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35
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 53 (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 43 (1 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.
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 8 (1 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
Markov Switching Models for GDP Growth in a Small Open Economy: The New Zealand Experience
, 2004
"... This paper fits Markov switching models to quarterly New Zealand aggregate GDP growth rates for the period 1978:1 to 2003:2 in order to analyse changes in mean and volatility over time. The models considered are drawn from a simple class of parsimonious, four state, Markov switching models which enc ..."
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Cited by 6 (0 self)
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This paper fits Markov switching models to quarterly New Zealand aggregate GDP growth rates for the period 1978:1 to 2003:2 in order to analyse changes in mean and volatility over time. The models considered are drawn from a simple class of parsimonious, four state, Markov switching models which encompass a wide range of stationary time series behaviour from linear AR(1) models to nonlinear models with persistent cycles and outliers. An overall objective is to use the models to help understand and identify changes in the historical growth performance of New Zealand's small open economy, particularly pre and post wide ranging economic reforms. Conclusions to emerge are that, in contrast to the 1980s, New Zealand GDP growth experienced an unusually long period of time in high growth and low volatility regimes since the early 1990s. In addition, New Zealand does not appear to have experienced the oneoff drop in volatility in the early 1980's that has been commonly reported for other countries.
Fast nonlinear filter for continuousdiscrete time multiple models
 Proceeding of the 35th IEEE Conference on Decision and Control
, 1997
"... 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 points and performing part of the computations off line, the online complexity of the algorithm is ..."
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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 points and performing part of the computations off line, the online complexity of the algorithm is shown to be O(N) for all dimensions of the state process. The error of the approximation is also studied. Key words: finite element approximation, multiple model filtering, optimal filter.
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.
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 5 (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
Robust output feedback stabilization via risksensitive control
, 2002
"... We consider a problem of robust linear quadratic Gaussian (LQG) control for discretetime stochastic uncertain systems with partial state measurements. For a finitehorizon case, the problem was recently introduced by Petersen et al. (IEEE Trans. Automat. Control 45 ..."
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Cited by 4 (4 self)
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We consider a problem of robust linear quadratic Gaussian (LQG) control for discretetime stochastic uncertain systems with partial state measurements. For a finitehorizon case, the problem was recently introduced by Petersen et al. (IEEE Trans. Automat. Control 45
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...