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  • 1.
    Bacharach, Lucien
    et al.
    University of Toulouse - ISAE-Supaero.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Chaumette, Eric
    University of Toulouse - ISAE-Supaero.
    A Tighter Bayesian Cramer-Rao Bound2019In: Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, p. 5277-5281Conference paper (Refereed)
    Abstract [en]

    It has been shown lately that any ”standard” Bayesian lower bound (BLB) on the mean squared error (MSE) of the Weiss-Weinstein family (WWF) admits a ”tighter” form which upper bounds the ”standard” form. Applied to the Bayesian Cramer-Rao bound (BCRB), this result suggests to redefine the concept of efficient estimator relatively to the tighter form of the BCRB, an update supported by a noteworthy example. This paper lays the foundation to revisit some Bayesian estimation problems where the BCRB is not tight in the asymptotic region.

  • 2.
    Bacharach, Lucien
    et al.
    University of Toulouse - ISAE-Supaero.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Chaumette, Eric
    University of Toulouse - ISAE-Supaero.
    Some Inequalities Between Pairs of Marginal and Joint Bayesian Lower Bounds2019In: Proc. of 22nd International Conference on Information Fusion (FUSION), 2019, p. 1-8Conference paper (Refereed)
    Abstract [en]

    In this paper, tightness relations (or inequalities) between Bayesian lower bounds (BLBs) on the mean-squared-error are derived which result from the marginalization of a joint probability density function (pdf) depending on both parameters of interest and extraneous or nuisance parameters. In particular,it is shown that for a large class of BLBs, the BLB derived from the marginal pdf is at least as tight as the corresponding BLB derived from the joint pdf. A Bayesian linear regression example is used to illustrate the tightness relations

  • 3.
    Braga, André R.
    et al.
    Aeronautics Institute of Technology, Brazil.
    Bruno, Marcelo G.S.
    Aeronautics Institute of Technology, Brazil.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Cooperative Terrain Based Navigation and Coverage Identification Using Consensus2015In: 18th International Conference on Information Fusion (Fusion), 2015: Proceedings, IEEE , 2015, p. 1190-1197Conference paper (Refereed)
    Abstract [en]

    This paper presents a distributed online method for joint state and parameter estimation in a Jump Markov NonLinear System based on a distributed recursive Expectation Maximization algorithm. State inference is enabled via the use of Rao-Blackwellized Particle Filter and, for the parameter estimation, the E-step is performed independently at each sensor with the calculation of local sufficient statistics. An average consensus algorithm is used to diffuse local sufficient statistics to neighbors and approximate the global sufficient statistics throughout the network. The evaluation of the proposed algorithm is carried out on a Terrain Based Navigation problem where the unknown parameters of the observation noise model contain relevant information about the terrain properties.

  • 4.
    Braga, André R.
    et al.
    Federal University of Ceara, Quixada, Brazil.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bruno, Marcelo G. S.
    Aeronautics Institute of Technology, Sao Jose dos Campos, Brazil.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Rapid System Identification for Jump Markov Non-Linear Systems2017In: Proc. 2017 IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), IEEE, 2017, p. 714-718Conference paper (Refereed)
    Abstract [en]

    This work evaluates a previously introduced algorithm called Particle-Based Rapid Incremental Smoother within the framework of state inference and parameter identification in Jump Markov Non-Linear System. It is applied to the recursive form of two well-known Maximum Likelihood based algorithms who face the common challenge of online computation of smoothed additive functionals in order to accomplish the task of model parameter estimation. This work extends our previous contributions on identification of Markovian switching systems with the goal to reduce the computational complexity. A benchmark problem is used to illustrate the results.

