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  • 1.
    Bergström, Andreas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Ericsson Research.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gunnarsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Ericsson Research.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    TOA Estimation Improvements in Multipath Environments by Measurement Error Models2017In: Proceedings of the 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 1-8Conference paper (Refereed)
    Abstract [en]

    Many positioning systems rely on accuratetime of arrival measurements. In this paper, we addressnot only the accuracy but also the relevance of Time ofArrival (TOA) measurement error modeling. We discusshow better knowledge of these errors can improve relativedistance estimation, and compare the impact of differentlydetailed measurement error information. These models arecompared in simulations based on models derived froman Ultra Wideband (UWB) measurement campaign. Theconclusion is that significant improvements can be madewithout providing detailed received signal information butwith a generic and relevant measurement error model.

  • 2.
    Bianco, Giuseppe
    et al.
    Lund University, Sweden.
    Ilieva, Mihaela
    Lund University, Sweden; Bulgarian Academic Science, Bulgaria.
    Veibäck, Clas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Öfjäll, Kristoffer
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, Faculty of Science & Engineering.
    Gadomska, Alicja
    Lund University, Sweden.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Felsberg, Michael
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Åkesson, Susanne
    Lund University, Sweden.
    Emlen funnel experiments revisited: methods update for studying compass orientation in songbirds2016In: Ecology and Evolution, ISSN 2045-7758, E-ISSN 2045-7758, Vol. 6, no 19, p. 6930-6942Article in journal (Refereed)
    Abstract [en]

    1 Migratory songbirds carry an inherited capacity to migrate several thousand kilometers each year crossing continental landmasses and barriers between distant breeding sites and wintering areas. How individual songbirds manage with extreme precision to find their way is still largely unknown. The functional characteristics of biological compasses used by songbird migrants has mainly been investigated by recording the birds directed migratory activity in circular cages, so-called Emlen funnels. This method is 50 years old and has not received major updates over the past decades. The aim of this work was to compare the results from newly developed digital methods with the established manual methods to evaluate songbird migratory activity and orientation in circular cages. 2 We performed orientation experiments using the European robin (Erithacus rubecula) using modified Emlen funnels equipped with thermal paper and simultaneously recorded the songbird movements from above. We evaluated and compared the results obtained with five different methods. Two methods have been commonly used in songbirds orientation experiments; the other three methods were developed for this study and were based either on evaluation of the thermal paper using automated image analysis, or on the analysis of videos recorded during the experiment. 3 The methods used to evaluate scratches produced by the claws of birds on the thermal papers presented some differences compared with the video analyses. These differences were caused mainly by differences in scatter, as any movement of the bird along the sloping walls of the funnel was recorded on the thermal paper, whereas video evaluations allowed us to detect single takeoff attempts by the birds and to consider only this behavior in the orientation analyses. Using computer vision, we were also able to identify and separately evaluate different behaviors that were impossible to record by the thermal paper. 4 The traditional Emlen funnel is still the most used method to investigate compass orientation in songbirds under controlled conditions. However, new numerical image analysis techniques provide a much higher level of detail of songbirds migratory behavior and will provide an increasing number of possibilities to evaluate and quantify specific behaviors as new algorithms will be developed.

  • 3.
    Björklund, Svante
    et al.
    Swedish Defence Research Agency (FOI).
    Petersson, Henrik
    Swedish Defence Reserearch Agency (FOI).
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. Linköping University, Faculty of Science & Engineering.
    Features for micro-Doppler based activity classification2015In: IET radar, sonar & navigation, ISSN 1751-8784, E-ISSN 1751-8792, Vol. 9, no 9, p. 1181-1187Article in journal (Refereed)
    Abstract [en]

    Safety and security applications benefit from better situational awareness. Radar micro-Doppler signatures from an observed target carry information about the target's activity, and have potential to improve situational awareness. This article describes, compares, and discusses two methods to classify human activity based on radar micro-Doppler data. The first method extracts physically interpretable features from the time-velocity domain such as the main cycle time and properties of the envelope of the micro-Doppler spectra and use these in the classification. The second method derives its features based on the components with the most energy in the cadence-velocity domain (obtained as the Fourier transform of the time-velocity domain). Measurements from a field trial show that the two methods have similar activity classification performance. It is suggested that target base velocity and main limb cadence frequency are indirect features of both methods, and that they do often alone suffice to discriminate between the studied activities. This is corroborated by experiments with a reduced feature set. This opens up for designing new more compact feature sets. Moreover, weaknesses of the methods and the impact of non-radial motion are discussed.

  • 4.
    Björklund, Svante
    et al.
    Swedish Defence Research Agency (FOI), Linköping, Sweden.
    Petersson, Henrik
    Swedish Defence Research Agency (FOI), Linköping, Sweden.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. Swedish Defence Research Agency (FOI), Linköping, Sweden.
    On distinguishing between human individuals in micro-Doppler signatures2013In: 14th International Radar Symposium (IRS), 2013, p. 865-870Conference paper (Refereed)
    Abstract [en]

    Radar micro-Doppler signatures (MDS) of humans are created by movements of body parts, such as legs and arms. MDSs can be used in security applications to detect humans and classify their type and activity. Target association and tracking, which can facilitate the classification, become easier if it is possible to distinguish between human individuals by their MDSs. By this we mean to recognize the same individual in a short time frame but not to establish the identity of the individual. In this paper we perform a statistical experiment in which six test persons are able to distinguish between walking human individuals from their MDSs. From this we conclude that there is information in the MDSs of the humans to distinguish between different individuals, which also can be used by a machine. Based on the results of the best test persons we also discuss features in the MDSs that could be utilized to make this processing possible.

