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  • 1.
    Björklund, Svante
    et al.
    Swedish Defence Research Agency (FOI).
    Petersson, Henrik
    Swedish Defence Reserearch Agency (FOI).
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Tekniska fakulteten.
    Features for micro-Doppler based activity classification2015Inngår i: IET radar, sonar & navigation, ISSN 1751-8784, E-ISSN 1751-8792, Vol. 9, nr 9, s. 1181-1187Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 2.
    Björklund, Svante
    et al.
    Swedish Defence Research Agency (FOI), Linköping, Sweden.
    Petersson, Henrik
    Swedish Defence Research Agency (FOI), Linköping, Sweden.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan. Swedish Defence Research Agency (FOI), Linköping, Sweden.
    On distinguishing between human individuals in micro-Doppler signatures2013Inngår i: 14th International Radar Symposium (IRS), 2013, s. 865-870Konferansepaper (Fagfellevurdert)
    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.

  • 3.
    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
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    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 Networks2015Inngår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 10, nr 6, artikkel-id e0127769Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 4.
    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 disturbances2011Konferansepaper (Fagfellevurdert)
    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.

  • 5.
    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 alternative2009Inngår i: Mixed and Augmented Reality, 2009, IEEE , 2009, s. 175-176Konferansepaper (Fagfellevurdert)
    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.

  • 6.
    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 tracking2010Konferansepaper (Fagfellevurdert)
    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.

  • 7.
    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
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fradet, Laetitia
    Université de Poitiers, 86000, Poitiers, France.
    Personalized Physical Activity Monitoring Using Wearable Sensors2015Inngår i: Smart Health: Open Problems and Future Challenges / [ed] Andreas Holzinger, Carsten Röcker, Martina Ziefle, Springer International Publishing , 2015, s. 99-124Kapittel i bok, del av antologi (Fagfellevurdert)
    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.

  • 8.
    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
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för systemteknik, Reglerteknik.
    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 elderly2013Inngår i: Journal of Ambient Intelligence and Smart Environments, ISSN 1876-1364, E-ISSN 1876-1372, Vol. 5, nr 6, s. 547-562Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 9.
    Deleskog, Viktor
    et al.
    Totalförsvarets forskningsinstitut (FOI).
    Habberstad, Hans
    Totalförsvarets forskningsinstitut (FOI).
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Lindgren, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Wahlström, Niklas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Robust NLS Sensor Localization using MDS Initialization2014Inngår i: 17th International Conference on Information Fusion (FUSION), 2014, Institute of Electrical and Electronics Engineers (IEEE), 2014, s. 1-7Konferansepaper (Fagfellevurdert)
    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.

  • 10.
    Dil, Bram
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hoenders, Bernhard
    University of Groningen, Centre for Theoretical Physics, Zernike Institute for Advanced Materials.
    Approximate Diagonalized Covariance Matrix for Signals with Correlated Noise2016Inngår i: Proceedings of the 19th International Conference of Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2016, s. 521-527Konferansepaper (Fagfellevurdert)
    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.

  • 11.
    Forsling, Robin
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Sjanic, Zoran
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Consistent Distributed Track Fusion Under Communication Constraints2019Inngår i: Proceedings of the 22nd International Conference on Information Fusion (FUSION), 2019Konferansepaper (Fagfellevurdert)
    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.

  • 12.
    Grönwall, Christina
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten. FOI.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Kristian, Sinivaara
    Cybercom Sweden AB (Sweden).
    A proposal for combining mapping, localization and target recognition2015Inngår i: 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. 9649Konferansepaper (Fagfellevurdert)
    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.

  • 13.
    Gustafsson, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Some Relations Between Extended and Unscented Kalman Filters2012Inngår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, nr 2, s. 545-555Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 14.
    Gustafsson, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Lindgren, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Mathai, George
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Habberstad, Hans
    Swedish Defence Research Agency (FOI).
    Direction of Arrival Estimation in Sensor Arrays Using Local Series Expansion of the Received Signal2015Inngår i: 18th International Conference of Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2015Konferansepaper (Fagfellevurdert)
    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.

  • 15.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fundamental Estimation and Detection Limits in Linear Non-Gaussian Systems2005Licentiatavhandling, monografi (Annet vitenskapelig)
    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.