  • 5.
    Braga, André Ribeiro
    et al.
    Division of Electronics Engineering, Aeronautics Institute of Technology, São José dos Campos, Brazil.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bruno, Marcelo G. S.
    Division of Electronics Engineering, Aeronautics Institute of Technology, São José dos Campos, Brazil.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Cooperative Navigation and Coverage Identification with Random Gossip and Sensor Fusion2016In: Proc. IEEE 9th Sensor Array and Multichannel Signal Processing Workshop (SAM), Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 1-5Conference paper (Refereed)
    Abstract [en]

    This paper is concerned with cooperative Terrain Aided Navigation of a network of aircraft using fusion of Radar Altimeter and inter-node range measurements. State inference is performed using a Rao-Blackwellized Particle Filter with online measurement noise statistics estimation. For terrain coverage measurement noise parameter identification, an online Expectation Maximization algorithm is proposed, where local sufficient statistics at each node are calculated in the E-step, which are then distributed to neighboring nodes using a random gossip algorithm to perform the M-step at each node. Simulation results show that improvement on positioning and calibration performance can be achieved compared to a non-cooperative approach.

  • 6.
    Chaumette, Eric
    et al.
    ISAE-Supaero, Toulouse, France.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    A General Class of Bayesian Lower Bounds Tighter than the Weiss-Weinstein Family2018In: 2018 21th International Conference on Information Fusion (FUSION), 2018, p. 1-7Conference paper (Refereed)
    Abstract [en]

    In this paper, Bayesian lower bounds (BLBs) are obtained via a general form of the Pythagorean theorem where the inner product derives from the joint or the a-posteriori probability density function (pdf). When joint pdf is considered, the BLBs obtained encompass the Weiss-Weinstein family (WWF). When a-posteriori pdf is considered, by resorting to an embedding between two ad hoc subspaces, it is shown that any ”standard” BLBs of the WWF admits a ”tighter” form which upper bounds the ”standard” form. Interestingly enough, this latter result may explain why the ”standard” BLBs of the WWF are not always as tight as expected, as exemplified in the case of the Bayesian Cram´er-Rao Bound. As a consequence an updated definition of efficiency is proposed, as well as the introduction of an updated class of efficient estimators.

  • 7.
    Feng, Yin
    et al.
    Technical University, Darmstadt, Germany.
    Ang, Li
    Technical University Darmstadt, Germany.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Fritsche, Carsten
    IFEN GmbH, Poing, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    RSS-based sensor network localization in contaminated Gaussian measurement noise2013In: IEEE 5th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013, IEEE , 2013, p. 121-124Conference paper (Refereed)
    Abstract [en]

    We study received signal strength-based cooperative localization in wireless sensor networks. We assume that the measurement noise fits a contaminated Gaussian model so as to take into account some outlier conditions. In addition, some environment-dependent parameters are assumed to be unknown. We propose an expectation-maximization based algorithm for robust centralized network localization without offline training. As benchmark for comparison, we express the best achievable localization accuracy in terms of the Cramér-Rao bound. Experimental results demonstrate the advantages of the proposed algorithm as compared to some representative algorithms.

  • 8.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Linköpings universitet.
    Derivation of a Bayesian Bhattacharyya bound for discrete-time filtering2017Report (Other academic)
    Abstract [en]

    In this report, the derivation of the Bayesian Bhattacharyya bound for discrete-time filtering as proposed by Reece and Nicholson [1] is revisited. It turns out that the general results presented in [1] are incorrect, as some expectations appearing in the information matrix recursions are missing. This report presents the corrected results and it is argued that the missing expectations are only zero in a number of special cases. A nonlinear toy example is used to illustrate when this is not the case.

  • 9.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Supplementary material for “On parametric lower bounds for discrete-time filtering”2016Report (Other academic)
    Abstract [en]

    This report contains supplementary material for the paper, and gives detailed proofs of all theorems and lemmas that could not be included into the paper due to space limitations.

