gaussian systems, where the faults are monitored over a sliding window.

  • 555.
    Törnqvist, David
    et al.
    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.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Detecting Spurious Features using Parity Space2008Report (Other academic)
    Abstract [en]

    Detection of spurious features is instrumental in many computer vision applications. The standard approach is feature based, where extracted features are matched between the image frames. This approach requires only vision, but is computer intensive and not yet suitable for real-time applications. We propose an alternative based on algorithms from the statistical fault detection literature. It is based on image data and an inertial measurement unit (IMU). The principle of analytical redundancy is applied to batches of measurements from a sliding time window. The resulting algorithm is fast and scalable, and requires only feature positions as inputs from the computer vision system. It is also pointed out that the algorithm can be extended to also detect nonstationary features (moving targets for instance). The algorithm is applied to real data from an unmanned aerial vehicle in a navigation application.

  • 556.
    Törnqvist, David
    et al.
    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.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Detecting Spurious Features using Parity Space2008In: Proceedings of the 10th International Conference on Control, Automation, Robotics and Vision, 2008, p. 353-358Conference paper (Refereed)
    Abstract [en]

    Detection of spurious features is instrumental in many computer vision applications. The standard approach is feature based, where extracted features are matched between the image frames. This approach requires only vision, but is computer intensive and not yet suitable for real-time applications. We propose an alternative based on algorithms from the statistical fault detection literature. It is based on image data and an inertial measurement unit (IMU). The principle of analytical redundancy is applied to batches of measurements from a sliding time window. The resulting algorithm is fast and scalable, and requires only feature positions as inputs from the computer vision system. It is also pointed out that the algorithm can be extended to also detect nonstationary features (moving targets for instance). The algorithm is applied to real data from an unmanned aerial vehicle in a navigation application.

  • 557.
    Törnqvist, David
    et al.
    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.
    Karlsson, Rickard
    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.
    Particle Filter SLAM with High Dimensional Vehicle Model2008Report (Other academic)
    Abstract [en]

    This work presents a particle filter (PF) method closely related to FastSLAM for solving the simultaneous localization and mapping (SLAM) problem. Using the standard FastSLAM algorithm, only low-dimensional vehicle models can be handled due to computational constraints. In this work an extra factorization of the problem is introduced that makes high-dimensional vehicle models computationally feasible. Results using experimental data from a UAV (helicopter) are presented. The algorithm fuses measurements from on-board inertial sensors (accelerometer and gyro), barometer, and vision in order to solve the SLAM problem.

  • 558.
    Törnqvist, David
    et al.
    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.
    Karlsson, Rickard
    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.
    Particle Filter SLAM with High Dimensional Vehicle Model2009In: Journal of Intelligent and Robotic Systems, ISSN 0921-0296, E-ISSN 1573-0409, Vol. 55, no 4, p. 249-266Article in journal (Refereed)
    Abstract [en]

    This work presents a particle filter (PF) method closely related to FastSLAM for solving the simultaneous localization and mapping (SLAM) problem. Using the standard FastSLAM algorithm, only low-dimensional vehicle models can be handled due to computational constraints. In this work an extra factorization of the problem is introduced that makes high-dimensional vehicle models computationally feasible. Results using experimental data from a UAV (helicopter) are presented. The algorithm fuses measurements from on-board inertial sensors (accelerometer and gyro), barometer, and vision in order to solve the SLAM problem.

  • 559.
    Veibäck, Clas
    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.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    On Fusion of Sensor Measurements and Observation with Uncertain Timestamp for Target Tracking2016In: Proceedings of the 19th International Conference on Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 1268-1275Conference paper (Refereed)
    Abstract [en]

    We consider a target tracking problem where, in addition to the usual sensor measurements, accurate observations with uncertain timestamps are available. Such observations could, \eg, come from traces left by a target or from witnesses of an event, and have the potential in some scenarios to improve the accuracy of an estimate significantly. The Bayesian solution to the smoothing problem for one observation with uncertain timestamp is derived for a linear Gaussian state space model. The joint and marginal distributions of the states and uncertain time are derived, as well as the minimum mean squared error (MMSE) and maximum a posteriori (MAP) estimators. To attain an intuition for the problem in consideration a simple first-order example is presented and its posterior distributions and point estimators are compared and examined in some depth.

  • 560.
    Veibäck, Clas
    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.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Tracking of Dolphins in a Basin Using a Constrained Motion Model2015In: Proceedings of the 18th International Conference of Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)
    Abstract [en]

    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.