  • 16.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Performance and Implementation Aspects of Nonlinear Filtering2008Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [sv]

    I många fall är det viktigt att kunna få ut så mycket och så bra information som möjligt ur tillgängliga mätningar. Att utvinna information om till exempel position och hastighet hos ett flygplan kallas för filtrering. I det här fallet är positionen och hastigheten exempel på tillstånd hos flygplanet, som i sin tur är ett system. Ett typiskt exempel på problem av den här typen är olika övervakningssystem, men samma behov blir allt vanligare även i vanliga konsumentprodukter som mobiltelefoner (som talar om var telefonen är), navigationshjälpmedel i bilar och för att placera upplevelseförhöjande grafik i filmer och TV -program. Ett standardverktyg som används för att extrahera den information som behövs är olineär filtrering. Speciellt vanliga är metoderna i positionerings-, navigations- och målföljningstillämpningar. Den här avhandlingen går in på djupet på olika frågeställningar som har med olineär filtrering att göra:

    * Hur utvärderar man hur bra ett filter eller en detektor fungerar?

    * Vad skiljer olika metoder åt och vad betyder det för deras egenskaper?

    * Hur programmerar man de datorer som används för att utvinna informationen?

    Det mått som oftast används för att tala om hur effektivt ett filter fungerar är RMSE (root mean square error), som i princip är ett mått på hur långt ifrån det korrekta tillståndet man i medel kan förvänta sig att den skattning man får är. En fördel med att använda RMSE som mått är att det begränsas av Cramér-Raos undre gräns (CRLB). Avhandlingen presenterar metoder för att bestämma vilken betydelse olika brusfördelningar har för CRLB. Brus är de störningar och fel som alltid förekommer när man mäter eller försöker beskriva ett beteende, och en brusfördelning är en statistisk beskrivning av hur bruset beter sig. Studien av CRLB leder fram till en analys av intrinsic accuracy (IA), den inneboende noggrannheten i brus. För lineära system får man rättframma resultat som kan användas för att bestämma om de mål som satts upp kan uppnås eller inte. Samma metod kan också användas för att indikera om olineära metoder som partikelfiltret kan förväntas ge bättre resultat än lineära metoder som kalmanfiltret. Motsvarande metoder som är baserade på IA kan även användas för att utvärdera detektionsalgoritmer. Sådana algoritmer används för att upptäcka fel eller förändringar i ett system.

    När man använder sig av RMSE för att utvärdera filtreringsalgoritmer fångar man upp en aspekt av filtreringsresultatet, men samtidigt finns många andra egenskaper som kan vara intressanta. Simuleringar i avhandlingen visar att även om två olika filtreringsmetoder ger samma prestanda med avseende på RMSE så kan de tillståndsfördelningar de

    producerar skilja sig väldigt mycket åt beroende på vilket brus det studerade systemet utsätts för. Dessa skillnader kan vara betydelsefulla i vissa fall. Som ett alternativ till RMSE används därför här kullbackdivergensen som tydligt visar på bristerna med att bara förlita sig på RMSE-analyser. Kullbackdivergensen är ett statistiskt mått på hur mycket två fördelningar skiljer sig åt.

    Två filtreringsalgoritmer har analyserats mer i detalj: det rao-blackwelliserade partikelfiltret (RBPF) och den metod som kallas unscented Kalman filter (UKF). Analysen av RBPF leder fram till ett nytt sätt att presentera algoritmen som gör den lättare att använda i ett datorprogram. Dessutom kan den nya presentationen ge bättre förståelse för hur algoritmen fungerar. I undersökningen av UKF ligger fokus på den underliggande så kallade unscented transformation som används för att beskriva vad som händer med en brusfördelning när man transformerar den, till exempel genom en mätning. Resultatet består av ett antal simuleringsstudier som visar på de olika metodernas beteenden. Ett annat resultat är en jämförelse mellan UT och Gauss approximationsformel av första och andra ordningen.

    Den här avhandlingen beskriver även en parallell implementation av ett partikelfilter samt ett objektorienterat ramverk för filtrering i programmeringsspråket C ++. Partikelfiltret har implementerats på ett grafikkort. Ett grafikkort är ett exempel på billig hårdvara som sitter i de flesta moderna datorer och mest används för datorspel. Det används därför sällan till sin fulla potential. Ett parallellt partikelfilter, det vill säga ett program som kör flera delar av partikelfiltret samtidigt, öppnar upp för nya tillämpningar där snabbhet och bra prestanda är viktigt. Det objektorienterade ramverket för filtrering uppnår den flexibilitet och prestanda som behövs för storskaliga Monte-Carlo-simuleringar med hjälp av modern mjukvarudesign. Ramverket kan också göra det enklare att gå från en prototyp av ett signalbehandlingssystem till en slutgiltig produkt.