  • 10.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    The Marginal Bayesian Cramér–Rao Bound for Jump Markov Systems2016In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 23, no 5, p. 575-579Article in journal (Refereed)
    Abstract [en]

    In this letter, numerical algorithms for computing the marginal version of the Bayesian Cramér–Rao bound (M-BCRB) for jump Markov nonlinear systems and jump Markov linear Gaussian systems are proposed. Benchmark examples for both systems illustrate that the M-BCRB is tighter than three other recently proposed BCRBs

  • 11.
    Fritsche, Carsten
    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.
    Bayesian Bhattacharyya bound for discrete-time filtering revisited2017In: Proc. of 2017 IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2017, p. 719-723Conference paper (Refereed)
    Abstract [en]

    In this paper, the derivation of the Bayesian Bhattacharyya bound for discrete-time filtering as proposed ina paper by Reece and Nicholson is revisited. It turns out that the results presented in the aforementioned contribution are incorrect, as some expectations appearing in the information matrix recursions are missing. This paper gives a generalized derivation of the N-th order Bayesian Bhattacharyya bound and presents corrected expressions for the case N = 2. A nonlinear toy example is used to illustrate the results

  • 12.
    Fritsche, Carsten
    et al.
    IFEN GmbH, Germany .
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bounds on the Optimal Performance for Jump Markov Linear Gaussian Systems2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 1, p. 92-98Article in journal (Refereed)
    Abstract [en]

    The performance of an optimal filter is lower bounded by the Bayesian Cramer-Rao Bound (BCRB). In some cases, this bound is tight (achieved by the optimal filter) asymptotically in information, i.e., high signal-to-noise ratio (SNR). However, for jump Markov linear Gaussian systems (JMLGS) the BCRB is not necessarily achieved for any SNR. In this paper, we derive a new bound which is tight for all SNRs. The bound evaluates the expected covariance of the optimal filter which is represented by one deterministic term and one stochastic term that is computed with Monte Carlo methods. The bound relates to and improves on a recently presented BCRB and an enumeration BCRB for JMLGS. We analyze their relations theoretically and illustrate them on a couple of examples.

  • 13.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Klein, Anja
    Fachgebiet Kommunikationstechnik, Institut für Nachrichtentechnik,Technische Universität Darmstadt, Darmstadt, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bayesian Cramer-Rao Bound for Mobile Terminal Tracking in Mixed LOS/NLOS Environments2013In: IEEE Wireless Communications Letters, ISSN 2162-2337, E-ISSN 2162-2345, Vol. 2, no 3, p. 335-338Article in journal (Refereed)
    Abstract [en]

    A computational algorithm is presented for the Bayesian Cramer-Rao lower bound (BCRB) in filtering applications with measurement noise from mixture distributions with jump Markov switching structure. Such mixture distributions are common for radio propagation in mixed line- and non-line-of-sight environments. The newly derived BCRB is tighter than earlier more general bounds proposed in literature, and thus gives a more realistic bound on actual estimation performance. The resulting BCRB can be used to compute a lower bound on root mean square error of position estimates in a large class of radio localization applications. We illustrate this on an archetypical tracking application using a nearly constant velocity model and time of arrival observations.

  • 14.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Supplementary Material for “Bobrovsky-Zakai Bound for Filtering, Prediction and Smoothing of Nonlinear Dynamic Systems”2018Report (Other academic)
    Abstract [en]

    This report contains supplementary material for the paper [1], and gives detailed proofs of all lemmas and theorems that could not be included into the paper due to space limitations. The notation is adapted from the paper.

    [1] C. Fritsche, U. Orguner, and F. Gustafsson, “Bobrovsky-Zakai bound for filtering, prediction and smoothing ofnonlinear dynamic systems,” in International Conference on Information Fusion (FUSION), Cambridge, UK, Jul.2018, pp. 1–8.

  • 15.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Supplementary Material for “Recent results on Bayesian Cramer-Rao bounds for jump Markov systems”2016Report (Other academic)
    Abstract [en]

    This report contains supplementary material for the paper, and gives detailed proofs of all lemmas and propositions that could not be included into the paper due to space limitations. The notation is adaptedfrom the paper.