  • 561.
    Veibäck, Clas
    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.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Uncertain Timestamps in Linear State Estimation2019In: IEEE Transactions on Aerospace and Electronic Systems, ISSN 0018-9251, E-ISSN 1557-9603, Vol. 55, no 3, p. 1334-1346Article in journal (Refereed)
    Abstract [en]

    We consider a linear state estimation problem, where, in addition to the usual timestamped measurements, observations with uncertain timestamps are available. Such observations could, e.g., come from traces left by a target in a tracking scenario or from witnesses of an event and have the potential to improve the estimation accuracy significantly. We derive the posterior distribution and point estimators for a linear Gaussian smoothing formulation of this problem and illustrate with two numerical examples.

  • 562.
    Wahlström, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Axelsson, Patrik
    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.
    Discretizing stochastic dynamical systems using Lyapunov equations2014In: Proceedings of the 19th World Congress of the International Federation of Automatic Control / [ed] Edward Boje and Xiaohua Xia, International Federation of Automatic Control , 2014, p. 3726-3731Conference paper (Refereed)
    Abstract [en]

    Stochastic dynamical systems are fundamental in state estimation, systemidentification and control. System models are often provided incontinuous time, while a major part of the applied theory is developedfor discrete-time systems. Discretization of continuous-time models ishence 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.

  • 563.
    Wahlström, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Callmer, Jonas
    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.
    Magnetometers for Tracking Metallic Targets2010In: Proceedings of 13th International Conference on Information Fusion, 2010Conference paper (Refereed)
    Abstract [en]

    Starting from Maxwell's equations, we derive a sensor model for three-axis magnetometers suitable for localization and tracking applications. The model depends on the relative position between the sensor and the target, and a physical magnetic multipole model of the target. Both point targets (far-field) and extended target (near-field) models are provided. The models are validated on data taken from various road vehicles. The suitability of magnetometers for tracking is analyzed in terms of local observability and Cramér Rao lower bound as a function of the sensor positions in a two sensor scenario. Results from field test data indicate excellent tracking of position and velocity of the target, as well as identification of the magnetic target model suitable for target classification.

  • 564.
    Wahlström, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Callmer, Jonas
    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.
    Single Target Tracking using Vector Magnetometers2011In: Acoustics, Speech and Signal Processing (ICASSP), 2011, IEEE , 2011, p. 4332-4335Conference paper (Refereed)
    Abstract [en]

    With the electromagnetic theory as basis, we present a sensor model for three-axis magnetometers suitable for localization and tracking applications. The model depends on a physical magnetic dipole model of the target and its relative position to the sensor. Furthermore, the dependency between the magnetic dipole and the target orientation has been modeled enabling tracking of a maneuvering target. Due to multimodality, a bank of Extended Kalman Filters is proposed for tracking road vehicles. Results from field test data indicate excellent tracking of target position.

  • 565.
    Wahlström, Niklas
    et al.
    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.
    Magnetometer Modeling and Validation for Tracking Metallic Targets2014In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, ISSN 1053-587X, Vol. 62, no 3, p. 545-556Article in journal (Refereed)
    Abstract [en]

    With the electromagnetic theory as basis, we present a sensor model for three-axis magnetometers suitable for localization and tracking as required in intelligent transportation systems and security applications. The model depends on a physical magnetic dipole model of the target and its relative position to the sensor. Both point target and extended target models are provided as well as a target orientation dependent model. The suitability of magnetometers for tracking is analyzed in terms of local observability and the Cramér Rao lower bound as a function of the sensor positions in a two sensor scenario. The models are validated with real field test data taken from various road vehicles which indicate excellent localization as well as identification of the magnetic target model suitable for target classification. These sensor models can be combined with a standard motion model and a standard nonlinear filter to track metallic objects in a magnetometer network.

