SwePub - sökning: WFRF:(Granström Karl 1981)

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1.	Callmer, Jonas, 1981-, et al. (författare) Tree of Words for Visual Loop Closure Detection in Urban SLAM 2008 Ingår i: Proceedings of the '08 Australasian Conference on Robotics and Automation. - 9780646506432 ; , s. 102- Konferensbidrag (refereegranskat)abstract This paper introduces vision based loop closure detection in Simultaneous Localisation And Mapping (SLAM) using Tree of Words. The loop closure performance in a complex urban environment is examined and an additional feature is suggested for safer matching. A SLAM ground experiment in an urban area is performed using Tree of Words, a delayed state information ﬁlter and planar laser scans for relative pose estimation. Results show that a good map estimation using our vision based loop closure detection can be obtained in near real, yet constant, time. It is shown that an odometry supported recall rate of almost 70% can be obtained with a false detection rate of about 0.01%.
2.	Granström, Karl, 1981-, et al. (författare) Learning to Detect Loop Closure from Range Data 2009 Ingår i: Proceedings of '09 IEEE International Conference on Robotics and Automation. - 9781424427895 ; , s. 15-22 Konferensbidrag (refereegranskat)abstract Despite significant developments in the Simultaneous Localisation and Mapping (SLAM) problem, loop closure detection is still challenging in large scale unstructured environments. Current solutions rely on heuristics that lack generalisation properties, in particular when range sensors are the only source of information about the robot's surrounding environment. This paper presents a machine learning approach for the loop closure detection problem using range sensors. A binary classifier based on boosting is used to detect loop closures. The algorithm performs robustly, even under potential occlusions and significant changes in rotation and translation. We developed a number of features, extracted from range data, that are invariant to rotation. Additionally, we present a general framework for scan-matching SLAM in outdoor environments. Experimental results in large scale urban environments show the robustness of the approach, with a detection rate of 85% and a false alarm rate of only 1%. The proposed algorithm can be computed in real-time and achieves competitive performance with no manual specification of thresholds given the features.
3.	Xia, Yuxuan, 1993, et al. (författare) Extended Object Tracking with Automotive Radar Using Learned Structural Measurement Model 2020 Ingår i: IEEE National Radar Conference - Proceedings. - 1097-5659. ; 2020-September Konferensbidrag (refereegranskat)abstract This paper presents a data-driven measurement model for extended object tracking (EOT) with automotive radar. Specifically, the spatial distribution of automotive radar measurements is modeled as a hierarchical truncated Gaussian with structural geometry parameters (e.g., truncation bounds, their orientation, and a scaling factor) learned from the training data. The contribution is twofold. First, the learned measurement model can provide an adequate resemblance to the spatial distribution of real-world automotive radar measurements. Second, large-scale offline training datasets can be leveraged to learn the geometry-related parameters and offload the computationally demanding model parameter estimation from the state update step. The learned structural measurement model is further incorporated into the random matrix-based EOT approach with a new state update step. The effectiveness of the proposed approach is verified on the nuScenes dataset.
4.	Xia, Yuxuan, 1993, et al. (författare) Learning-Based Extended Object Tracking Using Hierarchical Truncation Measurement Model With Automotive Radar 2021 Ingår i: IEEE Journal on Selected Topics in Signal Processing. - 1941-0484 .- 1932-4553. ; 15:4, s. 1013-1029 Tidskriftsartikel (refereegranskat)abstract This paper presents a data-driven measurement model for extended object tracking (EOT) with automotive radar. Specifically, the spatial distribution of automotive radar measurements is modeled as a hierarchical truncated Gaussian (HTG) with structural geometry parameters that can be learned from the training data. The HTG measurement model provides an adequate resemblance to the spatial distribution of real-world automotive radar measurements. Moreover, large-scale radar datasets can be leveraged to learn the geometry-related model parameters and offload the computationally demanding model parameter estimation from the state update step. The learned HTG measurement model is further incorporated into a random matrix based EOT approach with two (multi-sensor) measurement updates: one is based on a factorized Gaussian inverse-Wishart density representation and the other is based on a Rao-Blackwellized particle density representation. The effectiveness of the proposed approaches is verified on both synthetic data and real-world nuScenes dataset over 300 trajectories.
5.	Beard, M., et al. (författare) Multiple Extended Target Tracking With Labeled Random Finite Sets 2016 Ingår i: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1941-0476 .- 1053-587X. ; 64:7, s. 1638-1653 Tidskriftsartikel (refereegranskat)abstract Targets that generate multiple measurements at a given instant in time are commonly known as extended targets. These present a challenge for many tracking algorithms, as they violate one of the key assumptions of the standard measurement model. In this paper, a new algorithm is proposed for tracking multiple extended targets in clutter, which is capable of estimating the number of targets, as well the trajectories of their states, comprising the kinematics, measurement rates, and extents. The proposed technique is based on modeling the multi-target state as a generalized labeled multi-Bernoulli (GLMB) random finite set (RFS), within which the extended targets are modeled using gamma Gaussian inverse Wishart (GGIW) distributions. A cheaper variant of the algorithm is also proposed, based on the labelled multi-Bernoulli (LMB) filter. The proposed GLMB/LMB-based algorithms are compared with an extended target version of the cardinalized probability hypothesis density (CPHD) filter, and simulation results show that the (G) LMB has improved estimation and tracking performance.