  • 16.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Bobrovsky-Zakai Bound for Filtering, Prediction and Smoothing of Nonlinear Dynamic Systems2018In: 2018 21st International Conference on Information Fusion (FUSION), 2018, p. 1-8Conference paper (Refereed)
    Abstract [en]

    In this paper, recursive Bobrovsky-Zakai bounds for filtering, prediction and smoothing of nonlinear dynamic systems are presented. The similarities and differences to an existing Bobrovsky-Zakai bound in the literature for the filtering case are highlighted. The tightness of the derived bounds are illustrated on a simple example where a linear system with non-Gaussian measurement likelihood is considered. The proposed bounds are also compared with the performance of some well known filters/predictors/smoothers and other Bayesian bounds.

  • 17.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    On parametric lower bounds for discrete-time filtering2016In: 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 4338-4342Conference paper (Refereed)
    Abstract [en]

    Parametric Cramer-Rao lower bounds (CRLBs) are given for discrete-time systems with non-zero process noise. Recursive expressions for the conditional bias and mean-square-error (MSE) (given a specific state sequence) are obtained for Kalman filter estimating the states of a linear Gaussian system. It is discussed that Kalman filter is conditionally biased with a non-zero process noise realization in the given state sequence. Recursive parametric CRLBs are obtained for biased estimators for linear state estimators of linear Gaussian systems. Simulation studies are conducted where it is shown that Kalman filter is not an efficient estimator in a conditional sense.

  • 18.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Svensson, Lennart
    Chalmers University of Technology, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Recent Results on Bayesian Cramer-Rao Bounds for Jump Markov Systems2016In: Proc. 19th International Conference on Information Fusion (FUSION), Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 512-520Conference paper (Refereed)
    Abstract [en]

    In this paper, recent results on the evaluation of the Bayesian Cramer-Rao bound for jump Markov systems are presented. In particular, previous work is extended to jump Markov systems where the discrete mode variable enters into both the process and measurement equation, as well as where it enters exclusively into the measurement equation. Recursive approximations are derived with finite memory requirements as well as algorithms for checking the validity of these approximations are established. The tightness of the bound and the validity of its approximation is investigated on a couple of examples.

  • 19.
    Fritsche, Carsten
    et al.
    IFEN GmbH, Germany .
    Orguner, Umut
    Middle E Technical University, Turkey .
    Svensson, Lennart
    Chalmers, Sweden .
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    The Marginal Enumeration Bayesian Cramer-Rao Bound for Jump Markov Systems2014In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 21, no 4, p. 464-468Article in journal (Refereed)
    Abstract [en]

    A marginal version of the enumeration Bayesian Cramer-Rao Bound (EBCRB) for jump Markov systems is proposed. It is shown that the proposed bound is at least as tight as EBCRB and the improvement stems from better handling of the nonlinearities. The new bound is illustrated to yield tighter results than BCRB and EBCRB on a benchmark example.

  • 20.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Özkan, Emre
    Middle East Technical University, Turkey.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Marginal Bayesian Bhattacharyya Bounds for discrete-time filtering2018In: Proc. of 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, Canada, 2018, IEEE, 2018, p. 4289-4293Conference paper (Refereed)
    Abstract [en]

    In this paper, marginal versions of the Bayesian Bhattacharyya lower bound (BBLB), which is a tighter alternative to the classical Bayesian Cramer-Rao bound, for discrete-time filtering are proposed. Expressions for the second and third-order marginal BBLBs are obtained and it is shown how these can be approximately calculated using particle filtering. A simulation example shows that the proposed bounds predict the achievable performance of the filtering algorithms better.

  • 21.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    On the Cramér-Rao lower bound under model mismatch2015In: 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP): Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 3986-3990Conference paper (Refereed)
    Abstract [en]

    Cramér-Rao lower bounds (CRLBs) are proposed for deterministic parameter estimation under model mismatch conditions where the assumed data model used in the design of the estimators differs from the true data model. The proposed CRLBs are defined for the family of estimators that may have a specified bias (gradient) with respect to the assumed model. The resulting CRLBs are calculated for a linear Gaussian measurement model and compared to the performance of the maximum likelihood estimator for the corresponding estimation problem.