  • 5.
    Bleser, Gabriele
    et al.
    Department Augmented Vision, German Research Center for Artificial Intelligence, Kaiserslautern, Germany; Department of Computer Science, Technical University of Kaiserslautern, Kaiserslautern, Germany.
    Damen, Dima
    Department of Computer Science, University of Bristol, Bristol, UK.
    Behera, Ardhendu
    School of Computing, University of Leeds, Leeds, UK; Department of Computing, Edge Hill University, Ormskirk, UK.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Mura, Katharina
    SmartFactory KL e.V., Kaiserslautern, Germany.
    Miezal, Markus
    Department of Computer Science, Technical University of Kaiserslautern, Kaiserslautern, Germany.
    Gee, Andrew
    Department of Computer Science, University of Bristol, Bristol, UK.
    Petersen, Nils
    Department Augmented Vision, German Research Center for Artificial Intelligence, Kaiserslautern, Germany.
    Maçães, Gustavo
    Department Computer Vision, Interaction and Graphics, Center for Computer Graphics, Guimarães, Portugal.
    Domingues, Hugo
    Department Computer Vision, Interaction and Graphics, Center for Computer Graphics, Guimarães, Portugal.
    Gorecky, Dominic
    SmartFactory KL e.V., Kaiserslautern, Germany.
    Almeida, Luis
    Department Computer Vision, Interaction and Graphics, Center for Computer Graphics, Guimarães, Portugal.
    Mayol-Cuevas, Walterio
    Department of Computer Science, University of Bristol, Bristol, UK.
    Calway, Andrew
    Department of Computer Science, University of Bristol, Bristol, UK.
    Cohn, Anthony G.
    School of Computing, University of Leeds, Leeds, UK.
    Hogg, David C.
    School of Computing, University of Leeds, Leeds, UK.
    Stricker, Didier
    Department Augmented Vision, German Research Center for Artificial Intelligence, Kaiserslautern, Germany.
    Cognitive Learning, Monitoring and Assistance of Industrial Workflows Using Egocentric Sensor Networks2015In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 10, no 6, article id e0127769Article in journal (Refereed)
    Abstract [en]

    Today, the workflows that are involved in industrial assembly and production activities are becoming increasingly complex. To efficiently and safely perform these workflows is demanding on the workers, in particular when it comes to infrequent or repetitive tasks. This burden on the workers can be eased by introducing smart assistance systems. This article presents a scalable concept and an integrated system demonstrator designed for this purpose. The basic idea is to learn workflows from observing multiple expert operators and then transfer the learnt workflow models to novice users. Being entirely learning-based, the proposed system can be applied to various tasks and domains. The above idea has been realized in a prototype, which combines components pushing the state of the art of hardware and software designed with interoperability in mind. The emphasis of this article is on the algorithms developed for the prototype: 1) fusion of inertial and visual sensor information from an on-body sensor network (BSN) to robustly track the user’s pose in magnetically polluted environments; 2) learning-based computer vision algorithms to map the workspace, localize the sensor with respect to the workspace and capture objects, even as they are carried; 3) domain-independent and robust workflow recovery and monitoring algorithms based on spatiotemporal pairwise relations deduced from object and user movement with respect to the scene; and 4) context-sensitive augmented reality (AR) user feedback using a head-mounted display (HMD). A distinguishing key feature of the developed algorithms is that they all operate solely on data from the on-body sensor network and that no external instrumentation is needed. The feasibility of the chosen approach for the complete action-perception-feedback loop is demonstrated on three increasingly complex datasets representing manual industrial tasks. These limited size datasets indicate and highlight the potential of the chosen technology as a combined entity as well as point out limitations of the system.

  • 6.
    Bleser, Gabriele
    et al.
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Hendeby, Gustaf
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Using egocentric vision to achieve robust inertial body tracking under magnetic disturbances2011Conference paper (Refereed)
    Abstract [en]

    In the context of a smart user assistance system for industrial manipulation tasks it is necessary to capture motions of the upper body and limbs of the worker in order to derive his or her interactions with the task space. While such capturing technology already exists, the novelty of the proposed work results from the strong requirements of the application context: The method should be flexible and use only on-body sensors, work accurately in industrial environments that suffer from severe magnetic disturbances, and enable consistent registration between the user body frame and the task space. Currently available systems cannot provide this. This paper suggests a novel egocentric solution for visual-inertial upper-body motion tracking based on recursive filtering and model-based sensor fusion. Visual detections of the wrists in the images of a chest-mounted camera are used as substitute for the commonly used magnetometer measurements. The on-body sensor network, the motion capturing system, and the required calibration procedure are described and successful operation is shown in a real industrial environment.

  • 7.
    Bleser, Gabriele
    et al.
    German Research Center for Artificial Intelligence, Kaiserslautern, Germany .
    Hendeby, Gustaf
    German Research Center for Artificial Intelligence, Kaiserslautern, Germany .
    Using optical flow as lightweight SLAM alternative2009In: Mixed and Augmented Reality, 2009, IEEE , 2009, p. 175-176Conference paper (Refereed)
    Abstract [en]

    Visual simultaneous localisation and mapping (SLAM) is since the last decades an often addressed problem. Online mapping enables tracking in unknown environments. However, it also suffers from high computational complexity and potential drift. Moreover, in augmented reality applications the map itself is often not needed and the target environment is partially known, e.g. in a few 3D anchor or marker points. In this paper, rather than using SLAM, measurements based on optical flow are introduced. With these measurements, a modified visual-inertial tracking method is derived, which in Monte Carlo simulations reduces the need for 3D points and allows tracking for extended periods of time without any 3D point registrations.

  • 8.
    Bleser, Gabriele
    et al.
    German Research Center for Artificial Intelligence, Kaiserslautern, Germany.
    Hendeby, Gustaf
    German Research Center for Artificial Intelligence, Kaiserslautern, Germany.
    Using optical flow for filling the gaps in visual-inertial tracking2010Conference paper (Refereed)
    Abstract [en]

    Egomotion tracking is since the last decades an often addressed problem and hybrid approaches evidentially have potential to provide accurate, efficient and robust results. Simultaneous localisation and mapping (SLAM) - in contrast to a model-based approach - is used to enable tracking in unknown environments. However, it also suffers from high computational complexity. Moreover, in many applications, the map itself is not needed and the target environment is partiall known, e.g. in a few 3D anchor points. In this paper, rather than using SLAM, optical flow measurements are introduced into a model-based system. With these measurements, a modified visual-inertial tracking method is derived, which in Monte Carlo simulations reduces the need for 3D points and thus allows tracking during extended gaps of 3D point registrations.

