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A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
- IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2002
"... Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view o ..."
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Cited by 2011 (2 self)
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Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or “particle”) representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.
Kernel-Based Object Tracking
, 2003
"... A new approach toward target representation and localization, the central component in visual tracking of non-rigid objects, is proposed. The feature histogram based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatially-smooth similarity fu ..."
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Cited by 907 (4 self)
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A new approach toward target representation and localization, the central component in visual tracking of non-rigid objects, is proposed. The feature histogram based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatially-smooth similarity functions suitable for gradient-based optimization, hence, the target localization problem can be formulated using the basin of attraction of the local maxima. We employ a metric derived from the Bhattacharyya coefficient as similarity measure, and use the mean shift procedure to perform the optimization. In the presented tracking examples the new method successfully coped with camera motion, partial occlusions, clutter, and target scale variations. Integration with motion filters and data association techniques is also discussed. We describe only few of the potential applications: exploitation of background information, Kalman tracking using motion models, and face tracking. Keywords: non-rigid object tracking; target localization and representation; spatially-smooth similarity function; Bhattacharyya coefficient; face tracking. 1
Color-based probabilistic tracking
- ECCV
, 2002
"... Color-based trackers recently proposed in [3,4,5] have been proved robust and versatile for a modest computational cost. They are especially appealing for tracking tasks where the spatial structure of the tracked objects exhibits such a dramatic variability that trackers based on a space-dependent ..."
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Cited by 357 (6 self)
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Color-based trackers recently proposed in [3,4,5] have been proved robust and versatile for a modest computational cost. They are especially appealing for tracking tasks where the spatial structure of the tracked objects exhibits such a dramatic variability that trackers based on a space-dependent appearance reference would break down very fast. Trackers in [3,4,5] rely on the deterministic search of a window whose color content matches a reference histogram color model. Relying on the same principle of color histogram distance, but within a probabilistic framework, we introduce a new Monte Carlo tracking technique. The use of a particle filter allows us to better handle color clutter in the background, as well as complete occlusion of the tracked entities over a few frames. This probabilistic approach is very flexible and can be extended in a number of useful ways. In particular, we introduce the following ingredi-ents: multi-part color modeling to capture a rough spatial layout ignored by global histograms, incorporation of a background color model when relevant, and extension to multiple objects.
Sequential Monte Carlo Samplers
, 2002
"... In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal ..."
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Cited by 303 (44 self)
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In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal which is a distribution of interest. To sample from these distributions, we use sequential Monte Carlo methods. We show that these methods can be interpreted as interacting particle approximations of a nonlinear Feynman-Kac flow in distribution space. One interpretation of the Feynman-Kac flow corresponds to a nonlinear Markov kernel admitting a specified invariant distribution and is a natural nonlinear extension of the standard Metropolis-Hastings algorithm. Many theoretical results have already been established for such flows and their particle approximations. We demonstrate the use of these algorithms through simulation.
A Survey of Convergence Results on Particle Filtering Methods for Practitioners
, 2002
"... Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closed-form expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the o ..."
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Cited by 246 (8 self)
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Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closed-form expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the optimal filtering problem numerically. The posterior distribution of the state is approximated by a large set of Dirac-delta masses (samples/particles) that evolve randomly in time according to the dynamics of the model and the observations. The particles are interacting; thus, classical limit theorems relying on statistically independent samples do not apply. In this paper, our aim is to present a survey of recent convergence results on this class of methods to make them accessible to practitioners.
Convergence of Sequential Monte Carlo Methods
- SEQUENTIAL MONTE CARLO METHODS IN PRACTICE
, 2000
"... Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data arise in many applications in statistics and related fields. Recently, a large number of algorithms and applications based on sequential Monte Carlo methods (also known as particle filter ..."
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Cited by 243 (13 self)
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Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data arise in many applications in statistics and related fields. Recently, a large number of algorithms and applications based on sequential Monte Carlo methods (also known as particle filtering methods) have appeared in the literature to solve this class of problems; see (Doucet, de Freitas & Gordon, 2001) for a survey. However, few of these methods have been proved to converge rigorously. The purpose of this paper is to address this issue. We present a general sequential Monte Carlo (SMC) method which includes most of the important features present in current SMC methods. This method generalizes and encompasses many recent algorithms. Under mild regularity conditions, we obtain rigorous convergence results for this general SMC method and therefore give theoretical backing for the validity of all the algorithms that can be obtained as particular cases of it.
Mixture Kalman filters
, 2000
"... In treating dynamic systems,sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the on-line `filtering' task. We propose a special sequential Monte Carlo metho ..."
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Cited by 222 (8 self)
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In treating dynamic systems,sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the on-line `filtering' task. We propose a special sequential Monte Carlo method,the mixture Kalman filter, which uses a random mixture of the Gaussian distributions to approximate a target distribution. It is designed for on-line estimation and prediction of conditional and partial conditional dynamic linear models,which are themselves a class of widely used non-linear systems and also serve to approximate many others. Compared with a few available filtering methods including Monte Carlo methods,the gain in efficiency that is provided by the mixture Kalman filter can be very substantial. Another contribution of the paper is the formulation of many non-linear systems into conditional or partial conditional linear form,to which the mixture Kalman filter can be applied. Examples in target tracking and digital communications are given to demonstrate the procedures proposed.
A tutorial on particle filtering and smoothing: fifteen years later
- OXFORD HANDBOOK OF NONLINEAR FILTERING
, 2011
"... Optimal estimation problems for non-linear non-Gaussian state-space models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. r ..."
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Cited by 214 (15 self)
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Optimal estimation problems for non-linear non-Gaussian state-space models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, up-to-date survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
The Unscented Particle Filter
, 2000
"... In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available info ..."
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Cited by 214 (8 self)
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In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.