  • 17.
    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 monitoring2010Konferansepaper (Annet (populærvitenskap, debatt, mm))
  • 18.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Detection Limits for Linear Non-Gaussian State-Space Models2006Inngår i: Proceedings of the 6th IFAC Symposium on Fault Detection, Supervision and Safty of Technical Processes, 2006, s. 282-287Konferansepaper (Fagfellevurdert)
    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.

  • 19.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Detection Limits for Linear Non-Gaussian State-Space Models2006Rapport (Annet vitenskapelig)
    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.

  • 20.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems2005Inngår i: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, 2005, s. 338-343Konferansepaper (Fagfellevurdert)
    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.

  • 21.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems2005Rapport (Annet vitenskapelig)
    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.

  • 22.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2006Inngår i: Proceedings of Reglermöte 2006, 2006Konferansepaper (Annet vitenskapelig)
    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.

  • 23.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2005Inngår i: Proceedings of the 16th IFAC World Congress, 2005, s. 45-45Konferansepaper (Fagfellevurdert)
    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.

  • 24.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2004Rapport (Annet vitenskapelig)
    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.

  • 25.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Fundamental Filtering Limitations in Linear Non-Gaussian Systems2005Rapport (Annet vitenskapelig)
    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.

  • 26.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för systemteknik, Reglerteknik.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    On Nonlinear Transformations of Stochastic Variables and its Application to Nonlinear Filtering2008Inngår i: Proceedings of the '08 IEEE International Conference on Acoustics, Speech and Signal Processing, 2008, s. 3617-3620Konferansepaper (Fagfellevurdert)
    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.

  • 27.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    On Nonlinear Transformations of Stochastic Variables and its Application to Nonlinear Filtering2007Rapport (Annet vitenskapelig)
    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.

  • 28.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    On Performance Measures for Approximative Parameter Estimation2004Inngår i: Proceedings of Reglermöte 2004, 2004Konferansepaper (Annet vitenskapelig)
    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.

  • 29.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    On Performance Measures for Approximative Parameter Estimation2004Rapport (Annet vitenskapelig)
    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.

  • 30.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Wahlström, Niklas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Teaching Sensor Fusion and Kalman Filtering using a Smartphone2014Inngår i: Proceedings of the 19th World Congress of the International Federation of Automatic Control (IFAC), IFAC Papers Online, 2014Konferansepaper (Fagfellevurdert)
    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.

  • 31.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hol, Jeroen
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Graphics Processing Unit Implementation of the Particle Filter2007Inngår i: Proceedings of the 15th European Statistical Signal Processing Conference, European Association for Signal, Speech, and Image Processing , 2007, s. 1639-1643Konferansepaper (Fagfellevurdert)
    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.

  • 32.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hol, Jeroen
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Graphics Processing Unit Implementation of the Particle Filter2007Rapport (Annet vitenskapelig)
    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.

  • 33.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hol, Jeroen
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Graphics Processing Unit Implementation of the Particle Filter2006Rapport (Annet vitenskapelig)
    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.

  • 34.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gaussian Mixture PHD Filtering with Variable Probability of Detection2014Inngår i: 17th International Conference on Information Fusion (FUSION), 2014, IEEE , 2014, s. 1-7Konferansepaper (Fagfellevurdert)
    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.

  • 35.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Target Tracking Performance Evaluation - A General Software Environment for Filtering2007Inngår i: Proceedings of the 2007 IEEE Aerospace Conference, 2007, s. 1-13Konferansepaper (Fagfellevurdert)
    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.

  • 36.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Target Tracking Performance Evaluation - A General Software Environment for Filtering2007Rapport (Annet vitenskapelig)
    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.

  • 37.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A New Formulation of the Rao-Blackwellized Particle Filter2007Inngår i: Proceedings of the 14th IEEE/SP Statistical Signal Processing Workshop, 2007, s. 84-88Konferansepaper (Fagfellevurdert)
    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.

  • 38.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A New Formulation of the Rao-Blackwellized Particle Filter2007Rapport (Annet vitenskapelig)
    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.