  • 9.
    Bleser, Gabriele
    et al.
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Steffen, Daniel
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Reiss, Attila
    ACTLab, University of Passau, 94032, Passau, Germany.
    Weber, Markus
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Fradet, Laetitia
    Université de Poitiers, 86000, Poitiers, France.
    Personalized Physical Activity Monitoring Using Wearable Sensors2015In: Smart Health: Open Problems and Future Challenges / [ed] Andreas Holzinger, Carsten Röcker, Martina Ziefle, Springer International Publishing , 2015, p. 99-124Chapter in book (Refereed)
    Abstract [en]

    It is a well-known fact that exercising helps people improve their overall well-being; both physiological and psychological health. Regular moderate physical activity improves the risk of disease progression, improves the chances for successful rehabilitation, and lowers the levels of stress hormones. Physical fitness can be categorized in cardiovascular fitness, and muscular strength and endurance. A proper balance between aerobic activities and strength exercises are important to maximize the positive effects. This balance is not always easily obtained, so assistance tools are important. Hence, ambient assisted living (AAL) systems that support and motivate balanced training are desirable. This chapter presents methods to provide this, focusing on the methodologies and concepts implemented by the authors in the physical activity monitoring for aging people (PAMAP) platform. The chapter sets the stage for an architecture to provide personalized activity monitoring using a network of wearable sensors, mainly inertial measurement units (IMU). The main focus is then to describe how to do this in a personalizable way: (1) monitoring to provide an estimate of aerobic activities performed, for which a boosting based method to determine activity type, intensity, frequency, and duration is given; (2) supervise and coach strength activities. Here, methodologies are described for obtaining the parameters needed to provide real-time useful feedback to the user about how to exercise safely using the right technique.

  • 10.
    Bleser, Gabriele
    et al.
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Steffen, Daniel
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Weber, Markus
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Hendeby, Gustaf
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Stricker, Didier
    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany.
    Fradet, Laetitia
    Université de Technologie de Compiègne, France.
    Marin, Frédéric
    Université de Technologie de Compiègne, France.
    Ville, Nathalie
    CIC-IT Inserm 804, Rennes, France.
    Carré, Francois
    CIC-IT Inserm 804, Rennes, France.
    A personalized exercise trainer for the elderly2013In: Journal of Ambient Intelligence and Smart Environments, ISSN 1876-1364, E-ISSN 1876-1372, Vol. 5, no 6, p. 547-562Article in journal (Refereed)
    Abstract [en]

    Regular and moderate physical activity practice provides many physiological benefits. It reduces the risk of disease outcomes and is the basis for proper rehabilitation after a severe disease. Aerobic activity and strength exercises are strongly recommended in order to maintain autonomy with ageing. Balanced activity of both types is important, especially to the elderly population. Several methods have been proposed to monitor aerobic activities. However, no appropriate method is available for controlling more complex parameters of strength exercises. Within this context, the present article introduces a personalized, home-based strength exercise trainer designed for the elderly. The system guides a user at home through a personalized exercise program. Using a network of wearable sensors the user's motions are captured. These are evaluated by comparing them to prescribed exercises, taking both exercise load and technique into account. Moreover, the evaluation results are immediately translated into appropriate feedback to the user in order to assist the correct exercise execution. Besides the direct feedback, a major novelty of the system is its generic personalization by means of a supervised teach-in phase, where the program is performed once under supervision of a physical activity specialist. This teach-in phase allows the system to record and learn the correct execution of exercises for the individual user and to provide personalized monitoring. The user-driven design process, the system development and its underlying activity monitoring methodology are described. Moreover, technical evaluation results as well as results concerning the usability of the system for ageing people are presented. The latter has been assessed in a clinical study with thirty participants of 60 years or older, some of them showing usual diseases or functional limitations observed in elderly population.

  • 11.
    Boström-Rost, Per
    et al.
    Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Automatic Control.
    Axehill, Daniel
    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, The Institute of Technology. Linköping University, Faculty of Science & Engineering. Linköping University.
    Informative Path Planning for Active Tracking of Agile Targets2019In: 2019 IEEE Aerospace Conference, Institute of Electrical and Electronics Engineers (IEEE), 2019, p. 1-11, article id 06.0701Conference paper (Refereed)
    Abstract [en]

    This paper proposes a method to generate informative trajectories for a mobile sensor that tracks agile targets.The goal is to generate a sensor trajectory that maximizes the tracking performance, captured by a measure of the covariance matrix of the target state estimate. The considered problem is acombination of estimation and control, and is often referred to as informative path planning (IPP). When using nonlinear sensors, the tracking performance depends on the actual measurements, which are naturally unavailable in the planning stage.The planning problem hence becomes a stochastic optimization problem, where the expected tracking performance is used inthe objective function. The main contribution of this work is anapproximation of the problem based on deterministic sampling of the predicted target distribution. This is in contrast to prior work, where only the most likely target trajectory is considered.It is shown that the proposed method greatly improves the ability to track agile targets, compared to a baseline approach.   

  • 12.
    Boström-Rost, Per
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Axehill, Daniel
    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.
    Informative Path Planning in the Presence of Adversarial Observers2019In: 2019 22nd International Conference on Information Fusion (FUSION), 2019Conference paper (Refereed)
    Abstract [en]

    This paper considers the problem of gathering information about features of interest in adversarial environments using mobile robots equipped with sensors. The problem is formulated as an informative path planning problem where the objective is to maximize the gathered information while minimizing the tracking performance of the adversarial observer. The optimization problem, that at first glance seems intractable to solve to global optimality, is shown to be equivalent to a mixed-integer semidefinite program that can be solved to global optimality using off-the-shelf optimization tools.

  • 13.
    Boström-Rost, Per
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Axehill, Daniel
    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.
    On Global Optimization for Informative Path Planning2018In: IEEE Control Systems Letters, ISSN 2475-1456, Vol. 2, no 4, p. 833-838Article in journal (Refereed)
    Abstract [en]

    The problem of path planning for mobilesensors with the task of target monitoring is considered. A receding horizon optimal control approach based on the information filter is presented, where the limited field of view of the sensor can be modeled by introducing binary variables. The resulting nonlinear mixed integer problem to be solved in each sample, with no apparent tractable solution, is shown to be equivalent to a problem that robustly can be solved to global optimality using off-the-shelf optimization tools.