6.	Edman, Viktor, et al. (författare) Pedestrian Group Tracking Using the GM-PHD Filter 2013 Ingår i: Proceedings of the 21st European Signal Processing Conference. Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract A GM-PHD filter is used for pedestrian tracking in a crowdsurveillance application. The purpose is to keep track of thedifferent groups over time as well as to represent the shape ofthe groups and the number of people within the groups. In-put data to the GM-PHD filter are detections using a state ofthe art algorithm applied to video frames from the PETS 2012benchmark data. In a first step, the detections in the framesare converted from image coordinates to world coordinates.This implies that groups can be defined in physical units interms of distance in meters and speed differences in metersper second. The GM-PHD filter is a Bayesian framework thatdoes not form tracks of individuals. Its output is well suitedfor clustering of individuals into groups. The results demon-strate that the GM-PHD filter has the capability of estimatingthe correct number of groups with an accurate representationof their sizes and shapes.
7.	Fatemi, Maryam, 1982, et al. (författare) Poisson multi-Bernoulli filter for extended object tracking 2016 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract This paper presents a track-oriented Poisson multi-Bernoulli(PMB) filter for extended objects. The PMB filter is based onthe Poisson multi-Bernoulli mixture (PMBM) conjugate priorand approximates the posterior PMBM by merging tracks acrossdata association hypotheses. A method to create new tracks ina reasonable manner is proposed which uses a combination ofpre-clustering, recycling and equivalence class among PMBMdistributions.To approximate the marginal distributions of different tracks we use Gibbs sampling. The performance of thePMB is compared to the PMBM using a simulated scenario.
8.	Fatemi, Maryam, 1982, et al. (författare) Poisson Multi-Bernoulli Mapping Using Gibbs Sampling 2017 Ingår i: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1941-0476 .- 1053-587X. ; 65:11, s. 2814-2827 Tidskriftsartikel (refereegranskat)abstract This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multiobject posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multiobject posterior. The proposed method can handle uncertainties in the data associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform a state-of-the-art method.
9.	Fatemi, Maryam, 1982, et al. (författare) Poisson Multi-Bernoulli Radar Mapping Using Gibbs Sampling 2016 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract This paper addresses the radar mapping problem.Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects, and the measurements are described as a Poisson process, conditioned on the map. We use a Poisson process prior on the map and prove that the posterior distribution is a hybrid Poisson, multi-Bernoulli mixture distribution. We devise a Gibbs sampling algorithm to sample from the batch multi-object posterior. The proposed method can handle uncertainties in thedata associations and the cardinality of the set of landmarks, and is parallelizable, making it suitable for large-scale problems. The performance of the proposed method is evaluated on synthetic data and is shown to outperform an state-of-the-art method.
10.	Fröhle, Markus, 1984, et al. (författare) Decentralized Poisson Multi-Bernoulli Filtering for Vehicle Tracking 2020 Ingår i: IEEE Access. - 2169-3536 .- 2169-3536. ; 8, s. 126414-126427 Tidskriftsartikel (refereegranskat)abstract A decentralized Poisson multi-Bernoulli filter is proposed to track multiple vehicles using multiple high-resolution sensors. Independent filters estimate the vehicles' presence, state, and shape using a Gaussian process extent model; a decentralized filter is realized through fusion of the filters posterior densities. An efficient implementation is achieved by parametric state representation, utilization of single hypothesis tracks, and fusion of vehicle information based on a fusion mapping. Numerical results demonstrate the performance.
11.	Fröhle, Markus, 1984, et al. (författare) Multiple Target Tracking With Uncertain Sensor State Applied To Autonomous Vehicle Data 2018 Ingår i: 2018 IEEE Statistical Signal Processing Workshop (SSP). - 9781538615706 ; , s. 628-632 Konferensbidrag (refereegranskat)abstract In a conventional multitarget tracking (MTT) scenario, the sensor position is assumed known. When the MTT sensor, e.g., an automotive radar, is mounted to a moving vehicle with uncertain state, it becomes necessary to relax this assumption and model the unknown sensor position explicitly. In this paper, we compare a recently proposed filter that models the unknown sensor state [1], to two versions of the track-oriented marginal MeMBer/Poisson (TOMB/P) filter: the first does not model the sensor state uncertainty; the second models it approximately by artificially increasing the measurement variance. The results, using real measurement data, show that in terms of tracking performance, the proposed filter can outperform TOMB/P without sensor state uncertainty, and is comparable to TOMB/P with increased variance.
12.	Fröhle, Markus, 1984, et al. (författare) Multisensor Poisson Multi-Bernoulli Filter for Joint Target-Sensor State Tracking 2019 Ingår i: IEEE Transactions on Intelligent Vehicles. - 2379-8858. ; 4:4, s. 609-621 Tidskriftsartikel (refereegranskat)abstract In a typical multitarget tracking (MTT) scenario, the sensor state is either assumed known, or tracking is performed in the sensor's (relative) coordinate frame. This assumption does not hold when the sensor, e.g., an automotive radar, is mounted on a vehicle, and the target state should be represented in a global (absolute) coordinate frame. Then it is important to consider the uncertain location of the vehicle on which the sensor is mounted for MTT. In this paper, we present a multisensor low complexity Poisson multi-Bernoulli MTT filter, which jointly tracks the uncertain vehicle state and target states. Measurements collected by different sensors mounted on multiple vehicles with varying location uncertainty are incorporated sequentially based on the arrival of new sensor measurements. In doing so, targets observed from a sensor mounted on a well-localized vehicle reduce the state uncertainty of other poorly localized vehicles, provided that a common non-empty subset of targets is observed. A low complexity filter is obtained by approximations of the joint sensor-target state density minimizing the Kullback-Leibler divergence (KLD). Results from synthetic as well as experimental measurement data, collected in a vehicle driving scenario, demonstrate the performance benefits of joint vehicle-target state tracking.