  • 566.
    Wahlström, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Tracking Position and Orientation of Magnetic Objects Using Magnetometer Networks2015Manuscript (preprint) (Other academic)
    Abstract [en]

    A framework for estimation and filtering of magnetic dipoles in anetwork of magnetometers is presented. The application in mind istracking of objects consisting of permanent magnets for controllingcomputer applications, though the framework can also be applied totracking larger objects such as vehicles. A general sensor model forthe network is presented for tracking objects consisting of (i) asingle dipole, (ii) a structure of dipoles and (iii) several freely moving(structures of) dipoles, respectively. A single dipole generates amagnetic field with rotation symmetry, so at best five degrees offreedom (5D) tracking can be achieved, where the SNR decays cubicallywith distance. One contribution is the use of structures ofdipoles, which allows for full 6D tracking if the dipole structure is largeenough. An observability analysis shows that the sixth degree of freedom is weaklyobservable, where the SNR decays to the power of four withdistance, and that there is a 180 degree ambiguity around a specificsymmetry axis. Experimental results are presented and compared to areference tracking system, and four public demonstrators based on thisframework are briefly described.

  • 567.
    Wahlström, Niklas
    et al.
    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.
    Åkesson, Susanne
    Lund University, Sweden.
    A Voyage to Africa by Mr Swift2012In: Proceedings of the 15th International Conference on Information Fusion, IEEE conference proceedings, 2012, p. 808-815Conference paper (Refereed)
    Abstract [en]

    A male common swift Apus apus was equipped witha light logger on August 5, 2010, and again captured in his nest 298 days later. The data stored in the light logger enables analysis of the fascinating travel it made in this time period. The state of the art algorithm for geolocation based on light loggers consists in computing first sunrise and sunset from thelogged data, which are then converted to midday (gives longitude) and day length (gives latitude). This approach has singularities at the spring and fall equinoxes, and gives a bias for fast day transitions in the east-west direction. We derive a flexible particle filter solution, where sunset and sunrise are processed in separately measurement updates, and where the motion model has two modes, one for migration and one for stationary long time visits, which are designed to fit the flying pattern of the swift. This approach circumvents the aforementioned problems with singularity and bias, and provides realistic confidence bounds on the geolocation as well as an estimate of the migration mode.

  • 568.
    Wahlström, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hostettler, Roland
    Luleå University of Technology, Division of Systems and Interaction.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Birk, Wolfgang
    Luleå University of Technology, Division of Systems and Interaction.
    Classification of Driving Direction in Traffic Surveillance using Magnetometers2014In: IEEE transactions on intelligent transportation systems (Print), ISSN 1524-9050, E-ISSN 1558-0016, Vol. 15, no 4, p. 1405-1418Article in journal (Refereed)
    Abstract [en]

    We present an approach for computing the driving direction of a vehicle by processing measurements from one 2-axis magnetometer. The proposed method relies on a non-linear transformation of the measurement data comprising only two inner products. Deterministic analysis of the signal model reveals how the driving direction affects the measurement signal and the proposed classifier is analyzed in terms of its statistical properties. The method is compared with a model based likelihood test using both simulated and experimental data. The experimental verification indicates that good performance is achieved under the presence of saturation, measurement noise, and near field effects.

  • 569.
    Wahlström, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hostettler, Roland
    Luleå University of Technology, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Birk, Wolfgang
    Luleå University of Technology, Sweden.
    Rapid Classification of Vehicle Heading Direction with Two-Axis Magnetometer2012In: Acoustics, Speech and Signal Processing (ICASSP), 2012, IEEE , 2012, p. 3385-3388Conference paper (Refereed)
    Abstract [en]

    We present an approach for computing the heading direction of avehicle by processing measurements from a 2-axis magnetometer rapidly. The proposed method relies on a non-linear transformation of the measurement data comprising only two inner products. Deterministic analysis of the signal model shows how the heading direction is contained in the signal and the proposed estimator is analyzed in terms of its statistical properties. Experimental verification indicates that good performance is achieved under the presence of saturation, measurement noise, and near field effects.

  • 570.
    Wahlström, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Kok, Manon
    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.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Modeling Magnetic Fields using Gaussian Processes2013In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013, IEEE conference proceedings, 2013, p. 3522-3526Conference paper (Refereed)
    Abstract [en]

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

  • 571.
    Yin, Feng
    et al.
    Technical University of Darmstadt, Germany .
    Fritsche, Carsten
    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.
    Zoubir, Abdelhak M.
    Technical University of Darmstadt, Germany .
    EM- and JMAP-ML Based Joint Estimation Algorithms for Robust Wireless Geolocation in Mixed LOS/NLOS Environments2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 1, p. 168-182Article in journal (Refereed)
    Abstract [en]