  • 22.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Saha, Saikat
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bayesian Cramer-Rao Bound for Nonlinear Filtering with Dependent Noise Processes2013In: 16th International Conference on Information Fusion (FUSION 2013), IEEE , 2013, p. 797-804Conference paper (Refereed)
    Abstract [en]

    The Bayesian Cramer Rao Bound (BCRB) is de­rived for nonlinear state space models with dependent process and measurement noise processes. It generalizes the previously BCRB for the case of dependent noise. Two different dependence structures appearing in literature are considered, leading to two different recursions for BCRB. The special cases of Gaussian noise, and linear models are presented separately. Simulations demonstrate that correct treatment of dependencies is important for both filtering algorithms and the BCRB.

  • 23.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Klein, Anja
    Technische Universität Darmstadt, Germany.
    The Marginalized Auxiliary Particle Filter2010Report (Other academic)
    Abstract [en]

    In this paper we are concerned with nonlinear systems subject to a conditionally linear, Gaussian sub-structure. This structure is often exploited in high-dimensional state estimation problems using the marginalized (aka Rao-Blackwellized) particle filter. The main contribution in the present work is to show how an efficient filter can be derived by exploiting this structure within the auxiliary particle filter. Based on a multisensor aircraft tracking example, the superior performance of the proposed filter over conventional particle filtering approaches is demonstrated.

  • 24.
    Fritsche, Carsten
    et al.
    Technische Universität Darmstadt, Germany.
    Schön, Thomas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Klein, Anja
    Technische Universität Darmstadt, Germany.
    The Marginalized Auxiliary Particle Filter2009In: Proceedings of the 3rd International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2009, p. 289-292Conference paper (Refereed)
    Abstract [en]

    In this paper we are concerned with nonlinear systems subject to a conditionally linear, Gaussian sub-structure. This structure is often exploited in high-dimensional state estimation problems using the marginalized (aka Rao-Blackwellized) particle filter. The main contribution in the present work is to show how an efficient filter can be derived by exploiting this structure within the auxiliary particle filter. Based on a multisensor aircraft tracking example, the superior performance of the proposed filter over conventional particle filtering approaches is demonstrated.

  • 25.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Online EM algorithm for jump Markov systems2012In: 15th International Conference on Information Fusion (FUSION), 2012, 2012, p. 1941-1946Conference paper (Refereed)
    Abstract [en]

    The Expectation-Maximization (EM) algorithm in combination with particle filters is a powerful tool that can solve very complex problems, such as parameter estimation in general nonlinear non-Gaussian state space models. We here apply the recently proposed online EM algorithm to parameter estimation in jump Markov models, that contain both continuous and discrete states. In particular, we focus on estimating process and measurement noise distributions being modeled as mixtures of members from the exponential family.

  • 26.
    Fritsche, Carsten
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Orguner, Umut
    Middle East Technical University, Turkey.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Marginal Weiss-Weinstein bounds for discrete-time filtering2015In: 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP): Proceedings, IEEE , 2015, p. 3487-3491Conference paper (Refereed)
    Abstract [en]

    A marginal version of the Weiss-Weinstein bound (WWB) is proposed for discrete-time nonlinear filtering. The proposed bound is calculated analytically for linear Gaussian systems and approximately for nonlinear systems using a particle filtering scheme. Via simulation studies, it is shown that the marginal bounds are tighter than their joint counterparts.

  • 27.
    Fritsche, Carsten
    et al.
    IFEN GmbHPoing, Germany.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Svensson, L.
    Department of Signals and Systems, Chalmers University of of TechnologyGöteborg, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    A fresh look at Bayesian Cramér-Rao bounds for discrete-time nonlinear filtering2014In: FUSION 2014 - 17th International Conference on Information Fusion, Institute of Electrical and Electronics Engineers Inc. , 2014, no 6916255Conference paper (Refereed)
    Abstract [en]

    In this paper, we aim to relate different Bayesian Cramér-Rao bounds which appear in the discrete-time nonlinear filtering literature in a single framework. A comparative theoretical analysis of the bounds is provided in order to relate their tightness. The results can be used to provide a lower bound on the mean square error in nonlinear filtering. The findings are illustrated and verified by numerical experiments where the tightness of the bounds are compared.