13.	Garcaa-Fernandez, Angel F., et al. (författare) Gaussian implementation of the multi-Bernoulli mixture filter 2019 Ingår i: FUSION 2019 - 22nd International Conference on Information Fusion. Konferensbidrag (refereegranskat)abstract This paper presents the Gaussian implementation of the multi-Bernoulli mixture (MBM) filter. The MBM filter provides the filtering (multi-target) density for the standard dynamic and radar measurement models when the birth model is multi-Bernoulli or multi-Bernoulli mixture. Under linear/Gaussian models, the single target densities of the MBM mixture admit Gaussian closed-form expressions. Murty's algorithm is used to select the global hypotheses with highest weights. The MBM filter is compared with other algorithms in the literature via numerical simulations.
14.	Garcia, Angel, 1984, et al. (författare) Poisson Multi-Bernoulli Mixture Filter: Direct Derivation and Implementation 2018 Ingår i: IEEE Transactions on Aerospace and Electronic Systems. - 1557-9603 .- 0018-9251. ; 54:4, s. 1883-1901 Tidskriftsartikel (refereegranskat)abstract We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multitarget tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the δ-generalized labeled multi-Bernoulli (δ -GLMB) filter, showing that a δ-GLMB density represents a multi-Bernoulli mixture with labeled targets so it can be seen as a special case of PMBM. In addition, we propose an implementation for linear/Gaussian dynamic and measurement models and how to efficiently obtain typical estimators in the literature from the PMBM. The PMBM filter is shown to outperform other filters in the literature in a challenging scenario.
15.	Garcia, Angel, 1984, et al. (författare) Trajectory multi-Bernoulli filters for multi-target tracking based on sets of trajectories 2020 Ingår i: Proceedings of 2020 23rd International Conference on Information Fusion, FUSION 2020. ; , s. 313-320 Konferensbidrag (refereegranskat)abstract This paper presents two multi-Bernoulli filters on sets of trajectories for multiple target tracking. The first filter provides a multi-Bernoulli approximation of the posterior density over the set of alive trajectories at the current time step. The second filter provides a multi-Bernoulli approximation of the posterior density over the set of all trajectories (alive and dead) up to the current time. We also explain the Gaussian implementation of the filters and compare them with other multiple target tracking algorithms in a simulated scenario.
16.	Garcia, Angel, 1984, et al. (författare) Trajectory Poisson Multi-Bernoulli Filters 2020 Ingår i: IEEE Transactions on Signal Processing. - 1941-0476 .- 1053-587X. ; 68, s. 4933-4945 Tidskriftsartikel (refereegranskat)abstract This paper presents two trajectory Poisson multi-Bernoulli (TPMB) filters for multi-target tracking: one to estimate the set of alive trajectories at each time step and another to estimate the set of all trajectories, which includes alive and dead trajectories, at each time step. The filters are based on propagating a Poisson multi-Bernoulli (PMB) density on the corresponding set of trajectories through the filtering recursion. After the update step, the posterior is a PMB mixture (PMBM) so, in order to obtain a PMB density, a Kullback-Leibler divergence minimisation on an augmented space is performed. The developed filters are computationally lighter alternatives to the trajectory PMBM filters, which provide the closed-form recursion for sets of trajectories with Poisson birth model, and are shown to outperform previous multi-target tracking algorithms.
17.	Granström, Karl, 1981-, et al. (författare) A Gaussian Mixture PHD Filter for Extended Target Tracking 2010 Ingår i: Proceedings of the 13th International Conference on Information Fusion. - Linköping : Linköping University Electronic Press. - 9780982443811 Konferensbidrag (refereegranskat)abstract In extended target tracking, targets potentially produce more than one measurement per time step. Multiple extended targets are therefore usually hard to track, due to the resulting complex data association. The main contribution of this paper is the implementation of a Probability Hypothesis Density (PHD) filter for tracking of multiple extended targets. A general modification of the PHD filter to handle extended targets has been presented recently by Mahler, and the novelty in this work lies in the realisation of a Gaussian mixture PHD filter for extended targets. Furthermore, we propose a method to easily partition the measurements into a number of subsets, each of which is supposed to contain measurements that all stem from the same source. The method is illustrated in simulation examples, and the advantage of the implemented extended target PHD filter is shown in a comparison with a standard PHD filter.
18.	Granström, Karl, 1981-, et al. (författare) A New Prediction for Extended Targets with Random Matrices 2012 Annan publikation (övrigt vetenskapligt/konstnärligt)abstract This paper presents a new prediction update for extended targets whose extensions are modeled as random matrices. The prediction is based on several minimizations of the Kullback-Leibler divergence and allows for a kinematic state dependent transformation of the target extension. The results show that the extension prediction is a significant improvement over the previous work carried out on the topic.
19.	Granström, Karl, 1981-, et al. (författare) A PHD Filter for Tracking Multiple Extended Targets using Random Matrices 2012 Ingår i: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 60:11, s. 5657-5671 Tidskriftsartikel (refereegranskat)abstract This paper presents a random set based approach to tracking of an unknown number of extended targets, in the presence of clutter measurements and missed detections, where the targets extensions are modeled as random matrices. For this purpose, the random matrix framework developed recently by Koch et al. is adapted into the extended target PHD framework, resulting in the Gaussian inverse Wishart PHD (GIW-PHD) filter. A suitable multiple target likelihood is derived, and the main filter recursion is presented along with the necessary assumptions and approximations. The particularly challenging case of close extended targets is addressed with practical measurement clustering algorithms. The capabilities and limitations of the resulting extended target tracking framework are illustrated both in simulations and in experiments based on laser scans.