  • 14.
    Deleskog, Viktor
    et al.
    Totalförsvarets forskningsinstitut (FOI).
    Habberstad, Hans
    Totalförsvarets forskningsinstitut (FOI).
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Wahlström, Niklas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust NLS Sensor Localization using MDS Initialization2014In: 17th International Conference on Information Fusion (FUSION), 2014, Institute of Electrical and Electronics Engineers (IEEE), 2014, p. 1-7Conference paper (Refereed)
    Abstract [en]

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

  • 15.
    Dil, Bram
    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.
    Hoenders, Bernhard
    University of Groningen, Centre for Theoretical Physics, Zernike Institute for Advanced Materials.
    Approximate Diagonalized Covariance Matrix for Signals with Correlated Noise2016In: Proceedings of the 19th International Conference of Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 521-527Conference paper (Refereed)
    Abstract [en]

    This paper proposes a diagonal covariance matrix approximation for Wide-Sense Stationary (WSS) signals with correlated Gaussian noise. Existing signal models that incorporate correlations often require regularization of the covariance matrix, so that the covariance matrix can be inverted. The disadvantage of this approach is that matrix inversion is computational intensive and regularization decreases precision. We use Bienayme's theorem to approximate the covariance matrix by a diagonal one, so that matrix inversion becomes trivial, even with nonuniform rather than only uniform sampling that was considered in earlier work. This approximation reduces the computational complexity of the estimator and estimation bound significantly. We numerically validate this approximation and compare our approach with the Maximum Likelihood Estimator (MLE) and Cramer-Rao Lower Bound (CRLB) for multivariate Gaussian distributions. Simulations show that our approach differs less than 0.1% from this MLE and CRLB when the observation time is large compared to the correlation time. Additionally, simulations show that in case of non-uniform sampling, we increase the performance in comparison to earlier work by an order of magnitude. We limit this study to correlated signals in the time domain, but the results are also applicable in the space domain.

  • 16.
    Forsling, Robin
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Sjanic, Zoran
    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.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Consistent Distributed Track Fusion Under Communication Constraints2019In: Proceedings of the 22nd International Conference on Information Fusion (FUSION), 2019Conference paper (Refereed)
    Abstract [en]

    This paper addresses the problem of retrieving consistentestimates in a distributed network where the communication between the nodes is constrained such that only the diagonal elements of the covariance matrix are allowed to be exchanged. Several methods are developed for preserving and/or recovering consistency under the constraints imposed by the communication protocol. The proposed methods are used in conjunction with the covariance intersection method and the estimation performance is evaluated based on information usage and consistency. The results show that among the proposed methods, consistency can be preserved equally well at the transmitting node as at the receiving node.

  • 17.
    Grönwall, Christina
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. FOI.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Kristian, Sinivaara
    Cybercom Sweden AB (Sweden).
    A proposal for combining mapping, localization and target recognition2015In: ELECTRO-OPTICAL REMOTE SENSING, PHOTONIC TECHNOLOGIES, AND APPLICATIONS IX / [ed] Gary Kamerman; Ove Steinvall; Keith L. Lewis; John D. Gonglewski, SPIE - International Society for Optical Engineering, 2015, Vol. 9649Conference paper (Refereed)
    Abstract [en]

    Simultaneous localization and mapping (SLAM) is a well-known positioning approach in GPS-denied environments such as urban canyons and inside buildings. Autonomous/aided target detection and recognition (ATR) is commonly used in military application to detect threats and targets in outdoor environments. This papers present approaches to combine SLAM with ATR in ways that compensate for the drawbacks in each method. The methods use physical objects that are recognizable by ATR as unambiguous features in SLAM, while SLAM provides the ATR with better position estimates. Landmarks in the form of 3D point features based on normal aligned radial features (NARF) are used in conjunction with identified objects and 3D object models that replace landmarks when possible. This leads to a more compact map representation with fewer landmarks, which partly compensates for the introduced cost of the ATR. We analyze three approaches to combine SLAM and 3D-data; point-point matching ignoring NARF features, point-point matching using the set of points that are selected by NARF feature analysis, and matching of NARF features using nearest neighbor analysis. The first two approaches are is similar to the common iterative closest point (ICP). We propose an algorithm that combines EKF-SLAM and ATR based on rectangle estimation. The intended application is to improve the positioning of a first responder moving through an indoor environment, where the map offers localization and simultaneously helps locate people, furniture and potentially dangerous objects such as gas canisters.

  • 18.
    Gustafsson, Fredrik
    et al.
    Linköping University, The Institute of Technology. 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, The Institute of Technology. Linköping University, Faculty of Science & Engineering.
    Exploring New Localization Applications Using a Smartphone2017In: Sensing and Control for Autonomous Vehicles: Applications to Land, Water and Air Vehicles / [ed] Thor I. Fossen, Kristin Y. Pettersen, Henk Nijmeijer, Springer, 2017, p. 161-179Chapter in book (Refereed)
    Abstract [en]

    Localization is an enabling technology in many applications and services today and in the future. Satellite navigation often works fine for navigation, infotainment and location based services, and it is today the dominating solution in commercial products. A nice exception is the localization in Google Maps, where radio signal strength from WiFi and cellular networks are used as complementary information to increase accuracy and integrity. With the on-going trend with more autonomous functions being introduced in our vehicles and with all our connected devices, most of them operated in indoor enviroments where satellite signals are not available,there is an acute need for new solutions.

    At the same time, our smartphones are getting more sophisticated in their sensor configuration. Therefore, in this chapter we present a freely available Sensor Fusion app developed in-house, how it works, how it has been used, and how it can be used based on a variety of applications in our research and student projects.

