Karl Granström

Karl Granström
Chalmers University of Technology · Department of Signals and Systems

Ph.D.

About

92
Publications
21,199
Reads
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2,827
Citations
Additional affiliations
September 2015 - present
Chalmers University of Technology
Position
  • PostDoc Position
September 2014 - August 2015
University of Connecticut
Position
  • PostDoc Position
August 2013 - August 2014
Linköping University
Position
  • Lecturer
Description
  • Digital Signal Processing: discrete Fourier transform (DFT), signal modelling (both in the frequency and in the time domain), estimating models, spectral estimation, Wiener filtering, Kalman filtering and adaptive filtering.

Publications

Publications (92)
Preprint
Full-text available
In this paper, we propose a Poisson multi-Bernoulli (PMB) filter for extended object tracking (EOT), which directly estimates the set of object trajectories, using belief propagation (BP). The proposed filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the PMB mixture (PMBM) po...
Preprint
Full-text available
This paper presents a general solution for computing the multi-object posterior for sets of trajectories from a sequence of multi-object (unlabelled) filtering densities and a multi-object dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multi-object filters that do not explicitly estimate...
Preprint
Radio-based vehicular simultaneous localization and mapping (SLAM) aims to localize vehicles while mapping the landmarks in the environment. We propose a sequence of three Poisson multi-Bernoulli mixture (PMBM) based SLAM filters, which handle the entire SLAM problem in a theoretically optimal manner. The complexity of the three proposed SLAM filte...
Article
Full-text available
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, e.g., truncation bounds, orientation, and scaling, that can be learned from t...
Article
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)...
Preprint
This paper presents a solution for recovering full trajectory information, via the calculation of the posterior of the set of trajectories, from a sequence of multitarget (unlabelled) filtering densities and the multitarget dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multitarget filte...
Article
Full-text available
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 i...
Preprint
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)...
Article
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...
Preprint
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 perso...
Preprint
For the standard point target model with Poisson birth process, the Poisson Multi-Bernoulli Mixture (PMBM) is a conjugate multi-target density. The PMBM filter for sets of targets has been shown to have state-of-the-art performance and a structure similar to the Multiple Hypothesis Tracker (MHT). In this paper we consider a recently developed formu...
Preprint
The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multi-target distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multi-target tracking problem us...
Preprint
The Poisson multi-Bernoulli mixture (PMBM) is a multi-target distribution for which the prediction and update are closed. By applying the random finite set (RFS) framework to multi-target tracking with sets of trajectories as the variable of interest, the PMBM trackers can efficiently estimate the set of target trajectories. This paper derives two...
Article
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...
Preprint
5G millimeter wave (mmWave) signals can enable accurate positioning in vehicular networks when the base station (BS) 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 buil...
Preprint
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 mixtu...
Article
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...
Article
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 mod...
Preprint
A decentralized Poisson multi-Bernoulli filter is proposed to track multiple extended targets using multiple sensors. Independent filters estimate the targets 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...
Preprint
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 mod...
Preprint
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), bu...
Conference Paper
This paper proposes an efficient implementation of the Poisson multi-Bernoulli mixture (PMBM) trajectory filter. The proposed implementation performs track-oriented N-scan pruning to limit complexity, and uses dual decomposition to solve the involved multi-frame assignment problem. In contrast to the existing PMBM filter for sets of targets, the PM...
Article
Monocular cameras are one of the most commonly used sensors in the automotive industry for autonomous vehicles. One major drawback using a monocular camera is that it only makes observations in the two dimensional image plane and can not directly measure the distance to objects. In this paper, we aim at filling this gap by developing a multi-object...
Preprint
In this paper, a Poisson multi-Bernoulli (PMB) filter for multiple extended targets estimation is presented. The PMB filter is based on the Poisson multi-Bernoulli mixture (PMBM) conjugate prior and approximates the multi-Bernoulli mixture (MBM) in the posterior as a single multi-Bernoulli. By only having a single multi-Bernoulli representing detec...
Article
Full-text available
This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of an extended object and discuss its delimitation to other object types and sensor models. Next, different shape models and possibilities to model the number of measurements are extensively discussed. Subsequently, we give a t...
Article
This paper considers the problem of estimating the 3D states of a salvo of thrusting/ballistic endo-atmospheric objects using 2D Cartesian measurements from the focal plane array (FPA) of a single fixed optical sensor. Since the initial separations in the FP are smaller than the resolution of the sensor there are merged FP measurements, compounding...
Conference Paper
This paper considers the problem of estimating the 3D states of a salvo of thrusting/ballistic endo-atmospheric objects using 2D Cartesian measurements from the focal plane array (FPA) of a {\em single} fixed optical sensor. Since the initial separations in the FPA are smaller than the resolution of the sensor, this results in merged measurements i...
Article
Full-text available
In this paper, the multiple sensor measurement update is studied for the random matrix model. Four different updates are presented and evaluated: three updates based on parametric approximations of the extended target state probability density function, and one update based on a Rao-Blackwellized (RB) particle approximation of the state density. An...
Article
We comment on the errors in the formulation of Theorem 1 given in Extended Target Tracking Using a Gaussian-Mixture PHD Filter by K. Granström, C. Lundquist, and U. Orguner, and give a correct formulation.
Article
Full-text available
We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multi-target tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the \delta-generalised labelled multi-Bernoulli (\delta-GLMB) filter, showing that a \del...
Article
Full-text available
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...
Article
Full-text available