20.	Granström, Karl, 1981, et al. (författare) Approximate Multi-Hypothesis Multi-Bernoulli Multi-Object Filtering Made Multi-Easy 2016 Ingår i: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1941-0476 .- 1053-587X. ; 64:7, s. 1784-1797 Tidskriftsartikel (refereegranskat)abstract In multiple target tracking (MTT) it becomes necessary to use a multihypothesis approach if the trajectories of two or more targets cross. However, multihypothesis approaches, e.g., the multiple hypothesis tracker (MHT) or the emerging generalized labelled multi-Bernoulli (GLMB) filter, are computationally demanding. In this paper, we propose a simple multi-Bernoulli (MB) filter and a post processing method, which together deliver a multihypothesis tracking estimate at a computational cost that is only slightly larger than the cost of a single-hypothesis tracking filter even for many targets. The proposed MB filter is shown to be similar to the labeled MB filter, itself an approximation of the multihypothesis GLMB filter. In a simulation study with multiple targets and several trajectory crossings, the proposed filter is shown to be capable of correctly estimating the multihypothesis output. The filter is also tasked with presenting to an operator a principled perspective on a scene with many feasible track switches.
21.	Granström, Karl, 1981, et al. (författare) Asymmetric Threat Modeling Using HMMs: Bernoulli Filtering and Detectability Analysis 2016 Ingår i: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1941-0476 .- 1053-587X. ; 64:10, s. 2587-2601 Tidskriftsartikel (refereegranskat)abstract There is good reason to model an asymmetric threat (a structured action such as a terrorist attack) as an HMM whose observations are cluttered. Within this context, this paper presents two important contributions. The first is a Bernoulli filter that can process cluttered observations and is capable of detecting whether there is an HMM present, and if so, estimate the state of the HMM. The second is an analysis of the problem that, for a given HMM model, is able to make statements regarding the minimum complexity that an HMM would need to involve in order that it be detectable with reasonable fidelity, as well as upper bounds on the level of clutter (expected number of false measurements) and probability of miss of a relevant observation. In a simulation study, the Bernoulli filter is shown to give good performance provided that the probability of observation is larger than the probability of an irrelevant clutter observation. Further, the results show that the longer the delays are between the HMM state transitions, the larger the probability margin must be. The feasibility prediction shows that it is possible to predict the boundary between poor performance and good performance for the Bernoulli filter, i.e., it is possible to predict when the Bernoulli filter will be useful, and when it will not be.
22.	Granström, Karl, 1981, et al. (författare) Bayesian Extended Object Smoothing for the Random Matrix Model 2019 Ingår i: FUSION 2019 - 22nd International Conference on Information Fusion. Konferensbidrag (refereegranskat)abstract The random matrix model is popular in extended object tracking, due to its relative simplicity and versatility. In this model, the extended object state consists of a kinematic vector for the position and motion parameters (velocity, etc), and an extent matrix. Two versions of the model can be found in literature, one where the state density is modelled by a conditional density, and one where the state density is modelled by a factorized density. In this paper, we present closed form Bayesian smoothing expression for both the conditional and the factorised model. In a simulation study, we compare the performance of different versions of the smoother.
23.	Granström, Karl, 1981, et al. (författare) Bayesian Smoothing for the Extended Object Random Matrix Model 2019 Ingår i: IEEE Transactions on Signal Processing. - 1941-0476 .- 1053-587X. ; 67:14, s. 3732-3742 Tidskriftsartikel (refereegranskat)abstract The random matrix model is popular in extended object tracking, due to its relative simplicity and versatility. In this model, the extended object state consists of a kinematic vector for the position and motion parameters (velocity, etc.), and an extent matrix. Two versions of the model can be found in the literature, one where the state density is modeled by a conditional density, and one where the state density is modeled by a factorized density. In this paper, we present closed-form Bayesian smoothing expressions for both the conditional and the factorized model. In a simulation study, we compare the performance of different versions of the smoother. Code is published on GitHub.
24.	Granström, Karl, 1981, et al. (författare) Detectability prediction of hidden Markov models with cluttered observation sequences 2016 Ingår i: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. - 1520-6149. - 9781479999880 ; 2016-May, s. 4269-4273 Konferensbidrag (refereegranskat)abstract There is good reason to model an asymmetric threat (a structured action such as a terrorist attack) as an hmm whose observations are cluttered. Recently a Bernoulli filter was presented that can process cluttered observations («transactions») and is capable of detecting if there is an hmm present, and if so, estimate the state of the HMM. An important question in this context is: when is the HMM-in-clutter problem feasible? In other words, what system properties allow for a solvable problem? In this paper we show that, given a Gaussian approximation of the pdf of the log-likelihood, approximate detection error bounds can be derived. These error bounds allow a prediction of the detection performance, i.e. a prediction of the probability of detection given an «operating point» of transaction-level false alarm rate and miss probability. Simulations show that our analysis accurately predicts detectability of such threats. Our purpose here is to make statements about what sort of threats can be detected, and what quality of observations are necessary that this be accomplished.