  • 19.
    Gustafsson, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Some Relations Between Extended and Unscented Kalman Filters2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 2, p. 545-555Article in journal (Refereed)
    Abstract [en]

    The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

  • 20.
    Gustafsson, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Lindgren, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Mathai, George
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Habberstad, Hans
    Swedish Defence Research Agency (FOI).
    Direction of Arrival Estimation in Sensor Arrays Using Local Series Expansion of the Received Signal2015In: 18th International Conference of Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2015Conference paper (Refereed)
    Abstract [en]

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

  • 21.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Development and Evaluation of an Active Radio Frequency Seeker Model for a Missile with Data-Link Capability2002Independent thesis Basic level (professional degree)Student thesis
    Abstract [en]

    To develop and maintain a modern combat aircraft it is important to have simple, yet accurate, threat models to support early stages of functional development. Therefore this thesis develops and evaluates a model of an active radio frequency (RF) seeker for a missile with data-link capability. The highly parametrized MATLAB-model consists of a pulse level radar model, a tracker using either interacting multiple models (IMM) or particle filters, and a guidance law.

    Monte Carlo simulations with the missile model indicate that, under the given conditions, the missile performs well (hit rate>99%) with both filter types, and the model is relatively insensitive to lost data-link transmissions. It is therefore under normal conditions not worthwhile to use the more computer intense particle filter today, however when the data-link degrades the particle filter performs considerably better than the IMM filter. Analysis also indicate that the measurements generated by the radar model are neither independent, white nor Gaussian. This contradicts the assumptions made in this, and many other radar applications. However, the performance of the model suggests that the assumptions are acceptable approximations of actual conditions, but further studies within this are recommended to verify this.

  • 22.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Fundamental Estimation and Detection Limits in Linear Non-Gaussian Systems2005Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Many methods used for estimation and detection consider only the mean and variance of the involved noise instead of the full noise descriptions. One reason for this is that the mathematics is often considerably simplified this way. However, the implications of the simplifications are seldom studied, and this thesis shows that if no approximations are made performance is gained. Furthermore, the gain is quantified in terms of the useful information in the noise distributions involved. The useful information is given by the intrinsic accuracy, and a method to compute the intrinsic accuracy for a given distribution, using Monte Carlo methods, is outlined.

    A lower bound for the covariance of the estimation error for any unbiased estimator s given by the Cramér-Rao lower bound (CRLB). At the same time, the Kalman filter is the best linear unbiased estimator (BLUE) for linear systems. It is in this thesis shown that the CRLB and the BLUE performance are given by the same expression, which is parameterized in the intrinsic accuracy of the noise. How the performance depends on the noise is then used to indicate when nonlinear filters, e.g., a particle filter, should be used instead of a Kalman filter. The CRLB results are shown, in simulations, to be a useful indication of when to use more powerful estimation methods. The simulations also show that other techniques should be used as a complement to the CRLB analysis to get conclusive performance results.

    For fault detection, the statistics of the asymptotic generalized likelihood ratio (GLR) test provides an upper bound on the obtainable detection performance. The performance is in this thesis shown to depend on the intrinsic accuracy of the involved noise. The asymptotic GLR performance can then be calculated for a test using the actual noise and for a test using the approximative Gaussian noise. Based on the difference in performance, it is possible to draw conclusions about the quality of the Gaussian approximation. Simulations show that when the difference in performance is large, an exact noise representation improves the detection. Simulations also show that it is difficult to predict the exact influence on the detection performance caused by substituting the system noise with Gaussian noise approximations.

  • 23.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Performance and Implementation Aspects of Nonlinear Filtering2008Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Nonlinear filtering is an important standard tool for information and sensor fusion applications, e.g., localization, navigation, and tracking. It is an essential component in surveillance systems and of increasing importance for standard consumer products, such as cellular phones with localization, car navigation systems, and augmented reality. This thesis addresses several issues related to nonlinear filtering, including performance analysis of filtering and detection, algorithm analysis, and various implementation details.

    The most commonly used measure of filtering performance is the root mean square error (RMSE), which is bounded from below by the Cramér-Rao lower bound (CRLB). This thesis presents a methodology to determine the effect different noise distributions have on the CRLB. This leads up to an analysis of the intrinsic accuracy (IA), the informativeness of a noise distribution. For linear systems the resulting expressions are direct and can be used to determine whether a problem is feasible or not, and to indicate the efficacy of nonlinear methods such as the particle filter (PF). A similar analysis is used for change detection performance analysis, which once again shows the importance of IA.

    A problem with the RMSE evaluation is that it captures only one aspect of the resulting estimate and the distribution of the estimates can differ substantially. To solve this problem, the Kullback divergence has been evaluated demonstrating the shortcomings of pure RMSE evaluation.

    Two estimation algorithms have been analyzed in more detail; the Rao-Blackwellized particle filter (RBPF) by some authors referred to as the marginalized particle filter (MPF) and the unscented Kalman filter (UKF). The RBPF analysis leads to a new way of presenting the algorithm, thereby making it easier to implement. In addition the presentation can possibly give new intuition for the RBPF as being a stochastic Kalman filter bank. In the analysis of the UKF the focus is on the unscented transform (UT). The results include several simulation studies and a comparison with the Gauss approximation of the first and second order in the limit case.

    This thesis presents an implementation of a parallelized PF and outlines an object-oriented framework for filtering. The PF has been implemented on a graphics processing unit (GPU), i.e., a graphics card. The GPU is a inexpensive parallel computational resource available with most modern computers and is rarely used to its full potential. Being able to implement the PF in parallel makes new applications, where speed and good performance are important, possible. The object-oriented filtering framework provides the flexibility and performance needed for large scale Monte Carlo simulations using modern software design methodology. It can also be used to help to efficiently turn a prototype into a finished product.