  • 39.
    Hendeby, Gustaf
    et al.
    German Research Centre Artificial Intelligence, Germany.
    Karlsson, Rickard
    NIRA Dynamics AB, Sweden.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Particle Filtering: The Need for Speed2010Inngår i: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2010, nr 181403Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 40.
    Hendeby, Gustaf
    et al.
    German Research Centre for Artificial Intelligence, Germany.
    Karlsson, Rickard
    Swedish Defence Research Agency, Sweden.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    The Rao-Blackwellized Particle Filter: A Filter Bank Implementation2010Inngår i: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2010, nr 724087Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 41.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gordon, Neil
    DSTO, Australia.
    Performance Issues in Non-Gaussian Filtering Problems2006Inngår i: Proceedings of the 2006 IEEE Nonlinear Statistical Signal Workshop, 2006, s. 65-68Konferansepaper (Fagfellevurdert)
    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.

  • 42.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gordon, Neil
    DSTO, Australia.
    Performance Issues in Non-Gaussian Filtering Problems2006Rapport (Annet vitenskapelig)
    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.

  • 43.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gordon, Neil
    Defence Science and Technology Organisation, Australia.
    Recursive Triangulation Using Bearings-Only Sensors2006Inngår i: Proceedings of the 2006 IEE Seminar on Target Tracking: Algorithms and Applications, Institution of Electrical Engineers (IEE), 2006, s. 3-10Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Recursive triangulation, using a bearings-only sensor, is investigated for a fly-by scenario. In a simulation study, several estimators are compared, fundamental estimation limits are calculated for different measurement noise assumptions. The quality of the estimated state distributions is evaluated.

  • 44.
    Hendeby, Gustaf
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gordon, Neil
    Defence Science and Technology Organisation, Australia.
    Recursive Triangulation Using Bearings-Only Sensors2006Rapport (Annet vitenskapelig)
    Abstract [en]

    Recursive triangulation, using a bearings-only sensor, is investigated for a fly-by scenario. In a simulation study, several estimators are compared, fundamental estimation limits are calculated for different measurement noise assumptions. The quality of the estimated state distributions is evaluated.

  • 45.
    Ho, Du
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Linder, Jonas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Enqvist, Martin
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Mass estimation of a quadcopter using IMU data2017Inngår i: 2017 International Conference on Unmanned Aircraft Systems (ICUAS), June 13-16, 2017, Miami, FL, USA, Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 1260-1266Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, an approach to estimate the mass of a quadcopter using only inertial measurements and pilot commands is presented. For this purpose, a lateral dynamic model describing the relation between the roll rate and the lateral acceleration is formulated. Due to the quadcopter’s inherent instability, a controller is used to stabilize the system and the data is collected in closed loop. Under the effect of feedback and disturbances, the inertial measurements used as input and output are correlated with the disturbances, which complicates the parameter estimation. The parameters of the model are estimated using several methods. The simulation and experimental results show that the instrumental-variable method has the best potential to estimate the mass of the quadcopter in this setup.

  • 46.
    Ho, Du
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Linder, Jonas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Enqvist, Martin
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Vertical modeling of a quadcopter for mass estimation and diagnosis purposes2017Inngår i: Proceedings of the Workshop on Research, Education and Development on Unmanned Aerial Systems, RED-UAS, Linköping, Sweden, 3-5 October, 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this work, we estimate a model of the vertical dynamics of a quadcopter and explain how this model can be used for mass estimation and diagnosis of system changes. First, a standard thrust model describing the relation between the calculated control signals of the rotors and the thrust that is commonly used in literature is estimated. The estimation results are compared to those using a refined thrust model and it turns out that the refined model gives a significant improvement. The combination of a nonlinear model and closed-loop data poses some challenges and it is shown that an instrumental variables approach can be used to obtain accurate estimates. Furthermore, we show that the refined model opens up for fault detection of the quadcopter. More specifically, this model can be used for mass estimation and also for diagnosis of other parameters that might vary between and during missions.