25.	Granström, Karl, 1981-, et al. (författare) Estimation and Maintenance of Measurement Rates for Multiple Extended Target Tracking 2012 Ingår i: Proceedings of the International Conference on Information Fusion (FUSION). - : IEEE Press. - 9780982443842 - 9781467304177 ; , s. 2170-2176 Konferensbidrag (refereegranskat)abstract In Gilholm et al.'s extended target model, the number of measurements generated by a target is Poisson distributed with measurement rate γ. Practical use of this extended target model in multiple extended target tracking algorithms requires a good estimate of γ. In this paper, we first give a Bayesian recursion for estimating γ using the well-known conjugate prior Gamma-distribution. In multiple extended target tracking, consideration of different measurement set associations to a single target makes Gamma-mixtures arise naturally. This causes a need for mixture reduction, and we consider the reduction of Gamma-mixtures by means of merging. Analytical minimization of the Kullback-Leibler divergence is used to compute the single Gamma distribution that best approximates a weighted sum of Gamma distributions. Results from simulations show the merits of the presented multiple target measurement-rate estimator. The Bayesian recursion and presented reduction algorithm have important implications for multiple extended target tracking, e.g. using the implementations of the extended target PHD filter.
26.	Granström, Karl, 1981, et al. (författare) Extended OBJECT TRACKING: Introduction, overview, and applications 2017 Ingår i: Journal of Advances in Information Fusion. - 1557-6418. ; 12:2, s. 139-174 Tidskriftsartikel (refereegranskat)abstract This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches-the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (LIDAR), and red-green-blue-depth (RGB-D) sensors are highlighted.
27.	Granström, Karl, 1981-, et al. (författare) Extended Target Tracking using a Gaussian-Mixture PHD Filter 2011 Rapport (övrigt vetenskapligt/konstnärligt)abstract This paper presents a Gaussian-mixture implementation of the phd filter for tracking extended targets. The exact filter requires processing of all possible measurement set partitions, which is generally infeasible to implement. A method is proposed for limiting the number of considered partitions and possible alternatives are discussed. The implementation is used on simulated data and in experiments with real laser data, and the advantage of the filter is illustrated. Suitable remedies are given to handle spatially close targets and target occlusion.
28.	Granström, Karl, 1981-, et al. (författare) Extended Target Tracking Using a Gaussian-Mixture PHD Filter 2012 Ingår i: IEEE Transactions on Aerospace and Electronic Systems. - 0018-9251 .- 1557-9603. ; 48:4, s. 3268-3286 Tidskriftsartikel (refereegranskat)abstract This paper presents a Gaussian-mixture implementation of the phd filter for tracking extended targets. The exact filter requires processing of all possible measurement set partitions, which is generally infeasible to implement. A method is proposed for limiting the number of considered partitions and possible alternatives are discussed. The implementation is used on simulated data and in experiments with real laser data, and the advantage of the filter is illustrated. Suitable remedies are given to handle spatially close targets and target occlusion.
29.	Granström, Karl, 1981- (författare) Extended target tracking using PHD filters 2012 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract The world in which we live is becoming more and more automated, exemplified by the numerous robots, or autonomous vehicles, that operate in air, on land, or in water. These robots perform a wide array of different tasks, ranging from the dangerous, such as underground mining, to the boring, such as vacuum cleaning. In common for all different robots is that they must possess a certain degree of awareness, both of themselves and of the world in which they operate. This thesis considers aspects of two research problems associated with this, more specifically the Simultaneous Localization and Mapping (SLAM) problem and the Multiple Target Tracking (MTT) problem.The SLAM problem consists of having the robot create a map of an environment and simultaneously localize itself in the same map. One way to reduce the effect of small errors that inevitably accumulate over time, and could significantly distort the SLAM result, is to detect loop closure. In this thesis loop closure detection is considered for robots equipped with laser range sensors. Machine learning is used to construct a loop closure detection classifier, and experiments show that the classifier compares well to related work.The resulting SLAM map should only contain stationary objects, however the world also contains moving objects, and to function well a robot should be able to handle both types of objects. The MTT problem consists of having the robot keep track of where the moving objects, called targets, are located, and how these targets are moving. This function has a wide range of applications, including tracking of pedestrians, bicycles and cars in urban environments. Solving the MTT problem can be decomposed into two parts: one part is finding out the number of targets, the other part is finding out what the states of the individual targets are.In this thesis the emphasis is on tracking of so called extended targets. An extended target is a target that can generate any number of measurements, as opposed to a point target that generates at most one measurement. More than one measurement per target raise interesting possibilities to estimate the size and the shape of the target. One way to model the number of targets and the target states is to use random finite sets, which leads to the Probability Hypothesis Density (PHD) filters. Two implementations of an extended target PHD filter are given, one using Gaussian mixtures and one using Gaussian inverse Wishart (GIW) mixtures. Two models for the size and shape of an extended target measured with laser range sensors are suggested. A framework for estimation of the number of measurements generated by the targets is presented, and reduction of GIW mixtures is addressed. Prediction, spawning and combination of extended targets modeled using GIW distributions is also presented. The extended target tracking functions are evaluated in simulations and in experiments with laser range data.
30.	Granström, Karl, 1981, et al. (författare) Gamma Gaussian inverse-Wishart Poisson multi-Bernoulli filter for extended target tracking 2016 Ingår i: FUSION 2016 - 19th International Conference on Information Fusion, Proceedings. ; , s. 893-900 Konferensbidrag (refereegranskat)abstract This paper presents a gamma-Gaussian-inverse Wishart (GGIW) implementation of a Poisson multi-Bernoulli mixture (PMBM) filter for multiple extended target tracking. The GGIW density is the single extended target conjugate prior assuming a Poisson distributed number of Gaussian distributed measurements, and the PMBM density is the multi-object conju- gate prior assuming Poisson target measurements, Poisson clutter, and Poisson target birth. Specifically, the Poisson part of the GGIW-PMBM multi-object density represents the distribution of targets that have not yet been detected, and the multi-Bernoulli mixture part of the GGIW-PMBM multi-object density represents the distribution of targets that have been detected at least once.The update and the prediction of the GGIW-PMBM density parameters are given, and the filter is evaluated in a simulation study. The results show that the GGIW-PMBM filter outperforms PHD and CPHD filters for extended target tracking.