  • 24.
    Hendeby, Gustaf
    et al.
    German Research Center for Artificial Intelligence, Kaiserslautern, Germany.
    Bleser, Gabriele
    German Research Center for Artificial Intelligence, Kaiserslautern, Germany.
    Lamprinos, Illias
    Stricker, Didier
    German Research Center for Artificial Intelligence, Kaiserslautern, Germany.
    Healthy aging using physical activity monitoring2010Conference paper (Other (popular science, discussion, etc.))
  • 25.
    Hendeby, Gustaf
    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.
    Detection Limits for Linear Non-Gaussian State-Space Models2006In: Proceedings of the 6th IFAC Symposium on Fault Detection, Supervision and Safty of Technical Processes, 2006, p. 282-287Conference paper (Refereed)
    Abstract [en]

    The performance of nonlinear fault detection schemes is hard to decide objectively, so Monte Carlo simulations are often used to get a subjective measure and relative performance for comparing different algorithms. There is a strong need for a constructive way of computing an analytical performance bound, similar to the Cramér-Rao lower bound for estimation. This paper provides such a result for linear non-Gaussian systems. It is first shown how a batch of data from a linear state-space model with additive faults and non-Gaussian noise can be transformed to a residual described by a general linear non-Gaussian model. This also involves a parametric description of incipient faults. The generalized likelihood ratio test is then used as the asymptotic performance bound. The test statistic itself may be impossible to compute without resorting to numerical algorithms, but the detection performance scales analytically with a constant that depends only on the distribution of the noise. It is described how to compute this constant, and a simulation study illustrates the results.

  • 26.
    Hendeby, Gustaf
    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.
    Detection Limits for Linear Non-Gaussian State-Space Models2006Report (Other academic)
    Abstract [en]

    The performance of nonlinear fault detection schemes is hard to decide objectively, so Monte Carlo simulations are often used to get a subjective measure and relative performance for comparing different algorithms. There is a strong need for a constructive way of computing an analytical performance bound, similar to the Cramér-Rao lower bound for estimation. This paper provides such a result for linear non-Gaussian systems. It is first shown how a batch of data from a linear state-space model with additive faults and non-Gaussian noise can be transformed to a residual described by a general linear non-Gaussian model. This also involves a parametric description of incipient faults. The generalized likelihood ratio test is then used as the asymptotic performance bound. The test statistic itself may be impossible to compute without resorting to numerical algorithms, but the detection performance scales analytically with a constant that depends only on the distribution of the noise. It is described how to compute this constant, and a simulation study illustrates the results.

  • 27.
    Hendeby, Gustaf
    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.
    Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems2005In: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, 2005, p. 338-343Conference paper (Refereed)
    Abstract [en]

    Sophisticated fault detection (FD) algorithms often include nonlinear mappings of observed data to fault decisions, and simulation studies are used to support the methods. Objective statistically supported performance analysis of FDalgorithms is only possible for some special cases, including linear Gaussian models. The goal here is to derive general statistical performance bounds for any FD algorithm, given a nonlinear non-Gaussian model of the system. Recent advances in numerical algorithms for nonlinear filtering indicate that such bounds in many practical cases are attainable. This paper focuses on linear non-Gaussian models. A couple of different fault detection setups based on parity space and Kalman filter approaches are considered, where the fault enters a computable residual linearly. For this class of systems, fault detection can be based on the best linear unbiased estimate (BLUE) of the fault vector. Alternatively, a nonlinear filter can potentially compute the maximum likelihood (ML) state estimate, whose performance is bounded by the Cramér-Rao lower bound (CRLB). The contribution in this paper is general expressions for the CRLB for this class of systems, interpreted in terms offault detectability. The analysis is exemplified for a case with measurements affected by outliers.

  • 28.
    Hendeby, Gustaf
    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.
    Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems2005Report (Other academic)
    Abstract [en]

    Sophisticated fault detection (FD) algorithms often include nonlinear mappings of observed data to fault decisions, and simulation studies are used to support the methods. Objective statistically supported performance analysis of FDalgorithms is only possible for some special cases, including linear Gaussian models. The goal here is to derive general statistical performance bounds for any FD algorithm, given a nonlinear non-Gaussian model of the system. Recent advances in numerical algorithms for nonlinear filtering indicate that such bounds in many practical cases are attainable. This paper focuses on linear non-Gaussian models. A couple of different fault detection setups based on parity space and Kalman filter approaches are considered, where the fault enters a computable residual linearly. For this class of systems, fault detection can be based on the best linear unbiased estimate (BLUE) of the fault vector. Alternatively, a nonlinear filter can potentially compute the maximum likelihood (ML) state estimate, whose performance is bounded by the Cramér-Rao lower bound (CRLB). The contribution in this paper is general expressions for the CRLB for this class of systems, interpreted in terms offault detectability. The analysis is exemplified for a case with measurements affected by outliers.

  • 29.
    Hendeby, Gustaf
    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.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2006In: Proceedings of Reglermöte 2006, 2006Conference paper (Other academic)
    Abstract [en]

    The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. The procedure is derived in terms of the posterior Cramer-Rao lower bound. Results are shown for a class of standard distributions and models in practice.

  • 30.
    Hendeby, Gustaf
    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.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2005In: Proceedings of the 16th IFAC World Congress, 2005, p. 45-45Conference paper (Refereed)
    Abstract [en]

    The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. The procedure is derived in terms of the posterior Cramér-Rao lower bound. Results are shown for a class of standard distributions and models in practice.

  • 31.
    Hendeby, Gustaf
    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.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2004Report (Other academic)
    Abstract [en]

    The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. The procedure is derived in terms of the posterior Cramer-Rao lower bound. Results are shown for a class of standard distributions and models in practice.

  • 32.
    Hendeby, Gustaf
    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.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2005Report (Other academic)
    Abstract [en]

    The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. The procedure is derived in terms of the posterior Cramér-Rao lower bound. Results are shown for a class of standard distributions and models in practice.

  • 33.
    Hendeby, Gustaf
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On Nonlinear Transformations of Stochastic Variables and its Application to Nonlinear Filtering2008In: Proceedings of the '08 IEEE International Conference on Acoustics, Speech and Signal Processing, 2008, p. 3617-3620Conference paper (Refereed)
    Abstract [en]

    A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed. The nonlinear transformations that can be used include first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation. The unscented Kalman filter (UKF) is by construction a special case, but also nonstandard implementations of the Kalman filter (KF) and the extended Kalman filter (EKF) are included, where there are no explicit Riccati equations. The theoretical properties of these mappings are important for the performance of the NLTF. TT 2 does by definition take care of the bias and covariance of the second order term that is neglected in the TT 1 based EKF. The UT computes this bias term accurately, but the covariance is correct only for scalar state vectors. This result is demonstrated with a simple example and a general theorem, which explicitly shows the difference between TT 1, TT 2, UT, and MCT.

