arXiv subjects

Franz Hlawatsch

Publications and source records attributed to Franz Hlawatsch.

At least 19 recordsLinked to original sources

arXiv2024

Track Coalescence and Repulsion in Multitarget Tracking: An Analysis of MHT, JPDA, and Belief Propagation Methods

Joint probabilistic data association (JPDA) filter methods and multiple hypothesis tracking (MHT) methods are widely used for multitarget tracking (MTT). However, they are known to exhibit undesirable behavior in tracking scenarios with targets in close proximity: JPDA filter methods suffer from the track coalescence effect, i.e., the estimated tracks of targets in close proximity tend to merge and can become indistinguishable, and MHT methods suffer from an opposite effect known as track repulsion. In this paper, we review the JPDA filter and MHT methods and discuss the track coalescence and track repulsion effects. We also consider a more recent methodology for MTT that is based on the belief propagation (BP) algorithm, and we argue that BP-based MTT exhibits significantly reduced track coalescence and no track repulsion. Our theoretical arguments are confirmed by numerical results.

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arXiv2022

An Efficient Labeled/Unlabeled Random Finite Set Algorithm for Multiobject Tracking

We propose an efficient random finite set (RFS) based algorithm for multiobject tracking in which the object states are modeled by a combination of a labeled multi-Bernoulli (LMB) RFS and a Poisson RFS. The less computationally demanding Poisson part of the algorithm is used to track potential objects whose existence is unlikely. Only if a quantity characterizing the plausibility of object existence is above a threshold, a new labeled Bernoulli component is created and the object is tracked by the more accurate but more computationally demanding LMB part of the algorithm. Conversely, a labeled Bernoulli component is transferred back to the Poisson RFS if the corresponding existence probability falls below another threshold. Contrary to existing hybrid algorithms based on multi-Bernoulli and Poisson RFSs, the proposed method facilitates track continuity and implements complexity-reducing features. Simulation results demonstrate a large complexity reduction relative to other RFS-based algorithms with comparable performance.

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arXiv2022

Fusion of Probability Density Functions

Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a continuous random variable or vector. Although the case of continuous random variables and the problem of pdf fusion frequently arise in multisensor signal processing, statistical inference, and machine learning, a universally accepted method for pdf fusion does not exist. The diversity of approaches, perspectives, and solutions related to pdf fusion motivates a unified presentation of the theory and methodology of the field. We discuss three different approaches to fusing pdfs. In the axiomatic approach, the fusion rule is defined indirectly by a set of properties (axioms). In the optimization approach, it is the result of minimizing an objective function that involves an information-theoretic divergence or a distance measure. In the supra-Bayesian approach, the fusion center interprets the pdfs to be fused as random observations. Our work is partly a survey, reviewing in a structured and coherent fashion many of the concepts and methods that have been developed in the literature. In addition, we present new results for each of the three approaches. Our original contributions include new fusion rules, axioms, and axiomatic and optimization-based characterizations; a new formulation of supra-Bayesian fusion in terms of finite-dimensional parametrizations; and a study of supra-Bayesian fusion of posterior pdfs for linear Gaussian models.

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arXiv2021

Fusion of Sensor Measurements and Target-Provided Information in Multitarget Tracking

Tracking multiple time-varying states based on heterogeneous observations is a key problem in many applications. Here, we develop a statistical model and algorithm for tracking an unknown number of targets based on the probabilistic fusion of observations from two classes of data sources. The first class, referred to as target-independent perception systems (TIPSs), consists of sensors that periodically produce noisy measurements of targets without requiring target cooperation. The second class, referred to as target-dependent reporting systems (TDRSs), relies on cooperative targets that report noisy measurements of their state and their identity. We present a joint TIPS-TDRS observation model that accounts for observation-origin uncertainty, missed detections, false alarms, and asynchronicity. We then establish a factor graph that represents this observation model along with a state evolution model including target identities. Finally, by executing the sum-product algorithm on that factor graph, we obtain a scalable multitarget tracking algorithm with inherent TIPS-TDRS fusion. The performance of the proposed algorithm is evaluated using simulated data as well as real data from a maritime surveillance experiment.

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arXiv2020

Classification-Aided Multitarget Tracking Using the Sum-Product Algorithm

Multitarget tracking (MTT) is a challenging task that aims at estimating the number of targets and their states from measurements of the target states provided by one or multiple sensors. Additional information, such as imperfect estimates of target classes provided by a classifier, can facilitate the target-measurement association and thus improve MTT performance. In this letter, we describe how a recently proposed MTT framework based on the sum-product algorithm can be extended to efficiently exploit class information. The effectiveness of the proposed approach is demonstrated by simulation results.