    We consider robust geolocation in mixed line-of-sight (LOS)/non-LOS (NLOS) environments in cellular radio networks. Instead of assuming known propagation channel states (LOS or NLOS), we model the measurement error with a general two-mode mixture distribution although it deviates from the underlying error statistics. To avoid offline calibration, we propose to jointly estimate the geographical coordinates and the mixture model parameters. Two iterative algorithms are developed based on the well-known expectation-maximization (EM) criterion and joint maximum a posteriori-maximum likelihood (JMAP-ML) criterion to approximate the ideal maximum-likelihood estimator (MLE) of the unknown parameters with low computational complexity. Along with concrete examples, we elaborate the convergence analysis and the complexity analysis of the proposed algorithms. Moreover, we numerically compute the Cramer-Rao lower bound (CRLB) for our joint estimation problem and present the best achievable localization accuracy in terms of the CRLB. Various simulations have been conducted based on a real-world experimental setup, and the results have shown that the ideal MLE can be well approximated by the JMAP-ML algorithm. The EM estimator is inferior to the JMAP-ML estimator but outperforms other competitors by far.

  • 572.
    Yin, Feng
    et al.
    Technical University Darmstadt, Germany.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Received signal strength-based joint parameter estimation algorithm for robust geolocation in LOS/NLOS environments2013In: Proc. of 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2013, p. 6471-6475Conference paper (Refereed)
    Abstract [en]

    We consider received-signal-strength-based robust geolocation in mixed line-of-sight/non-line-of-sight propagation environments. Herein, we assume a mode-dependent propagation model with unknown parameters. We propose to jointly estimate the geographical coordinates and propagation model parameters. In order to approximate the maximum-likelihood estimator (MLE), we develop an iterative algorithm based on the well-known expectation and maximization criterion. As compared to the standard ML implementation, the proposed algorithm is simpler to implement and capable of reproducing the MLE. Simulation results show that the proposed algorithm attains the best geolocation accuracy as the number of measurements increases.

  • 573.
    Yin, Feng
    et al.
    Technical University of Darmstadt, Germany.
    Fritsche, Carsten
    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.
    Zoubir, Abdelhak M
    Technical University of Darmstadt, Germany.
    TOA-Based Robust Wireless Geolocation and Cramér-Rao Lower Bound Analysis in Harsh LOS/NLOS Environments2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 9, p. 2243-2255Article in journal (Refereed)
    Abstract [en]

    We consider time-of-arrival based robust geolocation in harsh line-of-sight/non-line-of-sight environments. Herein, we assume the probability density function (PDF) of the measurement error to be completely unknown and develop an iterative algorithm for robust position estimation. The iterative algorithm alternates between a PDF estimation step, which approximates the exact measurement error PDF (albeit unknown) under the current parameter estimate via adaptive kernel density estimation, and a parameter estimation step, which resolves a position estimate from the approximate log-likelihood function via a quasi-Newton method. Unless the convergence condition is satisfied, the resolved position estimate is then used to refine the PDF estimation in the next iteration. We also present the best achievable geolocation accuracy in terms of the Cramér-Rao lower bound. Various simulations have been conducted in both real-world and simulated scenarios. When the number of received range measurements is large, the new proposed position estimator attains the performance of the maximum likelihood estimator (MLE). When the number of range measurements is small, it deviates from the MLE, but still outperforms several salient robust estimators in terms of geolocation accuracy, which comes at the cost of higher computational complexity.

  • 574.
    Yin, Feng
    et al.
    Technical University of Darmstadt, Germany.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Jin, Di
    Technical University of Darmstadt, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Zoubir, Abdelhak M.
    Technical University of Darmstadt, Germany.
    Cooperative Localization in WSNs Using Gaussian Mixture Modeling: Distributed ECM Algorithms2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 6, p. 1448-1463Article in journal (Refereed)
    Abstract [en]

    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.

  • 575.
    Yin, Feng
    et al.
    Technical University Darmstadt, Germany.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Fritsche, Carsten
    IFEN GmbH, Poing, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Robust cooperative sensor network localization via the EM criterion in LOS/NLOS environments2013In: IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2013, IEEE , 2013, p. 505-509Conference paper (Refereed)
    Abstract [en]

    We investigate robust cooperative localization in LOS/NLOS environments in wireless sensor networks. Round-trip time-of-arrival signal metric is considered so that time synchronization among sensors can be avoided. Owing to the non-line-of-sight effect, we model the measurement error by a two-mode Gaussian mixture distribution. However, its parameters are assumed completely unknown. We propose a centralized localization algorithm, which jointly estimates the unknown geographical coordinates and the nuisance mixture model parameters. The expectation-maximization criterion is adopted here to implement the maximum likelihood estimator. In addition, we also compute the Cramér-Rao lower bound (CRLB) for our estimation problem and present the best achievable positioning accuracy in terms of the CRLB.