  • 47.
    Karabacak, Cesur
    et al.
    Department of Electrical and Electronics Engineering, TOBB University of Economics and Technology, Ankara 06560, Turkey; and Meteksan Defense Industries, Inc., Ankara 06560, Turkey.
    Gurbuz, Sevgi Z.
    e Department of Electrical and Electronics Engineering, TOBB University of Economics and Technology, Ankara 06560, Turkey; and the TUBITAK Space Technologies Research Institute, Ankara 06800, Turkey.
    Gurbuz, Ali C.
    Department of Electrical and Electronics Engineering, TOBB University of Economics and Technology, Ankara 06560..
    Guldogan, Mehmet B.
    Department of Electrical and Electronics Engineering, Turgut Ozal University, Ankara 06560, Turkey..
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Knowledge Exploitation for Human Micro-Doppler Classification2015Inngår i: IEEE Geoscience and Remote Sensing Letters, ISSN 1545-598X, E-ISSN 1558-0571, Vol. 12, nr 10, s. 2125-2129Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Micro-Doppler radar signatures have great potential for classifying pedestrians and animals, as well as their motion pattern, in a variety of surveillance applications. Due to the many degrees of freedom involved, real data need to be complemented with accurate simulated radar data to be able to successfully design and test radar signal processing algorithms. In many cases, the ability to collect real data is limited by monetary and practical considerations, whereas in a simulated environment, any desired scenario may be generated. Motion capture (MOCAP) has been used in several works to simulate the human micro-Doppler signature measured by radar; however, validation of the approach has only been done based on visual comparisons of micro-Doppler signatures. This work validates and, more importantly, extends the exploitation of MOCAP data not just to simulate micro-Doppler signatures but also to use the simulated signatures as a source of a priori knowledge to improve the classification performance of real radar data, particularly in the case when the total amount of data is small.

  • 48.
    Kasebzadeh, Parinaz
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Fritsche, Carsten
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Gunnarsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten. Ericsson Research, Linköping, Sweden.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Improved Pedestrian Dead Reckoning Positioning With Gait Parameter Learning2016Inngår i: Proceedings of the 19th International Conference on Information Fusion, IEEE conference proceedings, 2016, , s. 7s. 379-385Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We consider personal navigation systems in devices equipped with inertial sensors and GPS, where we propose an improved Pedestrian Dead Reckoning (PDR) algorithm that learns gait parameters in time intervals when position estimates are available, for instance from GPS or an indoor positioning system (IPS). A novel filtering approach is proposed that is able to learn internal gait parameters in the PDR algorithm, such as the step length and the step detection threshold. Our approach is based on a multi-rate Kalman filter bank that estimates the gait parameters when position measurements are available, which improves PDR in time intervals when the position is not available, for instance when passing from outdoor to indoor environments where IPS is not available. The effectiveness of the new approach is illustrated on several real world experiments. 

  • 49.
    Lindfors, Martin
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Gustafsson, Fredrik
    Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för systemteknik, Reglerteknik.
    Karlsson, Rickard
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.
    Vehicle Speed Tracking Using Chassis Vibrations2016Inngår i: Proceedings of the 2016 IEEE Intelligent Vehicles Symposium (IV), IEEE conference proceedings, 2016, s. 214-219Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The speed of a wheeled vehicle is usually estimatedusing wheel speed sensors (WSS) or GPS. If these signals are unavailable, other methods must be used. We propose a novelapproach exploiting the fact that vibrations from rotating axles,with fundamental frequency proportional to vehicle speed, aretransmitted via the vehicle chassis. Using an accelerometer, these vibrations can be tracked to estimate vehicle speed whileother sources of vibrations act as disturbances. A state-space model for the dynamics of the harmonics is presented andformulated such that there is a conditional linear-Gaussiansubstructure, enabling efficient Rao-Blackwellized methods. Avariant of the Rao-Blackwellized point-mass filter is derived, significantly reducing computational complexity, and reducingthe memory requirements from quadratic to linear in thenumber of grid points. It is applied to experimental data from the sensor cluster of a car and validated using therotational frequency from WSS data. The proposed methodshows improved performance and robustness in comparisonto a Rao-Blackwellized particle filter implementation and afrequency spectrum maximization method.

  • 50.
    Lindgren, David
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Guldogan, Mehmet B.
    Turgut Ozal University, Turkiet.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Habberstad, Hans
    Totalförsvarets Forskningsinstitut, FOI.
    Hendeby, Gustaf
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Acoustic Source Localization in a Network of Doppler Shift Sensors2013Inngår i: 16th International Conference on Information Fusion, Institute of Electrical and Electronics Engineers (IEEE), 2013Konferansepaper (Fagfellevurdert)
    Abstract [en]

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

12 1 - 50 of 73
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