To track an extended target presents challenges because the hypothesis of " one target means one detection " is not valid. Several approaches to extended target tracking have been found promising, and in particular those involving random matrices have demonstrated their appeal. When targets are extended and the data is multistatic the issues are co...
Conference Paper
Full-text available
The objective of extended object tracking is to simultaneously track a target object and estimate its shape. As a consequence, it becomes necessary to incorporate both location and shape errors in the performance assessment of extended object tracking methods. In this work, we highlight the difficulties of selecting a proper metric for this purpose...
Conference Paper
Full-text available
The tracking of extended targets is attracting a growing literature thanks to the high resolution of several modern radar systems. A fully Bayesian solution has been proposed in the random matrix framework. In this paper, the fusion of detections acquired by multiple sensors is analyzed. Four different methods are proposed to track and to estimate...
Article
Full-text available
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 conjugacy property allows the posterior PMBM...
Conference Paper
Multiple target tracking (MTT) is a challenging task that aims to estimate the number of targets and their states in the presence of process noise, measurement noise and data association uncertainty. This paper considers a special MTT problem characterized by additional complexity. In this problem, multiple targets are launched simultaneously in ne...
Article
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...
Article
Full-text available
X-band marine radar systems are flexible and lowcost tools for monitoring multiple targets in a surveillance area. They can provide high resolution measurements both in space and time. Such features offer the opportunity to get accurate information not only about the target kinematics, as other conventional sensors, but also about the target size....
Conference Paper
Full-text available
This paper shows a principled way for an interacting multiple model (IMM) tracker to mix information when there are states that are present in only a subset of the model set, they have no “match” in the other.
Article
Full-text available
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 pro...
Article
Full-text available
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, that is cap...
Conference Paper
Full-text available
Conventional tracking algorithms rely upon the hypothesis of one detection per target for each frame. However, very fine spatial resolution radars represent widespread systems that provides data for which this hypothesis could be no longer valid. This problem is often called in the literature extended target tracking. In this paper we propose to us...
Conference Paper
Full-text available
This paper presents a model for tracking of extended targets whose extent cannot be described by a simple geometric shape such as an ellipse or a rectangle. The extended target shape is represented by a number Ns of elliptic subobjects, where Ns is assumed known. Because an extended target is a rigid body, the subobject positions must necessarily b...
Conference Paper
Full-text available
There is good reason to model an asymmetric threat (a structured action such as a terrorist attack) as an HMM. Thence there is a means (described in earlier work) to detect it via the novel Bernoulli filter paradigm that is emerging as an integrated tracker/track-management tool. This paper details additional progress made to model the detectabilit...
Conference Paper
Full-text available
The PHD filter is a popular approach to the multiple target tracking problem, however, it suffers from the Poisson assumption which yields a cardinality estimate with too high variance. In recent work Le and Kaplan proposed to improve the performance of the PHD filter using a particle approximation of the predicted multiobject density and updating...
Conference Paper
Full-text available
This paper addresses extended multi-target tracking in clutter, i.e. tracking targets that may produce more than one measurement on each scan. We propose a new algorithm for solving this problem, that is capable of initiating and maintaining labelled estimates of the target kinematics, measurement rates and extents. Our proposed technique is based...
Article
In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a...
Article
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 sim...
Article
Common data preprocessing routines often introduce considerable flaws in laser-based tracking of extended objects. As an alternative, extended target tracking methods, such as the Gamma-Gaussian-Inverse Wishart (GGIW) probability hypothesis density (PHD) filter, work directly on raw data. In this paper, the GGIW-PHD filter is applied to real world...
Article
This paper presents an extended target tracking method for tracking cars in urban traffic using data from laser range sensors. Results are presented for three real world datasets that contain multiple cars, occlusions, and maneuver changes. The car's shape is approximated by a rectangle, and single track steering models are used for the target kine...
Conference Paper
Full-text available
Micro unmanned aerial vehicles are becoming increasingly interesting for aiding and collaborating with human agents in myriads of applications, but in particular they are useful for monitoring inaccessible or dangerous areas. In order to interact with and monitor humans, these systems need robust and real-time computer vision subsystems that allow...
Conference Paper
Full-text available
X-band radar systems represent a flexible and low-cost tool for ship detection and tracking. These systems suffer the interference of the sea-clutter but at the same time they can provide high measurement resolutions, both in space and time. Such features offer the opportunity to get accurate information about the target's state and shape. Accordin...
Article
Full-text available
This paper presents a model for tracking of extended targets, where each target is represented by a given number of elliptic subobjects. A gamma Gaussian inverse Wishart implementation is derived, and necessary approximations are suggested to alleviate the data association complexity. A simulation study shows the merits of the model compared to pre...
Article
Full-text available
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 article, 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 si...
Conference Paper
Full-text available
A GM-PHD filter is used for pedestrian tracking in a crowd surveillance application. The purpose is to keep track of the different groups over time as well as to represent the shape of the groups and the number of people within the groups. Input data to the GM-PHD filter are detections using a state of the art algorithm applied to video frames from...
Article
Full-text available
Courses at the Master's level in automatic control and signal processing cover mathematical theories and algorithms for control, estimation, and filtering. However, giving students practical experience in how to use these algorithms is also an important part of these courses. A goal is that the students should not only be able to understand and der...
Article
Full-text available
This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has been derived by Mahler, and different implementations have been proposed recently. To achieve better estimation performance t...
Article
Full-text available
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 functi...