  • 28.
    Jin, Di
    et al.
    Technical University Darmstadt, Germany.
    Yin, Feng
    Ericsson AB, Linköping, Sweden.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Cooperative localization based on severely quantized RSS measurements in wireless sensor network2016In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 4214-4218Conference paper (Refereed)
    Abstract [en]

    We study severely quantized received signal strength (RSS)-based cooperative localization in wireless sensor networks. We adopt the well-known sum-product algorithm over a wireless network (SPAWN) framework in our study. To address the challenge brought by severely quantized measurements, we adopt the principle of importance sampling and design appropriate proposal distributions. Moreover, we propose a parametric SPAWN in order to reduce both the communication overhead and the computational complexity. Experiments with real data corroborate that the proposed algorithms can achieve satisfactory localization accuracy for severely quantized RSS measurements. In particular, the proposed parametric SPAWN outperforms its competitors by far in terms of communication cost. We further demonstrate that knowledge about non-connected sensors can further improve the localization accuracy of the proposed algorithms.

  • 29.
    Jin, Di
    et al.
    Technical University Darmstadt, Germany.
    Yin, Feng
    Ericsson AB, Sweden.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Efficient Cooperative Localization Algorithm in LOS/NLOS Environments2015In: Proc. 23rd European Signal Processing Conference (EUSIPCO), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 185-189Conference paper (Refereed)
    Abstract [en]

    The well-known cooperative localization algorithm, ‘sum-product algorithm over a wireless network’ (SPAWN) hastwo major shortcomings, a relatively high computationalcomplexity and a large communication load. Using the Gaus-sian mixture model with a model selection criterion and thesigma-point (SP) methods, we propose the SPAWN-SP toovercome these problems. The SPAWN-SP easily accommo-dates different localization scenarios due to its high flexibilityin message representation. Furthermore, harsh LOS/NLOSenvironments are considered for the evaluation of coopera-tive localization algorithms. Our simulation results indicatethat the proposed SPAWN-SP demonstrates high localizationaccuracy in different localization scenarios, thanks to its highflexibility in message representation.

  • 30.
    Jin, Di
    et al.
    Technical University Darmstadt, Germany.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Yin, Feng
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Dithering in Quantized RSS Based Localization2015In: Proc. IEEE 6th Int. Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 245-248Conference paper (Refereed)
    Abstract [en]

    We study maximum likelihood (ML) position estimation using quantized received signal strength measurements. In order to mitigate the undesired quantization effect in the observations, the dithering technique is adopted. Various dither noise distributions are considered and the corresponding likelihood functions are derived. Simulation results show that the proposed ML estimator with dithering is able to generate a significantly reduced bias but a modestly increased mean-square error as compared to the conventional ML estimator without dithering.

  • 31.
    Kasebzadeh, Parinaz
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    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, Linköping, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Improved Pedestrian Dead Reckoning Positioning With Gait Parameter Learning2016In: Proceedings of the 19th International Conference on Information Fusion, IEEE conference proceedings, 2016, , p. 7p. 379-385Conference paper (Refereed)
    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. 

  • 32.
    Kasebzadeh, Parinaz
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Özkan, Emre
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gunnarsson, Fredrik
    Ericsson Research, Linköping, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Joint Antenna and Propagation Model Parameter Estimation using RSS measurements2015Conference paper (Refereed)
    Abstract [en]

    In this paper, a semi-parametric model for RSS measurements is introduced that can be used to predict coverage in cellular radio networks. The model is composed of an empirical log-distance model and a deterministic antenna gain model that accounts for possible non-uniform base station antenna radiation. A least-squares estimator is proposed to jointly estimate the path loss and antenna gain model parameters. Simulation as well as experimental results verify the efficacy of this approach. The method can provide improved accuracy compared to conventional path loss based estimation methods. 

