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26
A Bayesian Framework for Multicue 3D Object Tracking
 In Proceedings of European Conference on Computer Vision
, 2004
"... This paper presents a Bayesian framework for multicue 3D object tracking of deformable objects. The proposed spatiotemporal object representation involves a set of distinct linear subspace models or Dynamic Point Distribution Models (DPDMs), which can deal with both continuous and discontinuou ..."
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Cited by 40 (1 self)
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This paper presents a Bayesian framework for multicue 3D object tracking of deformable objects. The proposed spatiotemporal object representation involves a set of distinct linear subspace models or Dynamic Point Distribution Models (DPDMs), which can deal with both continuous and discontinuous appearance changes; the representation is learned fully automatically from training data. The representation is enriched with texture information by means of intensity histograms, which are compared using the Bhattacharyya coe#cient. Direct 3D measurement is furthermore provided by a stereo system.
A Survey of Maneuvering Target Tracking  Part V: MultipleModel Methods
, 2003
"... ... without addressing the socalled measurementorigin uncertainty. Part I and Part II deal with target motion models. Part III covers measurement models and associated techniques. Part IV is concerned with tracking techniques that are based on decisions regarding target maneuvers. This part surv ..."
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Cited by 20 (0 self)
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... without addressing the socalled measurementorigin uncertainty. Part I and Part II deal with target motion models. Part III covers measurement models and associated techniques. Part IV is concerned with tracking techniques that are based on decisions regarding target maneuvers. This part surveys the multiplemodel methodsthe use of multiple models (and filters) simultaneouslywhich is the prevailing approach to maneuvering target tracking in the recent years. The survey is presented in a structured way, centered around three generations of algorithms: autonomous, cooperating, and variable structure. It emphasizes on the underpinning of each algorithm and covers various issues in algorithm design, application, and performance.
Fast Nonlinear Filter for ContinuousDiscrete Time Multiple Models
 PROC. 35TH IEEE CONF. ON DECISION AND CONTROL
, 1998
"... A fast algorithm is proposed for computing on line the optimal nonlinear filter in the continuousdiscrete time, multiple model setting. Using the finite element approximation on a spatial grid with N ..."
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Cited by 6 (2 self)
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A fast algorithm is proposed for computing on line the optimal nonlinear filter in the continuousdiscrete time, multiple model setting. Using the finite element approximation on a spatial grid with N
Model robustness of finite state nonlinear filtering over the infinite time horizon
 Ann. Appl. Probab
"... Abstract. We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converge ..."
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Cited by 5 (5 self)
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Abstract. We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converges to zero uniformly over the infinite time interval as the misspecified model converges to the true model, provided the signal obeys a mixing condition. The filtering error is controlled through the exponential decay of the derivative of the nonlinear filter with respect to its initial condition. We allow simultaneously for misspecification of the initial condition, of the transition rates of the signal, and of the observation function. The first two cases are treated by relatively elementary means, while the latter case requires the use of Skorokhod integrals and tools of anticipative stochastic calculus. 1.
Modelbased clustering with Hidden Markov Models and its application to financial timeseries data
, 2002
"... We have developed a method to partition a set of data into clusters by use of Hidden Markov Models. Given a number of clusters, each of which is represented by one Hidden Markov Model, an iterative procedure finds the combination of cluster models and an assignment of data points to cluster models w ..."
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Cited by 5 (0 self)
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We have developed a method to partition a set of data into clusters by use of Hidden Markov Models. Given a number of clusters, each of which is represented by one Hidden Markov Model, an iterative procedure finds the combination of cluster models and an assignment of data points to cluster models which maximizes the joint likelihood of the clustering. To reflect the
Rainflow Cycles for Switching Processes with Markov Structure
, 1998
"... The concept of rainflow cycles is often used in fatigue of materials for analysing load processes, which in most realistic cases should be modelled stochastically. Methods are developed for computation of the rainflow matrix for random loads that are changing properties over time due to changes of t ..."
