Corrections on: “Extended Target Tracking Using a Gaussian-Mixture PHD Filter”
01 Apr 2017-IEEE Transactions on Aerospace and Electronic Systems (IEEE)-Vol. 53, Iss: 2, pp 1055-1058
TL;DR: This paper presents a Gaussian-mixture implementation of the probability hypothesis density (PHD) filter for tracking extended targets and suitable remedies are given to handle spatially close targets and target occlusion.
Abstract: We comment on the errors in the formulation of Theorem 1 given in Extended Target Tracking Using a Gaussian-Mixture PHD Filter by K. Granstrom, C. Lundquist, and U. Orguner, and give a correct formulation.
Citations
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TL;DR: 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, resulting in the Gaussian inverse Wishart phd (giw-phd) filter.
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 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
270 citations
Cites background or methods from "Corrections on: “Extended Target Tr..."
...In this work, due to space considerations, we are not able to give all the details about the main partitioning algorithm described originally in [17]....
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...A Gaussian mixture implementation of the extended target PHD filter [14], called the ET-GM-PHD-filter, has been presented in [17], with an early version given in [18]....
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...A method called distance partition was suggested in [18], and it was augmented with the subpartition algorithm in [17] to better handle the case of spatially close targets....
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...The measurement pseudolikelihood (8) requires a summation over all possible partitions, which quickly becomes intractable because the number of possible partitions increases very rapidly as the size of increases [14], [17]....
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...In the subpartition algorithm presented in [17], this problem was solved by generating additional partitions by considering the number of measurements in each cell , and comparing it to the expected number of measurements from a single target....
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TL;DR: A new algorithm is proposed for tracking multiple extended targets in clutter, capable of estimating the number of targets, as well the trajectories of their states, comprising the kinematics, measurement rates, and extents, and results show that the (G)LMB has improved estimation and tracking performance.
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.
180 citations
Cites methods from "Corrections on: “Extended Target Tr..."
...Based on these models, we then propose a GLMB filter for tracking multiple extended targets in clutter, as well as a cheaper approximation based on the LMB filter....
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TL;DR: This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion, including Markov Chain Monte Carlo methods, the random matrices approach and Random Finite Set Statistics methods.
171 citations
Cites methods from "Corrections on: “Extended Target Tr..."
...Practical implementations of the PHD filter include two main implementations: the SMC solutions [142] and Gaussian mixtures [144,86, 57,30,29]....
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TL;DR: This paper proposes using Gaussian processes to track an extended object or group of objects, that generates multiple measurements at each scan, that creates a model that describes the shape and the kinematics of the object.
Abstract: In this paper, we propose using Gaussian processes to track an extended object or group of objects, that generates multiple measurements at each scan. The shape and the kinematics of the object are ...
163 citations
TL;DR: A cardinalized probability hypothesis density filter for extended targets that can result in multiple measurements at each scan is presented, and it is compared to its PHD counterpart in a simulation study, showing that the CPHD filter has a more robust cardinality estimate leading to smaller OSPA errors.
Abstract: 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 this work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers. A gamma Gaussian inverse Wishart mixture implementation, which is capable of estimating the target extents and measurement rates as well as the kinematic state of the target, is proposed, and it is compared to its PHD counterpart in a simulation study. The results clearly show that the CPHD filter has a more robust cardinality estimate leading to smaller OSPA errors, which confirms that the extended target CPHD filter inherits the properties of its point target counterpart.
143 citations
Additional excerpts
...Section III-B gives a brief comparison between the ET-CPHD model and the model used in [32]....
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References
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TL;DR: This book covers a broad range of topics for regular factorial designs and presents all of the material in very mathematical fashion and will surely become an invaluable resource for researchers and graduate students doing research in the design of factorial experiments.
Abstract: (2007). Pattern Recognition and Machine Learning. Technometrics: Vol. 49, No. 3, pp. 366-366.
18,802 citations
07 Jan 2007
TL;DR: By augmenting k-means with a very simple, randomized seeding technique, this work obtains an algorithm that is Θ(logk)-competitive with the optimal clustering.
Abstract: The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster. Although it offers no accuracy guarantees, its simplicity and speed are very appealing in practice. By augmenting k-means with a very simple, randomized seeding technique, we obtain an algorithm that is Θ(logk)-competitive with the optimal clustering. Preliminary experiments show that our augmentation improves both the speed and the accuracy of k-means, often quite dramatically.
7,539 citations
TL;DR: This section will review those books whose content and level reflect the general editorial poltcy of Technometrics.
Abstract: This section will review those books whose content and level reflect the general editorial poltcy of Technometrics. Publishers should send books for review to Ejaz Ahmed, Depatment of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4 (techeditor@uwindsoxca). The opinions expressed in this section are those of the reviewers These opinions do not represent positions of the reviewer's organization and may not reflect those of the editors or the sponsoring societies. Listed prices reflect information provided by the publisher and may not be current The book purchase programs of the American Society for Quality can provide some of these books at reduced prices for members. For infbrmation, contact the American Society for Quality at 1-800-248-1946.
2,342 citations
"Corrections on: “Extended Target Tr..." refers background in this paper
...Let us exemplify1 the process of partitioning with a measurement set containing three individual measurements, Zk = { z (1) k , z (2) k , z (3) k } ....
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TL;DR: Recursion Bayes filter equations for the probability hypothesis density are derived that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets and it is shown that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense.
Abstract: The theoretically optimal approach to multisensor-multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. Even in single-target problems, this optimal filter is so computationally challenging that it must usually be approximated. Consequently, multitarget Bayes filtering will never be of practical interest without the development of drastic but principled approximation strategies. In single-target problems, the computationally fastest approximate filtering approach is the constant-gain Kalman filter. This filter propagates a first-order statistical moment - the posterior expectation - in the place of the posterior distribution. The purpose of this paper is to propose an analogous strategy for multitarget systems: propagation of a first-order statistical moment of the multitarget posterior. This moment, the probability hypothesis density (PHD), is the function whose integral in any region of state space is the expected number of targets in that region. We derive recursive Bayes filter equations for the PHD that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets. We also show that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense.
2,088 citations
Book•
28 Feb 2007
TL;DR: This comprehensive resource provides an in-depth understanding of finite-set statistics (FISST) - a recently developed method which unifies much of information fusion under a single probabilistic, in fact Bayesian, paradigm.
Abstract: This comprehensive resource provides you with an in-depth understanding of finite-set statistics (FISST) - a recently developed method which unifies much of information fusion under a single probabilistic, in fact Bayesian, paradigm. The book helps you master FISST concepts, techniques, and algorithms, so you can use FISST to address real-world challenges in the field. You learn how to model, fuse, and process highly disparate information sources, and detect and track non-cooperative individual/platform groups and conventional non-cooperative targets. You find a rigorous Bayesian unification for many aspects of expert systems theory. Moreover, the book presents systematic integral and differential calculus for multisource-multitarget problems, providing a methodology for devising rigorous new techniques. This accessible and detailed book is supported with over 3,000 equations, 90 clear examples, 70 explanatory figures, and 60 exercises with solutions.
2,004 citations