  • 34.
    Hendeby, Gustaf
    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.
    On Nonlinear Transformations of Stochastic Variables and its Application to Nonlinear Filtering2007Report (Other academic)
    Abstract [en]

    A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed. The nonlinear transformations that can be used include first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation. The unscented Kalman filter (UKF) is by construction a special case, but also nonstandard implementations of the Kalman filter (KF) and the extended Kalman filter (EKF) are included, where there are no explicit Riccati equations. The theoretical properties of these mappings are important for the performance of the NLTF. TT 2 does by definition take care of the bias and covariance of the second order term that is neglected in the TT 1 based EKF. The UT computes this bias term accurately, but the covariance is correct only for scalar state vectors. This result is demonstrated with a simple example and a general theorem, which explicitly shows the difference between TT 1, TT 2, UT, and MCT.

  • 35.
    Hendeby, Gustaf
    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.
    On Performance Measures for Approximative Parameter Estimation2004In: Proceedings of Reglermöte 2004, 2004Conference paper (Other academic)
    Abstract [en]

    The Kalman filter computes the minimum variance state estimate as a linear function of measurements in the case of a linear model with Gaussian noise processes. There are plenty of examples of non-linear estimators that outperform the Kalman filter when the noise processes deviate from Gaussianity, for instance in target tracking with occasionally maneuvering targets. Here we present, in a preliminary study, a detailed analysis of the well-known parameter estimation problem. This time with Gaussian mixture measurement noise. We compute the discrepancy of the best linear unbiased estimator BLUE and the Cramer-Rao lower bound, and based on this conclude when computationally intensive Kalman filter banks or particle filters may be used to improve performance.

  • 36.
    Hendeby, Gustaf
    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.
    On Performance Measures for Approximative Parameter Estimation2004Report (Other academic)
    Abstract [en]

    The Kalman filter computes the minimum variance state estimate as a linear function of measurements in the case of a linear model with Gaussian noise processes. There are plenty of examples of non-linear estimators that outperform the Kalman filter when the noise processes deviate from Gaussianity, for instance in target tracking with occasionally maneuvering targets. Here we present, in a preliminary study, a detailed analysis of the well-known parameter estimation problem. This time with Gaussian mixture measurement noise. We compute the discrepancy of the best linear unbiased estimator BLUE and the Cramer-Rao lower bound, and based on this conclude when computationally intensive Kalman filter banks or particle filters may be used to improve performance.

  • 37.
    Hendeby, Gustaf
    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.
    Wahlström, Niklas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Teaching Sensor Fusion and Kalman Filtering using a Smartphone2014In: Proceedings of the 19th World Congress of the International Federation of Automatic Control (IFAC), IFAC Papers Online, 2014Conference paper (Refereed)
    Abstract [en]

    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 tohave been successful in reaching the pedagogic goals and to engage the students.

  • 38.
    Hendeby, Gustaf
    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.
    Wahlström, Niklas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gunnarsson, Svante
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Platform for Teaching Sensor Fusion Using a Smartphone2017In: International journal of engineering education, ISSN 0949-149X, Vol. 33, no 2B, p. 781-789Article in journal (Refereed)
    Abstract [en]

    A platform for sensor fusion consisting of a standard smartphone equipped with the specially developed Sensor Fusion appis presented. The platform enables real-time streaming of data over WiFi to a computer where signal processingalgorithms, e.g., the Kalman filter, can be developed and executed in a Matlab framework. The platform is an excellenttool for educational purposes and enables learning activities where methods based on advanced theory can be implementedand evaluated at low cost. The article describes the app and a laboratory exercise developed around these new technologicalpossibilities. The laboratory session is part of a course in sensor fusion, a signal processing continuation course focused onmultiple sensor signal applications, where the goal is to give the students hands on experience of the subject. This is done byestimating the orientation of the smartphone, which can be easily visualized and also compared to the built-in filters in thesmartphone. The filter can accept any combination of sensor data from accelerometers, gyroscopes, and magnetometers toexemplify their importance. This way different tunings and tricks of important methods are easily demonstrated andevaluated on-line. The presented framework facilitates this in a way previously impossible.

  • 39.
    Hendeby, Gustaf
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hol, Jeroen
    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.
    A Graphics Processing Unit Implementation of the Particle Filter2007In: Proceedings of the 15th European Statistical Signal Processing Conference, European Association for Signal, Speech, and Image Processing , 2007, p. 1639-1643Conference paper (Refereed)
    Abstract [en]

    Modern graphics cards for computers, and especially their graphics processing units (GPUs), are designed for fast rendering of graphics. In order to achieve this GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper GPGPU techniques are used to make a parallel GPU implementation of state-of-the-art recursive Bayesian estimation using particle filters (PF). The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to one achieved with a traditional CPU implementation. The resulting GPU filter is faster with the same accuracy as the CPU filter for many particles, and it shows how the particle filter can be parallelized.

  • 40.
    Hendeby, Gustaf
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hol, Jeroen
    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.
    A Graphics Processing Unit Implementation of the Particle Filter2007Report (Other academic)
    Abstract [en]

    Modern graphics cards for computers, and especially their graphics processing units (GPUs), are designed for fast rendering of graphics. In order to achieve this GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper GPGPU techniques are used to make a parallel GPU implementation of state-of-the-art recursive Bayesian estimation using particle filters (PF). The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to one achieved with a traditional CPU implementation. The resulting GPU filter is faster with the same accuracy as the CPU filter for many particles, and it shows how the particle filter can be parallelized.

  • 41.
    Hendeby, Gustaf
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hol, Jeroen
    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.
    Graphics Processing Unit Implementation of the Particle Filter2006Report (Other academic)
    Abstract [en]

    Modern graphics cards for computers, and especially their graphics processing units (GPUs), are designed for fast rendering of graphics. In order to achieve this GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper GPGPU techniques are used to make a parallel GPU implementation of state-of-the-art recursive Bayesian estimation using particle filters (PF). The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to one achieved with a traditional CPU implementation. The resulting GPU filter is faster with the same accuracy as the CPU filter for many particles, and it shows how the particle filter can be parallelized.