31.	Granström, Karl, 1981, et al. (författare) Guest editorial: Foreword to the special issue on extended object tracking 2017 Ingår i: Journal of Advances in Information Fusion. - 1557-6418. ; 12:2, s. 137-138 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
32.	Granström, Karl, 1981-, et al. (författare) Implementation of the GIW-PHD filter 2012 Rapport (övrigt vetenskapligt/konstnärligt)abstract This report contains pseudo-code for, and a computational complexity analysis of, the Gaussian inverse Wishart Probability Hypothesis Density filter.
33.	Granström, Karl, 1981-, et al. (författare) Learning to Close Loops from Range Data 2011 Ingår i: The international journal of robotics research. - : Sage Publications. - 0278-3649 .- 1741-3176. ; 30:14, s. 1728-1754 Tidskriftsartikel (refereegranskat)abstract In this paper we address the loop closure detection problem in simultaneous localization and mapping (SLAM), and present a method for solving the problem using pairwise comparison of point clouds in both two and three dimensions. The point clouds are mathematically described using features that capture important geometric and statistical properties. The features are used as input to the machine learning algorithm AdaBoost, which is used to build a non-linear classifier capable of detecting loop closure from pairs of point clouds. Vantage point dependency in the detection process is eliminated by only using rotation invariant features, thus loop closure can be detected from an arbitrary direction. The classifier is evaluated using publicly available data, and is shown to generalize well between environments. Detection rates of 66%, 63% and 53% for 0% false alarm rate are achieved for 2D outdoor data, 3D outdoor data and 3D indoor data, respectively. In both two and three dimensions, experiments are performed using publicly available data, showing that the proposed algorithm compares favourably with related work.
34.	Granström, Karl, 1981-, et al. (författare) Learning to Close the Loop from 3D Point Clouds 2010 Ingår i: Proceedings of the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems. - Linköping : Linköping University Electronic Press. - 9781424466740 ; , s. 2089-2095 Konferensbidrag (refereegranskat)abstract This paper presents a new solution to the loop closing problem for 3D point clouds. Loop closing is the problem of detecting the return to a previously visited location, and constitutes an important part of the solution to the Simultaneous Localisation and Mapping (SLAM) problem. It is important to achieve a low level of false alarms, since closing a false loop can have disastrous effects in a SLAM algorithm. In this work, the point clouds are described using features, which efficiently reduces the dimension of the data by a factor of 300 or more. The machine learning algorithm AdaBoost is used to learn a classifier from the features. All features are invariant to rotation, resulting in a classifier that is invariant to rotation. The presented method does neither rely on the discretisation of 3D space, nor on the extraction of lines, corners or planes. The classifier is extensively evaluated on publicly available outdoor and indoor data, and is shown to be able to robustly and accurately determine whether a pair of point clouds is from the same location or not. Experiments show detection rates of 63% for outdoor and 53% for indoor data at a false alarm rate of 0%. Furthermore, the classifier is shown to generalise well when trained on outdoor data and tested on indoor data in a SLAM experiment.
35.	Granström, Karl, 1981, et al. (författare) Likelihood-Based Data Association for Extended Object Tracking Using Sampling Methods 2018 Ingår i: IEEE Transactions on Intelligent Vehicles. - 2379-8858. ; 3:1, s. 30-45 Tidskriftsartikel (refereegranskat)abstract Environment perception is a key enabling technology in autonomous vehicles, and multiple object tracking is an important part of this. The use of high resolution sensors, such as automotive radar and lidar, leads to the extended object tracking problem, with multiple detections per tracked object. For computationally feasible multiple extended object tracking, the data association problem must be handled. Previous work has relied on a two-step approach, using clustering algorithms, together with assignment algorithms, to achieve this. In this paper, we show that it is possible to handle the data association in a single step that works directly on the desired likelihood function. Single step data association is beneficial, because it enables better use of the measurement model and the predicted multiobject density. For single step data association, we use algorithms based on stochastic sampling, and integrate them into a Poisson Multi-Bernoulli Mixture filter. In a simulation study, and in an experiment with Velodyne data acquired in an urban environment, four sampling algorithms are compared to clustering and assignment. The results from the simulations and the experiment show that single-step likelihood-based data association achieves better performance than two-step clustering and assignment data association does.
36.	Granström, Karl, 1981- (författare) Loop detection and extended target tracking using laser data 2011 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract In the past two decades, robotics and autonomous vehicles have received ever increasing research attention. For an autonomous robot to function fully autonomously alongside humans, it must be able to solve the same tasks as humans do, and it must be able to sense the surrounding environment. Two such tasks are addressed in this thesis, using data from laser range sensors.The first task is recognising that the robot has returned to a previously visited location, a problem called loop closure detection. Loop closure detection is a fundamental part of the simultaneous localisation and mapping problem, which consists of mapping an unknown area and simultaneously localise in the same map. In this thesis, a classification approach is taken to the loop closure detection problem. The laser range data is described in terms of geometrical and statistical properties, called features. Pairs of laser range data from two different locations are compared by using adaptive boosting to construct a classifier that takes as input the computed features. Experiments using real world laser data are used to evaluate the properties of the classifier, and the classifier is shown to compare well to existing solutions.The second task is keeping track of objects that surround the robot, a problem called target tracking. Target tracking is an estimation problem in which data association between the estimates and measurements is of high importance. The data association is complicated by things such as noise and false measurements. In this thesis, extended targets, i.e. targets that potentially generate more than one measurement per time step, are considered. The multiple measurements per time step further complicate the data association. Tracking of extended targets is performed using an implementation of a probability hypothesis density filter, which is evaluated in simulations using the optimal sub-pattern assignment metric. The filter is also used to track humans with real world laser range data, and the experiments show that the filter can handle the so called occlusion problem.