  • 576.
    Zhao, Yuxin
    et al.
    Research, Ericsson AB, 39174 Stockholm, Sweden.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Yin, Feng
    SSE, Chinese University of Hong Kong Shenzhen, Shenzhen, China.
    Gunnarsson, Fredrik
    Ericsson Research, Linköping, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Sequential Monte Carlo Methods and Theoretical Bounds for Proximity Report Based Indoor Positioning2018In: IEEE Transactions on Vehicular Technology, ISSN 0018-9545, E-ISSN 1939-9359, Vol. 67, no 6, p. 5372-5386Article in journal (Refereed)
    Abstract [en]

    The commercial interest in proximity services is increasing. Application examples include location-based information and advertisements, logistics, social networking, file sharing, etc. In this paper, we consider positioning of devices based on a time series of proximity reports from a mobile device to a network node. This corresponds to nonlinear measurements with respect to the device position in relation to the network nodes. Motion model will be needed together with the measurements to determine the position of the device. Therefore, sequential Monte Carlo methods, namely particle filtering and smoothing, are applicable for positioning. Positioning performance is evaluated in a typical office area with Bluetooth-low-energy beacons deployed for proximity detection and report, and is further compared to parametric Cramér-Rao lower bounds. Finally, the position accuracy is also evaluated with real experimental data.

  • 577.
    Zhao, Yuxin
    et al.
    Ericsson Research, Linköping, Sweden.
    Yin, Feng
    Ericsson Research, Linköping, Sweden.
    Gunnarsson, Fredrik
    Ericsson Research, Linköping, Sweden.
    Amirijoo, Mehdi
    Ericsson Research, Linköping, Sweden.
    Özkan, Emre
    ISY, Linköping University.
    Gustafsson, Fredrik
    ISY, Linköping University.
    Particle Filtering for Positioning Based on Proximity Reports2015Conference paper (Refereed)
    Abstract [en]

    The commercial interest in proximity services is increasing. Application examples include location-based information and advertisements, logistics, social networking, file sharing, etc. In this paper, we consider positioning of devices based on time series proximity reports from a mobile device to a network node. This corresponds to nonlinear measurements with respect to the device position in relation to the network nodes. Therefore, particle filtering is applicable for positioning. Positioning performance is evaluated in a typical office area with Bluetooth-low-energy beacons deployed for proximity detection and report. Accuracy is concluded to vary spatially over the office floor, and in relation to the beacon deployment density.

  • 578.
    Örn, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Szilassy, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Dil, Bram
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    A Novel Multi-Step Algorithm for Low-Energy Positioning Using GPS2016In: Fusion 2016, 19th International Conference on Information Fusion: Proceedings, 2016, p. 1469-1476Conference paper (Refereed)
    Abstract [en]

    GPS is widely used for localization and tracking, however traditional GPS receivers consume too much energy for many applications. This paper implements and evaluates the performance of a low-energy GPS prototype. The main difference is that a traditional GPS needs to sample signals transmitted by satellites for 30 seconds to estimate its position. Our prototype reduces this time by three orders of magnitude and it can compute positions from only 2 milliseconds of data. We present a new algorithm that increases robustness by filtering on estimated residuals instead of using an altitude database. In addition, we show that our new algorithm works with both fixed and moving targets. The solution consists of (1) a portable device that samples the GPS signal and (2) a server that utilizes Doppler navigation and Coarse Time Navigation to estimate positions. We performed tests in a wide variety of environments and situations. These tests show that our prototype provides a median positioning error of roughly 40 meters even when the GPS receiver is moving at 80 kilometres per hour.

  • 579.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Online EM algorithm for joint state and mixture measurement noise estimation2012In: 15th International Conference on Information Fusion (FUSION), 2012, IEEE , 2012, p. 1935-1940Conference paper (Refereed)
    Abstract [en]

    In this study, we aim to estimate the unknown multi-modal measurement noise distribution of nonlinear state space models. The unknown noise distribution is modeled as a mixture of exponential family of distributions. We use the Expectation-Maximization (EM) method in order to jointly estimate the unknown parameters as well as the states. The online version of the EM algorithm is implemented by using particle filtering techniques. The resulting algorithm is a noise adaptive particle filter which is applicable to many sensor models having multi-modal noise distributions with unknown parameters.