  • 42.
    Hendeby, Gustaf
    et al.
    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.
    Gaussian Mixture PHD Filtering with Variable Probability of Detection2014In: 17th International Conference on Information Fusion (FUSION), 2014, IEEE , 2014, p. 1-7Conference paper (Refereed)
    Abstract [en]

    The probabilistic hypothesis density (PHD) filter has grown in popularity during the last decade as a way to address the multi-target tracking problem. Several algorithms exist; for instance under linear-Gaussian assumptions, the Gaussian mixture PHD (GM-PHD) filter. This paper extends the GM-PHD filter to the common case with variable probability of detection throughout the tracking volume. This allows for more efficient utilization, e.g., in situations with distance dependent probability of detection or occluded regions. The proposed method avoids previous algorithmic pitfalls that can result in a not well-defined PHD. The method is illustrated and compared to the standard GM-PHD in a simplified multi-target tracking example as well asin a realistic nonlinear underwater sonar simulation application, both demonstrating the effectiveness of the proposed method.

  • 43.
    Hendeby, Gustaf
    et al.
    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.
    Target Tracking Performance Evaluation - A General Software Environment for Filtering2007In: Proceedings of the 2007 IEEE Aerospace Conference, 2007, p. 1-13Conference paper (Refereed)
    Abstract [en]

    In this paper, several recursive Bayesian filtering methods for target tracking are discussed. Performance for target tracking problems is usually measured using the second-order moment. For nonlinear or non-Gaussian applications, this measure is not always sufficient. The Kullback divergence is proposed as an alternative to mean square error analysis, and it is extensively used to compare estimated posterior distributions for various applications. The important issue of efficient software development, for nonlinear and non-Gaussian estimation, is also addressed. A new framework in C++ is detailed. Utilizing modern design techniques an object oriented filtering and simulation framework is provided to allow for easy and efficient comparisons of different estimators. The software environment is extensively used in several applications and examples.

  • 44.
    Hendeby, Gustaf
    et al.
    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.
    Target Tracking Performance Evaluation - A General Software Environment for Filtering2007Report (Other academic)
    Abstract [en]

    In this paper, several recursive Bayesian filtering methods for target tracking are discussed. Performance for target tracking problems is usually measured using the second-order moment. For nonlinear or non-Gaussian applications, this measure is not always sufficient. The Kullback divergence is proposed as an alternative to mean square error analysis, and it is extensively used to compare estimated posterior distributions for various applications. The important issue of efficient software development, for nonlinear and non-Gaussian estimation, is also addressed. A new framework in C++ is detailed. Utilizing modern design techniques an object oriented filtering and simulation framework is provided to allow for easy and efficient comparisons of different estimators. The software environment is extensively used in several applications and examples.

  • 45.
    Hendeby, Gustaf
    et al.
    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.
    A New Formulation of the Rao-Blackwellized Particle Filter2007In: Proceedings of the 14th IEEE/SP Statistical Signal Processing Workshop, 2007, p. 84-88Conference paper (Refereed)
    Abstract [en]

    For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes- rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.

  • 46.
    Hendeby, Gustaf
    et al.
    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.
    A New Formulation of the Rao-Blackwellized Particle Filter2007Report (Other academic)
    Abstract [en]

    For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes- rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.

  • 47.
    Hendeby, Gustaf
    et al.
    German Research Centre Artificial Intelligence, Germany.
    Karlsson, Rickard
    NIRA Dynamics AB, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Particle Filtering: The Need for Speed2010In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2010, no 181403Article in journal (Refereed)
    Abstract [en]

    The particle filter (PF) has during the last decade been proposed for a wide range of localization and tracking applications. There is a general need in such embedded system to have a platform for efficient and scalable implementation of the PF. One such platform is the graphics processing unit (GPU), originally aimed to be used for fast rendering of graphics. To achieve this, GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper, GPGPU techniques are used to make a parallel recursive Bayesian estimation implementation using particle filters. The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to the one achieved with a traditional CPU implementation. The comparison is made using a minimal sensor network with bearings-only sensors. The resulting GPU filter, which is the first complete GPU implementation of a PF published to this date, is faster than the CPU filter when many particles are used, maintaining the same accuracy. The parallelization utilizes ideas that can be applicable for other applications.

  • 48.
    Hendeby, Gustaf
    et al.
    German Research Centre for Artificial Intelligence, Germany.
    Karlsson, Rickard
    Swedish Defence Research Agency, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    The Rao-Blackwellized Particle Filter: A Filter Bank Implementation2010In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2010, no 724087Article in journal (Refereed)
    Abstract [en]

    For computational efficiency, it is important to utilize model structure in particle filtering. One of the most important cases occurs when there exists a linear Gaussian substructure, which can be efficiently handled by Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF). This contribution suggests an alternative formulation of this well-known result that facilitates reuse of standard filtering components and which is also suitable for object-oriented programming. Our RBPF formulation can be seen as a Kalman filter bank with stochastic branching and pruning.

  • 49.
    Hendeby, Gustaf
    et al.
    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.
    Gordon, Neil
    DSTO, Australia.
    Performance Issues in Non-Gaussian Filtering Problems2006In: Proceedings of the 2006 IEEE Nonlinear Statistical Signal Workshop, 2006, p. 65-68Conference paper (Refereed)
    Abstract [en]

    Performance for many filtering problems is usually measured using the second order moment. For non-Gaussian application this measure is not always sufficient. In the paper the Kullback divergence is extensively used to compare distributions. Several estimation techniques are compared, and methods such as the particle filter are shown to give superior performance over some classical second-order estimators.

  • 50.
    Hendeby, Gustaf
    et al.
    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.
    Gordon, Neil
    DSTO, Australia.
    Performance Issues in Non-Gaussian Filtering Problems2006Report (Other academic)
    Abstract [en]

    Performance for many filtering problems is usually measured using the second order moment. For non-Gaussian application this measure is not always sufficient. In the paper the Kullback divergence is extensively used to compare distributions. Several estimation techniques are compared, and methods such as the particle filter are shown to give superior performance over some classical second-order estimators.

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