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247
Towards improved observation models for visual tracking: selective adaptation
 In Proc. Europ. Conf. Computer Vision
, 2002
"... Abstract. An important issue in tracking is how to incorporate an appropriate degree of adaptivity into the observation model. Without any adaptivity, tracking fails when object properties change, for example when illumination changes affect surface colour. Conversely, if an observation model adapts ..."
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Cited by 39 (5 self)
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Abstract. An important issue in tracking is how to incorporate an appropriate degree of adaptivity into the observation model. Without any adaptivity, tracking fails when object properties change, for example when illumination changes affect surface colour. Conversely, if an observation model adapts too readily then, during some transient failure of tracking, it is liable to adapt erroneously to some part of the background. The approach proposed here is to adapt selectively, allowing adaptation only during periods when two particular conditions are met: that the object should be both present and in motion. The proposed mechanism for adaptivity is tested here with a foreground colour and motion model. The experimental setting itself is novel in that it uses combined colour and motion observations from a fixed filter bank, with motion used also for initialisation via a Monte Carlo proposal distribution. Adaptation is performed using a stochastic EM algorithm, during periods that meet the conditions above. Tests verify the value of such adaptivity, in that immunity to distraction from clutter of similar colour to the object is considerably enhanced. 1
Kalman filtering with state constraints: a survey of linear and nonlinear algorithms’. http://academic. csuohio.edu/simond/ConstrKF, accessed
, 2010
"... Abstract: The Kalman filter is the minimumvariance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is nonGaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed ..."
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Cited by 37 (0 self)
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Abstract: The Kalman filter is the minimumvariance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is nonGaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results. 1
Particle filters for partially observed diffusions
, 2006
"... In this paper we introduce novel particle filters for a class of partiallyobserved continuoustime dynamic models where the signal is given by a multivariate diffusion process. We consider a variety of observation schemes, including diffusion observed with error, observation of a subset of the comp ..."
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Cited by 36 (8 self)
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In this paper we introduce novel particle filters for a class of partiallyobserved continuoustime dynamic models where the signal is given by a multivariate diffusion process. We consider a variety of observation schemes, including diffusion observed with error, observation of a subset of the components of the multivariate diffusion and arrival times of a Poisson process whose intensity is a known function of the diffusion (Cox process). Unlike available methods, our particle filters do not require approximations of the transition and/or the observation density using timediscretisations. Instead, they build on recent methodology for the exact simulation of diffusion process and the unbiased estimation of the transition density as described in the recent article Beskos et al. (2005c). In particular, we require the Generalised Poisson Estimator, which is a substantial generalisation of the Poisson Estimator (Beskos et al., 2005c), and it is introduced in this paper. Thus, our filters avoid the systematic biases caused by timediscretisations and they have significant computational advantages over alternative continuoustime filters. These advantages are supported by a central limit theorem which is established in this paper. Keywords: Continuoustime filtering, Exact Algorithm, Central Limit Theorem, Cox Process 1
A survey of sequential Monte Carlo methods for economics and finance
, 2009
"... This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in ..."
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Cited by 34 (7 self)
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This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macroeconomics to option pricing. The objective of this paper is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.
Multitarget tracking using the joint multitarget probability density
 IEEE Transactions on Aerospace and Electronic Systems
, 2005
"... This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurem ..."
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Cited by 33 (8 self)
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This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as nonGaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signaltonoise ratio (SNR).
A basic convergence result for particle filtering
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2007
"... The basic nonlinear ltering problem for dynamical systems is considered. Approximating the optimal lter estimate by particle lter methods has become perhaps the most common and useful method in recent years. Many variants of particle lters have been suggested, and there is an extensive literature o ..."
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Cited by 32 (8 self)
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The basic nonlinear ltering problem for dynamical systems is considered. Approximating the optimal lter estimate by particle lter methods has become perhaps the most common and useful method in recent years. Many variants of particle lters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still, a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to in nity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result.
Variable Resolution Particle Filter
 INTERNATIONAL JOINT CONFERENCE OF ARTIFICIAL INTELLIGENCE
, 2003
"... Particle filters are used extensively for tracking the state of nonlinear dynamic systems. This paper presents a new particle filter that maintains samples in the state space at dynamically varying resolution for computational efficiency. Resolution within statespace varies by region, dependin ..."
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Cited by 31 (4 self)
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Particle filters are used extensively for tracking the state of nonlinear dynamic systems. This paper presents a new particle filter that maintains samples in the state space at dynamically varying resolution for computational efficiency. Resolution within statespace varies by region, depending on the belief that the true state lies within each region. Where belief is strong, resolution is fine. Where belief is low, resolution is coarse, abstracting multiple similar states together. The resolution of the statespace is dynamically updated as the belief changes. The proposed
Particle Filtering for Multisensor Data Fusion with Switching Observation Models. Application to Land Vehicle
 Positioning, in &quot;IEEE transactions on Signal Processing
, 2006
"... This paper concerns the sequential estimation of a hidden state vector from noisy observations delivered by several sensors. Different from the standard framework, we assume here that the sensors may switch autonomously between different sensor states, that is, between different observation models. ..."
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Cited by 30 (4 self)
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This paper concerns the sequential estimation of a hidden state vector from noisy observations delivered by several sensors. Different from the standard framework, we assume here that the sensors may switch autonomously between different sensor states, that is, between different observation models. This includes sensor failure or sensor functioning conditions change. In our model, sensor states are represented by discrete latent variables, which prior probabilities are Markovian. We propose a family of efficient particle filters, for both synchronous and asynchronous sensor observations, as well as for important special cases. Moreover, we discuss connections with previous works. Finally, we study thoroughly a wheel land vehicle positioning problem where the GPS information may be unreliable because of multipath/masking effects. EDICS: SEN FUS
On Resampling Algorithms for Particle Filters
 Nonlinear Statistical Signal Processing Workshop
, 2006
"... In this paper a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms with respec ..."
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Cited by 29 (4 self)
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In this paper a comparison is made between four frequently encountered resampling algorithms for particle filters. A theoretical framework is introduced to be able to understand and explain the differences between the resampling algorithms. This facilitates a comparison of the algorithms with respect to their resampling quality and computational complexity. Using extensive Monte Carlo simulations the theoretical results are verified. It is found that systematic resampling is favourable, both in terms of resampling quality and computational complexity. 1.
"Shape Activity": A Continuous State HMM for Moving/Deforming Shapes with Application to Abnormal Activity Detection
"... The aim is to model "activity" performed by a group of moving and interacting objects (which can be people or cars or different rigid components of the human body) and use the models for abnormal activity detection. Previous approaches to modeling group activity include cooccurrence stati ..."
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Cited by 25 (11 self)
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The aim is to model "activity" performed by a group of moving and interacting objects (which can be people or cars or different rigid components of the human body) and use the models for abnormal activity detection. Previous approaches to modeling group activity include cooccurrence statistics (individual and joint histograms) and Dynamic Bayesian Networks, neither of which is applicable when the number of interacting objects is large. We treat the objects as point objects (referred to as "landmarks") and propose to model their changing configuration as a moving and deforming "shape" (using Kendall's shape theory for discrete landmarks). A continuous state Hidden Markov Model (HMM) is defined for landmark shape dynamics in an activity. The configuration of landmarks at a given time forms the observation vector and the corresponding shape and the scaled Euclidean motion parameters form the hidden state vector. An abnormal activity is then defined as a change in the shape activity model, which could be slow or drastic and whose parameters are unknown. Results are shown on a real abnormal activity detection problem involving multiple moving objects.