  • 33.
    Radnosrati, Kamiar
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    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, Linköping, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fusion of TOF and TDOA for 3GPP Positioning2016In: Fusion 2016, 19th International Conference on Information Fusion: Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 1454-1460Conference paper (Refereed)
    Abstract [en]

    Positioning in cellular networks is often based on mobile-assisted measurements of serving and neighboring base stations. Traditionally, positioning is considered to be enabled when the mobile provides measurements of three different base stations. In this paper, we additionally investigate positioning based on time series of Time Of Flight (TOF) and Time Difference of Arrival (TDOA) measurements gathered from two base stations with known positions, where the specific base stations involved depend on the trajectory of the mobile station.. The set of two base stations is different along the trajectory. Each report contains TOF for the serving base station, and one TDOA measurement for the most favorable neighboring base station relative the serving base station. We derive explicit analytical solution related to the intersection of the absolute distance circle (from TOF) and relative distance hyperbola (from TDOA). We consider both geometric noise-free problem and the more realistic problem with additive noise as delivered in the 3rd Generation Partnership Project (3GPP) Long-Term Evolution (LTE). Positioning performance is evaluated using the Cramer-Rao lower bound.

  • 34.
    Roth, Michael
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Swedish Defence Research Agency (FOI), Linköping, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    The Ensemble Kalman Filter and its Relations to Other Nonlinear Filters2015In: Proceedings of the 2015 European Signal Processing Conference (EUSIPCO 2015), Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 1236-1240Conference paper (Refereed)
    Abstract [en]

    The Ensemble Kalman filter (EnKF) is a standard algorithm in oceanography and meteorology, where it has got thousands of citations. It is in these communities appreciated since it scales much better with state dimension n than the standard Kalman filter (KF). In short, the EnKF propagates ensembles with N state realizations instead of mean values and covariance matrices and thereby avoids the computational and storage burden of working on n×n matrices. Perhaps surprising, very little attention has been devoted to the EnKF in the signal processing community. In an attempt to change this, we present the EnKF in a Kalman filtering context. Furthermore, its application to nonlinear problems is compared to sigma point Kalman filters and the particle filter, so as to reveal new insights and improvements for high-dimensional filtering algorithms in general. A simulation example shows the EnKF performance in a space debris tracking application.

  • 35.
    Sjanic, Zoran
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Gunnarsson, Fredrik
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Cellular Network Non-Line-of-Sight Reflector Localisation Based on Synthetic Aperture Radar Methods2014In: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 62, no 4, p. 2284-2287Article in journal (Refereed)
    Abstract [en]

    The dependence of radio signal propagation on the environment is  well known, and both statistical and deterministic methods have been presented in the literature. Such methods are either based on randomised or actual reflectors of radio signals. In this work, we instead aim at estimating the location of the reflectors based on geo-localised radio channel impulse reponse measurements and using methods from synthetic aperture radar (SAR). Radio channel data measurements from 3GPP E-UTRAN have been used to verify the usefulness of the proposed approach. The obtained images show that  the estimated reflectors are well correlated with the aerial map of the environment. Also, which part of the trajectory contributed to different reflectors have been estimated with promising results.

  • 36.
    Yin, Feng
    et al.
    Technical University of Darmstadt, Germany .
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Zoubir, Abdelhak M.
    Technical University of Darmstadt, Germany .
    EM- and JMAP-ML Based Joint Estimation Algorithms for Robust Wireless Geolocation in Mixed LOS/NLOS Environments2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 1, p. 168-182Article in journal (Refereed)
    Abstract [en]

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

  • 37.
    Yin, Feng
    et al.
    Technical University Darmstadt, Germany.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Received signal strength-based joint parameter estimation algorithm for robust geolocation in LOS/NLOS environments2013In: Proc. of 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2013, p. 6471-6475Conference paper (Refereed)
    Abstract [en]