37.	Granström, Karl, 1981-, et al. (författare) On Extended Target Tracking Using PHD Filters 2012 Annan publikation (övrigt vetenskapligt/konstnärligt)abstract This paper presents an overview of the extended target tracking research undertaken at the division of Automatic Control at Linköping University. The PHD and CPHD filters for multiple extended target tracking under clutter and unknown association are summarized, with focus on the Gaussian mixture and Gaussian inverse Wishart implementations. The paper elaborates on measurement set partitioning, the measurement generating Poisson rates, the probability of detection, and practical examples of measurement models.
38.	Granström, Karl, 1981-, et al. (författare) On Spawning and Combination of Extended/Group Targets Modeled with Random Matrices 2013 Ingår i: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 61:3, s. 678-692 Tidskriftsartikel (refereegranskat)abstract In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events.
39.	Granström, Karl, 1981-, et al. (författare) On the Reduction of Gaussian inverse Wishart Mixtures 2012 Ingår i: Proceedings of the International Conference on Information Fusion (FUSION). - : IEEE Press. - 9780982443842 - 9781467304177 ; , s. 2162-2169 Konferensbidrag (refereegranskat)abstract This paper presents an algorithm for reduction of Gaussian inverse Wishart mixtures. Sums of an arbitrary number of mixture components are approximated with single components by analytically minimizing the Kullback-Leibler divergence. The Kullback-Leibler difference is used as a criterion for deciding whether or not two components should be merged, and a simple reduction algorithm is given. The reduction algorithm is tested in simulation examples in both one and two dimensions. The results presented in the paper are useful in extended target tracking using the random matrix framework.
40.	Granström, Karl, 1981-, et al. (författare) On the Use of Multiple Measurement Models for Extended Target Tracking 2013 Ingår i: Proceedings of the 16th International Conference on Information Fusion. - 9786058631113 ; , s. 1534-1541 Konferensbidrag (refereegranskat)abstract This paper considers extended targets that have constant extension shapes, but generate measurements whose appearance can change abruptly. The problem is approached using multiple measurement models, where each model corresponds to a measurement appearance mode. Mode transitions are modeled as dependent on the extended target kinematic state, and a multiple model extended target PHD filter is used to handle multiple targets with multiple appearance modes. The extended target tracking is evaluated using real world data where a laser range sensor is used to track multiple bicycles.
41.	Granström, Karl, 1981, et al. (författare) Pedestrian tracking using Velodyne data-Stochastic optimization for extended object tracking 2017 Ingår i: 28th IEEE Intelligent Vehicles Symposium, IV 2017, Redondo Beach, United States, 11-14 June 2017. ; , s. 39-46 Konferensbidrag (refereegranskat)abstract Environment perception is a key enabling technology in autonomous vehicles, and multiple object tracking is an important part of this. High resolution sensors, such as automotive radar and lidar, leads to the so called extended target tracking problem, in which there are multiple detections per tracked object. For computationally feasible multiple extended target tracking, the data association problem must be handled. Previous work has relied on the use of clustering algorithms, together with assignment algorithms, to achieve this. In this paper we present a stochastic optimisation method that directly maximises the desired likelihood function, and solves the problem in a single step, rather than two steps (clustering+assignment). The proposed method is evaluated against previous work in an experiment where Velodyne data is used to track pedestrians, and the results clearly show that the proposed method achieves the best performance, especially in challenging scenarios.
42.	Granström, Karl, 1981, et al. (författare) Poisson multi-Bernoulli conjugate prior for estimation of both detected and undetected extended objects 2016 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract This paper presents a Poisson multi-Bernoulli mixture(PMBM) conjugate prior for multiple extended object estimation. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the predictionand the update preserve the PMBM form of the density, andin this sense the PMBM density is a conjugate prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter outperforms the extended target PHD, CPHD and LMB filters.
43.	Granström, Karl, 1981, et al. (författare) Poisson Multi-Bernoulli Mixture Conjugate Prior for Multiple Extended Target Filtering 2020 Ingår i: IEEE Transactions on Aerospace and Electronic Systems. - 1557-9603 .- 0018-9251. ; 56:1, s. 208-225 Tidskriftsartikel (refereegranskat)abstract This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object filtering. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense, the PMBM density is a conjugate prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart implementation is presented, along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter performs well in comparison to the extended target \delta-generalized labelled multi-Bernoulli and LMB filters. An experiment with Lidar data illustrates the benefit of tracking both detected and undetected targets.