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Cited by 4 (1 self)
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The concept of rainflow cycles is often used in fatigue of materials for analysing load processes, which in most realistic cases should be modelled stochastically. Methods are developed for computation of the rainflow matrix for random loads that are changing properties over time due to changes of the system dynamics. For a random vehicle load the change of properties could reflect dioeerent driving conditions. Mathematically, the random load is modelled by a switching process with Markov regime, i.e. the random load changes properties according to a hidden (not observed) Markov chain. An algorithm is developed for a switching process where each part of the load is modelled by a Markov chain. As only the local extremes are of importance for rainflow analysis, another approach is to model the sequence of turning points by a Markov chain. The main result of this paper is an algorithm for computation of the rainflow matrix for a switching process where each part is described by a Markov c...
MAXIMUM LIKELIHOOD ESTIMATION OF HIDDEN MARKOV PROCESSES
"... We consider the process dYt = ut dt + dWt, where u is a process not necessarily adapted to F Y (the filtration generated by the process Y) and W is a Brownian motion. We obtain a general representation for the likelihood ratio of the law of the Y process relative to Brownian measure. This representa ..."
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Cited by 4 (0 self)
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We consider the process dYt = ut dt + dWt, where u is a process not necessarily adapted to F Y (the filtration generated by the process Y) and W is a Brownian motion. We obtain a general representation for the likelihood ratio of the law of the Y process relative to Brownian measure. This representation involves only one basic filter (expectation of u conditional on observed process Y). This generalizes the result of Kailath and Zakai [Ann. Math. Statist. 42 (1971) 130–140] where it is assumed that the process u is adapted to F Y. In particular, we consider the model in which u is a functional of Y and of a random element X which is independent of the Brownian motion W. For example, X could be a diffusion or a Markov chain. This result can be applied to the estimation of an unknown multidimensional parameter θ appearing in the dynamics of the process u based on continuous observation of Y on the time interval [0,T]. For a specific hidden diffusion financial model in which u is an unobserved meanreverting diffusion, we give an explicit form for the likelihood function of θ. For this model we also develop a computationally explicit E–M algorithm for the estimation of θ. In contrast to the likelihood ratio, the algorithm involves evaluation of a number of filtered integrals in addition to the basic filter. 1. Introduction. Let (�,F,P), {Ft,t ≤ T
Recursive filters for partially observable finite Markov chains
 J. Appl. Probab
, 2005
"... In this note, we consider discretetime finite Markov Chains and assume that they are only partly observed. We obtain finitedimensional normalized filters for basic statistics associated with such processes. Recursive equations for these filters are derived by means of simple computations involving ..."
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Cited by 3 (3 self)
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In this note, we consider discretetime finite Markov Chains and assume that they are only partly observed. We obtain finitedimensional normalized filters for basic statistics associated with such processes. Recursive equations for these filters are derived by means of simple computations involving conditional expectations. An application to the estimation of parameters for the socalled discretetime Batch Markovian Arrival Processes is outlined.
Hidden Markov model segmentation of hydrological and enviromental time series
, 2002
"... Motivated by Hubert's segmentation procedure [16, 17], we discuss the application of hidden Markov models (HMM) to the segmentation of hydrological and enviromental time series. We use a HMM algorithm which segments time series of several hundred terms in a few seconds and is computationally feas ..."
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Cited by 2 (0 self)
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Motivated by Hubert's segmentation procedure [16, 17], we discuss the application of hidden Markov models (HMM) to the segmentation of hydrological and enviromental time series. We use a HMM algorithm which segments time series of several hundred terms in a few seconds and is computationally feasible for even longer time series. The segmentation algorithm computes the Maximum Likelihood segmentation by use of an expectation / maximization iteration. We rigorously prove algorithm convergence and use numerical experiments, involving temperature and river discharge time series, to show that the algorithm usually converges to the globally optimal segmentation. The relation of the proposed algorithm to Hubert's segmentation procedure is also discussed.