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

  • 38.
    Yin, Feng
    et al.
    Technical University of Darmstadt, Germany.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Zoubir, Abdelhak M
    Technical University of Darmstadt, Germany.
    TOA-Based Robust Wireless Geolocation and Cramér-Rao Lower Bound Analysis in Harsh LOS/NLOS Environments2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 9, p. 2243-2255Article in journal (Refereed)
    Abstract [en]

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

  • 39.
    Yin, Feng
    et al.
    Technical University of Darmstadt, Germany.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Jin, Di
    Technical University of Darmstadt, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Zoubir, Abdelhak M.
    Technical University of Darmstadt, Germany.
    Cooperative Localization in WSNs Using Gaussian Mixture Modeling: Distributed ECM Algorithms2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 6, p. 1448-1463Article in journal (Refereed)
    Abstract [en]

    We study cooperative sensor network localization in a realistic scenario where 1) the underlying measurement errors more probably follow a non-Gaussian distribution; 2) the measurement error distribution is unknown without conducting massive offline calibrations; and 3) non-line-of-sight identification is not performed due to the complexity constraint and/or storage limitation. The underlying measurement error distribution is approximated parametrically by a Gaussian mixture with finite number of components, and the expectation-conditional maximization (ECM) criterion is adopted to approximate the maximum-likelihood estimator of the unknown sensor positions and an extra set of Gaussian mixture model parameters. The resulting centralized ECM algorithms lead to easier inference tasks and meanwhile retain several convergence properties with a proof of the "space filling" condition. To meet the scalability requirement, we further develop two distributed ECM algorithms where an average consensus algorithm plays an important role for updating the Gaussian mixture model parameters locally. The proposed algorithms are analyzed systematically in terms of computational complexity and communication overhead. Various computer based tests are also conducted with both simulation and experimental data. The results pin down that the proposed distributed algorithms can provide overall good performance for the assumed scenario even under model mismatch, while the existing competing algorithms either cannot work without the prior knowledge of the measurement error statistics or merely provide degraded localization performance when the measurement error is clearly non-Gaussian.

  • 40.
    Yin, Feng
    et al.
    Technical University Darmstadt, Germany.
    Zoubir, Abdelhak M.
    Technical University Darmstadt, Germany.
    Fritsche, Carsten
    IFEN GmbH, Poing, Germany.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Robust cooperative sensor network localization via the EM criterion in LOS/NLOS environments2013In: IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2013, IEEE , 2013, p. 505-509Conference paper (Refereed)
    Abstract [en]

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

  • 41.
    Zhao, Yuxin
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Supplementary Materials for "Sequential Monte Carlo Methods and Theoretical Bounds for Proximity Report based Indoor Positioning"2017Report (Other academic)
    Abstract [en]

    This reportontains supplementary material for the paper [1].

  • 42.
    Zhao, Yuxin
    et al.
    Research, Ericsson AB, 39174 Stockholm, Sweden.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Yin, Feng
    SSE, Chinese University of Hong Kong Shenzhen, Shenzhen, China.
    Gunnarsson, Fredrik
    Ericsson Research, Linköping, Sweden.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Sequential Monte Carlo Methods and Theoretical Bounds for Proximity Report Based Indoor Positioning2018In: IEEE Transactions on Vehicular Technology, ISSN 0018-9545, E-ISSN 1939-9359, Vol. 67, no 6, p. 5372-5386Article in journal (Refereed)
    Abstract [en]

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

  • 43.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Online EM algorithm for joint state and mixture measurement noise estimation2012In: 15th International Conference on Information Fusion (FUSION), 2012, IEEE , 2012, p. 1935-1940Conference paper (Refereed)
    Abstract [en]

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

  • 44.
    Özkan, Emre
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindsten, Fredrik
    University of Cambridge, England.
    Fritsche, Carsten
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Recursive Maximum Likelihood Identification of Jump Markov Nonlinear Systems2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 3, p. 754-765Article in journal (Refereed)
    Abstract [en]

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

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