44.	Granström, Karl, 1981, et al. (författare) Poisson Multi-Bernoulli Mixture Trackers: Continuity Through Random Finite Sets of Trajectories 2018 Ingår i: 2018 21st International Conference on Information Fusion, FUSION 2018. ; , s. 973-981 Konferensbidrag (refereegranskat)abstract The Poisson multi-Bernoulli mixture (PMBM) is an unlabelled multi-target distribution for which the prediction and update are closed. It has a Poisson birth process, and new Bernoulli components are generated on each new measurement as a part of the Bayesian measurement update. The PMBM filter is similar to the multiple hypothesis tracker (MHT), but seemingly does not provide explicit continuity between time steps. This paper considers a recently developed formulation of the multi-target tracking problem as a random finite set (RFS) of trajectories, and derives two trajectory RFS filters, called PMBM trackers. The PMBM trackers efficiently estimate the set of trajectories, and share hypothesis structure with the PMBM filter. By showing that the prediction and update in the PMBM filter can be viewed as an efficient method for calculating the time marginals of the RFS of trajectories, continuity in the same sense as MHT is established for the PMBM filter.
45.	Granström, Karl, 1981-, et al. (författare) Properties and Approximations of some Matrix Variate Probability Density Functions 2011 Rapport (övrigt vetenskapligt/konstnärligt)abstract This report contains properties and approximations of some matrix valued probability density functions. Expected values of functions of generalised Beta type II distributed random variables are derived. In two Theorems, approximations of matrix variate distributions are derived. A third theorem contain a marginalisation result.
46.	Granström, Karl, 1981-, et al. (författare) Random Set Methods : Estimation of Multiple Extended Objects 2014 Ingår i: IEEE robotics & automation magazine. - : IEEE Robotics and Automation Society. - 1070-9932 .- 1558-223X. ; 21:2, s. 73-82 Tidskriftsartikel (refereegranskat)abstract Random set based methods have provided a rigorous Bayesian framework and have been used extensively in the last decade for point object estimation. In this paper, we emphasize that the same methodology offers an equally powerful approach to estimation of so called extended objects, i.e., objects that result in multiple detections on the sensor side. Building upon the analogy between Bayesian state estimation of a single object and random finite set estimation for multiple objects, we give a tutorial on random set methods with an emphasis on multiple extended object estimation. The capabilities are illustrated on a simple yet insightful real life example with laser range data containing several occlusions.
47.	Granström, Karl, 1981, et al. (författare) Spatiotemporal Constraints for Sets of Trajectories with Applications to PMBM Densities 2020 Ingår i: Proceedings of 2020 23rd International Conference on Information Fusion, FUSION 2020. ; , s. 343-350 Konferensbidrag (refereegranskat)abstract In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal contraints on trajectories can be used to answer a range of important questions, including, e.g., “where did the person that were in area A at time t, go afterwards?”. We discuss how multiple constraints can be combined into sets of constraints, and we then apply sets of constraints to set of trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM) densities. For Poisson target birth, the exact posterior density is PMBM for both point targets and extended targets. In the paper we show that if the unconstrained set of trajectories density is PMBM, then the constrained density is also PMBM. Examples of constrained trajectory densities motivate and illustrate the key results.
48.	Granström, Karl, 1981, et al. (författare) Systematic Approach to IMM Mixing for Unequal Dimension States 2015 Ingår i: IEEE Transactions on Aerospace and Electronic Systems. - : Institute of Electrical and Electronics Engineers (IEEE). - 1557-9603 .- 0018-9251. ; 51:4, s. 2975-2986 Tidskriftsartikel (refereegranskat)abstract The interacting multiple model (IMM) estimator outperforms fixed model filters, e.g. the Kalman filter, in scenarios where the targets have periods of disparate behavior. Key to the good performance and low complexity is the mode mixing. Here we propose a systematic approach to mode mixing when the modes have states of different dimensions. The proposed approach is general and encompasses previously suggested solutions. Different mixing approaches are compared, and the proposed methodology is shown to perform very well.
49.	Granström, Karl, 1981-, et al. (författare) Tracking Rectangular and Elliptical Extended Targets Using Laser Measurements 2011 Ingår i: Proceedings of the 14th International Conference on Information Fusion. - 9781457702679 ; , s. 592-599 Konferensbidrag (refereegranskat)abstract This paper considers tracking of extended targets using data from laser range sensors. Two types of extended target shapes are considered, rectangular and elliptical, and a method to compute predicted measurements and corresponding innovation covariances is suggested. The proposed method can easily be integrated into any tracking framework that relies on the use of an extended Kalman filter. Here, it is used together with a recently proposed Gaussian mixture probability hypothesis density (GM-PHD) filter for extended target tracking, which enables estimation of not only position, orientation, and size of the extended targets, but also estimation of extended target type (i.e. rectangular or elliptical). In both simulations and experiments using laser data, the versatility of the proposed tracking framework is shown. In addition, a simple measure to evaluate the extended target tracking results is suggested.
50.	Kim, Hyowon, et al. (författare) 5G mmWave Cooperative Positioning and Mapping Using Multi-Model PHD Filter and Map Fusion 2020 Ingår i: IEEE Transactions on Wireless Communications. - 1558-2248 .- 1536-1276. ; 19:6, s. 3782-3795 Tidskriftsartikel (refereegranskat)abstract 5G millimeter wave (mmWave) signals can enable accurate positioning in vehicular networks when the base station and vehicles are equipped with large antenna arrays. However, radio-based positioning suffers from multipath signals generated by different types of objects in the physical environment. Multipath can be turned into a benefit, by building up a radio map (comprising the number of objects, object type, and object state) and using this map to exploit all available signal paths for positioning. We propose a new method for cooperative vehicle positioning and mapping of the radio environment, comprising a multiple-model probability hypothesis density filter and a map fusion routine, which is able to consider different types of objects and different fields of views. Simulation results demonstrate the performance of the proposed method.

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