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arXiv2019

A Belief Propagation Algorithm for Multipath-Based SLAM

We present a simultaneous localization and mapping (SLAM) algorithm that is based on radio signals and the association of specular multipath components (MPCs) with geometric features. Especially in indoor scenarios, robust localization from radio signals is challenging due to diffuse multipath propagation, unknown MPC-feature association, and limited visibility of features. In our approach, specular reflections at flat surfaces are described in terms of virtual anchors (VAs) that are mirror images of the physical anchors (PAs). The positions of these VAs and possibly also of the PAs are unknown. We develop a Bayesian model of the SLAM problem and represent it by a factor graph, which enables the use of belief propagation (BP) for efficient marginalization of the joint posterior distribution. The resulting BP-based SLAM algorithm detects the VAs associated with the PAs and estimates jointly the time-varying position of the mobile agent and the positions of the VAs and possibly also of the PAs, thereby leveraging the MPCs in the radio signal for improved accuracy and robustness of agent localization. The algorithm has a low computational complexity and scales well in all relevant system parameters. Experimental results using both synthetic measurements and real ultra-wideband radio signals demonstrate the excellent performance of the algorithm in challenging indoor environments.

cs.IT↗

arXiv2018

A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion

We propose a particle-based distributed PHD filter for tracking an unknown, time-varying number of targets. To reduce communication, the local PHD filters at neighboring sensors communicate Gaussian mixture (GM) parameters. In contrast to most existing distributed PHD filters, our filter employs an `arithmetic average' fusion. For particles--GM conversion, we use a method that avoids particle clustering and enables a significance-based pruning of the GM components. For GM--particles conversion, we develop an importance sampling based method that enables a parallelization of filtering and dissemination/fusion operations. The proposed distributed particle-PHD filter is able to integrate GM-based local PHD filters. Simulations demonstrate the excellent performance and small communication and computation requirements of our filter.

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arXiv2018

Rate-Distortion Theory of Finite Point Processes

We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on rate-distortion theory and the theory of finite point processes. We introduce fundamental information-theoretic concepts and quantities for point processes and present general lower and upper bounds on the rate-distortion function. To enable a comparison with the vector setting, we concretize our bounds for point processes of fixed cardinality. In particular, we analyze a fixed number of unordered Gaussian data points and show that we can significantly reduce the required rates compared to the best possible compression strategy for Gaussian vectors. As an example of point processes with variable cardinality, we study the best possible compression of Poisson point processes. For the specific case of a Poisson point process with uniform intensity on the unit square, our lower and upper bounds are separated by only a small gap and thus provide a good characterization of the rate-distortion function.

cs.IT↗

arXiv2017

Entropy and Source Coding for Integer-Dimensional Singular Random Variables

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension for the practically relevant class of integer-dimensional singular random variables. The proposed entropy definition contains the entropy of discrete random variables and the differential entropy of continuous random variables as special cases. We show that it transforms in a natural manner under Lipschitz functions, and that it is invariant under unitary transformations. We define joint entropy and conditional entropy for integer-dimensional singular random variables, and we show that the proposed entropy conveys useful expressions of the mutual information. As first applications of our entropy definition, we present a result on the minimal expected codeword length of quantized integer-dimensional singular sources and a Shannon lower bound for integer-dimensional singular sources.

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arXiv2016

Cooperative Simultaneous Localization and Synchronization in Mobile Agent Networks

Cooperative localization in agent networks based on interagent time-of-flight measurements is closely related to synchronization. To leverage this relation, we propose a Bayesian factor graph framework for cooperative simultaneous localization and synchronization (CoSLAS). This framework is suited to mobile agents and time-varying local clock parameters. Building on the CoSLAS factor graph, we develop a distributed (decentralized) belief propagation algorithm for CoSLAS in the practically important case of an affine clock model and asymmetric time stamping. Our algorithm allows for real-time operation and is suitable for a time-varying network connectivity. To achieve high accuracy at reduced complexity and communication cost, the algorithm combines particle implementations with parametric message representations and takes advantage of a conditional independence property. Simulation results demonstrate the good performance of the proposed algorithm in a challenging scenario with time-varying network connectivity.

cs.DC↗

arXiv2016

Multichannel group sparsity methods for compressive channel estimation in doubly selective multicarrier MIMO systems (extended version)

We consider channel estimation within pulse-shaping multicarrier multiple-input multiple-output (MIMO) systems transmitting over doubly selective MIMO channels. This setup includes MIMO orthogonal frequency-division multiplexing (MIMO-OFDM) systems as a special case. We show that the component channels tend to exhibit an approximate joint group sparsity structure in the delay-Doppler domain. We then develop a compressive channel estimator that exploits this structure for improved performance. The proposed channel estimator uses the methodology of multichannel group sparse compressed sensing, which combines the methodologies of group sparse compressed sensing and multichannel compressed sensing. We derive an upper bound on the channel estimation error and analyze the estimator's computational complexity. The performance of the estimator is further improved by introducing a basis expansion yielding enhanced joint group sparsity, along with a basis optimization algorithm that is able to utilize prior statistical information if available. Simulations using a geometry-based channel simulator demonstrate the performance gains due to leveraging the joint group sparsity and optimizing the basis.