  • 580.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindsten, Fredrik
    University of Cambridge, England.
    Fritsche, Carsten
    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.
    Recursive Maximum Likelihood Identification of Jump Markov Nonlinear Systems2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 3, p. 754-765Article in journal (Refereed)
    Abstract [en]

    We present an online method for joint state and parameter estimation in jump Markov non-linear systems (JMNLS). State inference is enabled via the use of particle filters which makes the method applicable to a wide range of non-linear models. To exploit the inherent structure of JMNLS, we design a Rao-Blackwellized particle filter (RBPF) where the discrete mode is marginalized out analytically. This results in an efficient implementation of the algorithm and reduces the estimation error variance. The proposed RBPF is then used to compute, recursively in time, smoothed estimates of complete data sufficient statistics. Together with the online expectation maximization algorithm, this enables recursive identification of unknown model parameters including the transition probability matrix. The method is also applicable to online identification of jump Markov linear systems(JMLS). The performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data.

  • 581.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lundquist, Christian
    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.
    A Bayesian Approach to Jointly Estimate Tire Radii and Vehicle Trajectory2011In: Proceedings of the International IEEE Conference on Intelligent Transportation Systems, Washington DC, USA: IEEE conference proceedings, 2011, p. 1-6Conference paper (Refereed)
    Abstract [en]

    High-precision estimation of vehicle tire radii is considered, based on measurements on individual wheel speeds and absolute position from a global navigation satellite system (GNSS). The wheel speed measurements are subject to noise with time-varying covariance that depends mainly on the road surface. The novelty lies in a Bayesian approach to estimate online the time-varying radii and noise parameters using a marginalized particle filter, where no model approximations are needed such as in previously proposed algorithms based on the extended Kalman filter. Field tests show that the absolute radius can be estimated with millimeter accuracy, while the relative wheel radius on one axle is estimated with submillimeter accuracy.

  • 582.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Saha, Saikat
    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.
    Smidl, Vaclav
    Institute of Information Theory and Automation, Czech Repbulic.
    Non-Parametric Bayesian Measurement Noise Density Estimation in Non-Linear Filtering2011In: Acoustics, Speech and Signal Processing (ICASSP), 2011, IEEE , 2011, p. 5924-5927Conference paper (Refereed)
    Abstract [en]

    In this study, we investigate online Bayesian estimation of the measurement noise density of a given state space model using particle filters and Dirichlet process mixtures. Dirichlet processes are widely used in statistics for nonparametric density estimation. In the proposed method, the unknown noise is modeled as a Gaussian mixture with unknown number of components. The joint estimation of the state and the noise density is done via particle filters. Furthermore, the number of components and the noise statistics are allowed to vary in time. An extension of the method for the estimation of time varying noise characteristics is also introduced.

  • 583.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Smidl, Vaclav
    Institute of Information Theory and Automation, Czech Republic.
    Saha, Saikat
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lundquist, Christian
    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.
    Marginalized Adaptive Particle Filtering for Nonlinear Models with Unknown Time-Varying Noise Parameters2013In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 6, p. 1566-1575Article in journal (Refereed)
    Abstract [en]

    Knowledge of the noise distribution is typically crucial for the state estimation of general state-space models. However, properties of the noise process are often unknown in the majority of practical applications. The distribution of the noise may also be non-stationary or state dependent and that prevents the use of off-line tuning methods. For linear Gaussian models, Adaptive Kalman filters (AKF) estimate unknown parameters in the noise distributions jointly with the state. For nonlinear models, we provide a Bayesian solution for the estimation of the noise distributions in the exponential family, leading to a marginalized adaptive particle filter (MAPF) where the noise parameters are updated using finite dimensional sufficient statistics for each particle. The time evolution model for the noise parameters is defined implicitly as a Kullback-Leibler norm constraint on the time variability, leading to an exponential forgetting mechanism operating on the sufficient statistics. Many existing methods are based on the standard approach of augmenting the state with the unknown variables and attempting to solve the resulting filtering problem. The MAPF is significantly more computationally efficient than a comparable particle filter that runs on the full augmented state. Further, the MAPF can handle sensor and actuator offsets as unknown means in the noise distributions, avoiding the standard approach of augmenting the state with such offsets. We illustrate the MAPF on first a standard example, and then on a tire radius estimation problem on real data.

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