Poisson models for extended target and group tracking
18 Aug 2005-Proceedings of SPIE (International Society for Optics and Photonics)-Vol. 5913, pp 230-241
TL;DR: In this paper, the measurements are modelled as a Poisson process with a spatially dependent rate parameter, which allows to model extended targets as an intensity distribution rather than a set of points and, for a target formation, it gives the option of modelling part of the group as a spatial distribution of target density.
Abstract: It is common practice to represent a target group (or an extended target) as set of point sources and attempt to formulate a tracking filter by constructing possible assignments between measurements and the sources. We suggest an alternative approach that produces a measurement model (likelihood) in terms of the spatial density of measurements over the sensor observation region. In particular, the measurements are modelled as a Poisson process with a spatially dependent rate parameter. This representation allows us to model extended targets as an intensity distribution rather than a set of points and, for a target formation, it gives the option of modelling part of the group as a spatial distribution of target density. Furthermore, as a direct consequence of the Poisson model, the measurement likelihood may be evaluated without constructing explicit association hypotheses. This considerably simplifies the filter and gives a substantial computational saving in a particle filter implementation. The Poisson target-measurement model will be described and its relationship to other filters will be discussed. Illustrative simulation examples will be presented.
Citations
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TL;DR: In this article, the problem of maintaining a track for an extended object or group target with varying number of detections was analyzed and discussed, and a new approach was derived that is expected to overcome some of the weaknesses the mentioned Bayesian approach suffers from in certain applications.
Abstract: The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to limited sensor resolution capabilities, group targets (i.e., a number of closely spaced targets moving in a coordinated fashion) may show a similar detection pattern as extended objects, namely a varying number of detections whose spread is determined by both the statistical sensor errors as well as the physical extension of the group or extended object. In both cases, tracking and data association under the “one target-one detection” assumption are no longer applicable. This paper deals with the problem of maintaining a track for an extended object or group target with varying number of detections. Herein, object extension is represented by a symmetric positive definite random matrix. A recently published Bayesian approach to tackling this problem is analyzed and discussed. From there, a new approach is derived that is expected to overcome some of the weaknesses the mentioned Bayesian approach suffers from in certain applications.
313 citations
01 Jan 2009
TL;DR: In this paper, a recently published Bayesian approach is discussed with regard to the estimator's self-assessment of the estimation error for both kinematics and extension, where physical extension is represented by a symmetric positive definite random matrix.
Abstract: The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to limited sensor resolution capabilities, group targets (i. e., a number of closely spaced targets moving in a coordinated fashion) may show a similar detection pattern as extended objects, namely a varying number of detections whose spread is determined by both the statistical sensor errors as well as the physical extension of the group or extended object. Different tracking approaches treating these situations have been proposed where physical extension is represented by a symmetric positive definite random matrix. In this paper, a recently published Bayesian approach is discussed with regard to the estimator’s self-assessment of the estimation error for both kinematics and extension.
280 citations
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
Proceedings Article•
05 Jul 2011TL;DR: In this paper, a star-convex RHM is introduced for tracking star- Convex shape approximations of targets and Bayesian inference is performed by means of a Gaussian-assumed state estimator allowing for an efficient recursive closed-form measurement update.
Abstract: This paper is about tracking an extended object or a group target, which gives rise to a varying number of measurements from different measurement sources. For this purpose, the shape of the target is tracked in addition to its kinematics. The target extent is modeled with a new approach called Random Hypersurface Model (RHM) that assumes varying measurement sources to lie on scaled versions of the shape boundaries. In this paper, a star-convex RHM is introduced for tracking star-convex shape approximations of targets. Bayesian inference for star-convex RHMs is performed by means of a Gaussian-assumed state estimator allowing for an efficient recursive closed-form measurement update. Simulations demonstrate the performance of this approach for typical extended object and group tracking scenarios.
199 citations
TL;DR: Comment on the errors in the formulation of Theorem 1 and give a correct formulation of theorem.
Abstract: This paper presents a Gaussian-mixture (GM) implementation of the probability hypothesis density (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.
197 citations
References
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Book•
01 Jan 1991TL;DR: In this paper, the authors present a survey of statistics for spatial data in the field of geostatistics, including spatial point patterns and point patterns modeling objects, using Lattice Data and spatial models on lattices.
Abstract: Statistics for Spatial Data GEOSTATISTICAL DATA Geostatistics Spatial Prediction and Kriging Applications of Geostatistics Special Topics in Statistics for Spatial Data LATTICE DATA Spatial Models on Lattices Inference for Lattice Models SPATIAL PATTERNS Spatial Point Patterns Modeling Objects References Author Index Subject Index.
8,631 citations
01 Apr 1993
TL;DR: An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.
Abstract: An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linear- ity or Gaussian noise: it may be applied to any state transition or measurement model. A simula- tion example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter.
8,018 citations
01 Feb 1994
TL;DR: Some of the mathematical techniques borrowed from algebraic geometry, projective geometry, and homotopy theory that are required to solve three-dimensional (3D) motion and structure of rigid objects when their corresponding features are known at different times or are viewed by different cameras are mentioned.
Abstract: We present a review of algorithms and their performance for determining three-dimensional (3D) motion and structure of rigid objects when their corresponding features are known at different times or are viewed by different cameras. Three categories of problems are considered, depending upon whether the features are two (2D) or three-dimensional (3D) and the type of correspondence: a) 3D to 3D (i.e., locations of corresponding features in 3D space are known at two different times), b) 2D to 3D (i.e., locations of features in 3D space and their projection on the camera plane are known, and c) 2D to 2D (i.e., projections of features on the camera plane are known at two different times). Features considered include points, straight lines, curved lines, and corners. Emphasis is on problem formulation, efficient algorithms for solution, existence and uniqueness of solutions, and sensitivity of solutions to noise in the observed data. Algorithms described have been used in a variety of applications. Some of these are: a) positioning and navigating 3D objects in a 3D world, b) camera calibration, i.e., determining location and orientation of a camera by observing 3D features whose location is known, c) estimating motion and structure of moving objects relative to a camera. We mention some of the mathematical techniques borrowed from algebraic geometry, projective geometry, and homotopy theory that are required to solve these problems, list unsolved problems, and give some directions for future research. >
525 citations
TL;DR: This work proposes an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler and is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem.
Abstract: We address the problem of multitarget tracking (MTT) encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies in the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies.
400 citations
17 Oct 2005
TL;DR: In this paper, a Bayesian filter was developed for tracking an extended object in clutter based on two simple axioms: (i) the number of received target and clutter measurements in a frame are Poisson distributed (so several measurements may originate from the target) and (ii) target extent is modelled by a spatial probability distribution and each targetrelated measurement is an independent 'random draw' from this spatial distribution (convolved with a sensor model).
Abstract: A Bayesian filter has been developed for tracking an extended object in clutter based on two simple axioms: (i) the numbers of received target and clutter measurements in a frame are Poisson distributed (so several measurements may originate from the target) and (ii) target extent is modelled by a spatial probability distribution and each target-related measurement is an independent 'random draw' from this spatial distribution (convolved with a sensor model). Diffuse spatial models of target extent are of particular interest. This model is especially suitable for a particle filter implementation, and examples are presented for a Gaussian mixture model and for a uniform stick target convolved with a Gaussian error. A rather restrictive special case that admits a solution in the form of a multiple hypothesis Kalman filter is also discussed and demonstrated.
303 citations