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arXiv2016

A Scalable Algorithm for Tracking an Unknown Number of Targets Using Multiple Sensors

We propose a method for tracking an unknown number of targets based on measurements provided by multiple sensors. Our method achieves low computational complexity and excellent scalability by running belief propagation on a suitably devised factor graph. A redundant formulation of data association uncertainty and the use of "augmented target states" including binary target indicators make it possible to exploit statistical independencies for a drastic reduction of complexity. An increase in the number of targets, sensors, or measurements leads to additional variable nodes in the factor graph but not to higher dimensions of the messages. As a consequence, the complexity of our method scales only quadratically in the number of targets, linearly in the number of sensors, and linearly in the number of measurements per sensors. The performance of the method compares well with that of previously proposed methods, including methods with a less favorable scaling behavior. In particular, our method can outperform multisensor versions of the probability hypothesis density (PHD) filter, the cardinalized PHD filter, and the multi-Bernoulli filter.

cs.DS↗

arXiv2016

Cooperative Localization for Mobile Networks: A Distributed Belief Propagation - Mean Field Message Passing Algorithm

We propose a hybrid message passing method for distributed cooperative localization and tracking of mobile agents. Belief propagation and mean field message passing are employed for, respectively, the motion-related and measurement-related part of the factor graph. Using a Gaussian belief approximation, only three real values per message passing iteration have to be broadcast to neighboring agents. Despite these very low communication requirements, the estimation accuracy can be comparable to that of particle-based belief propagation.

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arXiv2015

Distributed Localization and Tracking of Mobile Networks Including Noncooperative Objects - Extended Version

We propose a Bayesian method for distributed sequential localization of mobile networks composed of both cooperative agents and noncooperative objects. Our method provides a consistent combination of cooperative self-localization (CS) and distributed tracking (DT). Multiple mobile agents and objects are localized and tracked using measurements between agents and objects and between agents. For a distributed operation and low complexity, we combine particle-based belief propagation with a consensus or gossip scheme. High localization accuracy is achieved through a probabilistic information transfer between the CS and DT parts of the underlying factor graph. Simulation results demonstrate significant improvements in both agent self-localization and object localization performance compared to separate CS and DT, and very good scaling properties with respect to the numbers of agents and objects.

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arXiv2015

Distributed Estimation with Information-Seeking Control in Agent Network

We introduce a distributed, cooperative framework and method for Bayesian estimation and control in decentralized agent networks. Our framework combines joint estimation of time-varying global and local states with information-seeking control optimizing the behavior of the agents. It is suited to nonlinear and non-Gaussian problems and, in particular, to location-aware networks. For cooperative estimation, a combination of belief propagation message passing and consensus is used. For cooperative control, the negative posterior joint entropy of all states is maximized via a gradient ascent. The estimation layer provides the control layer with probabilistic information in the form of sample representations of probability distributions. Simulation results demonstrate intelligent behavior of the agents and excellent estimation performance for a simultaneous self-localization and target tracking problem. In a cooperative localization scenario with only one anchor, mobile agents can localize themselves after a short time with an accuracy that is higher than the accuracy of the performed distance measurements.

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arXiv2014

Degrees of Freedom of Generic Block-Fading MIMO Channels without A Priori Channel State Information

We studynthe high-SNR capacity of generic MIMO Rayleigh block-fading channels in the noncoherent setting where neither transmitter nor receiver has a priori channel state information but both are aware of the channel statistics. In contrast to the well-established constant block-fading model, we allow the fading to vary within each block with a temporal correlation that is "generic" (in the sense used in the interference-alignment literature). We show that the number of degrees of freedom of a generic MIMO Rayleigh block-fading channel with $T$ transmit antennas and block length $N$ is given by $T(1-1/N)$ provided that $T<N$ and the number of receive antennas is at least $T(N-1)/(N-T)$. A comparison with the constant block-fading channel (where the fading is constant within each block) shows that, for large block lengths, generic correlation increases the number of degrees of freedom by a factor of up to four.

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arXiv2014

Compressive Nonparametric Graphical Model Selection For Time Series

We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as, e.g., an autoregressive model) for the vector random process; rather, it only assumes certain spectral smoothness proper- ties. The proposed inference scheme is compressive in that it works for sample sizes that are (much) smaller than the number of scalar process components. We provide analytical conditions for our method to correctly identify the CIG with high probability.

stat.ML↗

arXiv2013

The RKHS Approach to Minimum Variance Estimation Revisited: Variance Bounds, Sufficient Statistics, and Exponential Families

The mathematical theory of reproducing kernel Hilbert spaces (RKHS) provides powerful tools for minimum variance estimation (MVE) problems. Here, we extend the classical RKHS based analysis of MVE in several directions. We develop a geometric formulation of five known lower bounds on the estimator variance (Barankin bound, Cramer-Rao bound, constrained Cramer-Rao bound, Bhattacharyya bound, and Hammersley-Chapman-Robbins bound) in terms of orthogonal projections onto a subspace of the RKHS associated with a given MVE problem. We show that, under mild conditions, the Barankin bound (the tightest possible lower bound on the estimator variance) is a lower semicontinuous function of the parameter vector. We also show that the RKHS associated with an MVE problem remains unchanged if the observation is replaced by a sufficient statistic. Finally, for MVE problems conforming to an exponential family of distributions, we derive novel closed-form lower bound on the estimator variance and show that a reduction of the parameter set leaves the minimum achievable variance unchanged.

math.ST↗