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66
On Sequential Monte Carlo Sampling Methods for Bayesian Filtering
 STATISTICS AND COMPUTING
, 2000
"... In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is develop ..."
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Cited by 1051 (76 self)
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In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses RaoBlackwellisation in order to take advantage of the analytic structure present in some important classes of statespace models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.
On sequential simulationbased methods for bayesian filtering
, 1998
"... Abstract. In this report, we present an overview of sequential simulationbased methods for Bayesian filtering of nonlinear and nonGaussian dynamic models. It includes in a general framework numerous methods proposed independently in various areas of science and proposes some original developments. ..."
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Cited by 251 (12 self)
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Abstract. In this report, we present an overview of sequential simulationbased methods for Bayesian filtering of nonlinear and nonGaussian dynamic models. It includes in a general framework numerous methods proposed independently in various areas of science and proposes some original developments.
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 211 (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.
Particle Filters for State Estimation of Jump Markov Linear Systems
, 2001
"... Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filter ..."
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Cited by 177 (15 self)
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Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixedlag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS. Computer
Estimating macroeconomic models: a likelihood approach
, 2006
"... This paper shows how particle filtering facilitates likelihoodbased inference in dynamic macroeconomic models. The economies can be nonlinear and/or nonnormal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing prefer ..."
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Cited by 102 (27 self)
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This paper shows how particle filtering facilitates likelihoodbased inference in dynamic macroeconomic models. The economies can be nonlinear and/or nonnormal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing preferences and technology, and to compare different economies. Both tasks can be implemented from either a classical or a Bayesian perspective. We illustrate the technique by estimating a business cycle model with investmentspecific technological change, preference shocks, and stochastic volatility.
Monte Carlo Filtering for MultiTarget Tracking and Data Association
 IEEE Transactions on Aerospace and Electronic Systems
, 2004
"... In this paper we present Monte Carlo methods for multitarget tracking and data association. The methods are applicable to general nonlinear and nonGaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data associat ..."
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Cited by 86 (5 self)
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In this paper we present Monte Carlo methods for multitarget tracking and data association. The methods are applicable to general nonlinear and nonGaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data association problem that arises due to unlabelled measurements in the presence of clutter, and the curse of dimensionality that arises due to the increased size of the statespace associated with multiple targets. We develop a number of algorithms to achieve this. The first, which we will refer to as the Monte Carlo Joint Probabilistic Data Association Filter (MCJPDAF), is a generalisation of the strategy proposed in [1], [2]. As is the case for the JPDAF, the distributions of interest are the marginal filtering distributions for each of the targets, but these are approximated with particles rather than Gaussians. We also develop two extensions to the standard particle filtering methodology for tracking multiple targets. The first, which we will refer to as the Sequential Sampling Particle Filter (SSPF), samples the individual targets sequentially by utilising a factorisation of the importance weights. The second, which we will refer to as the Independent Partition Particle Filter (IPPF), assumes the associations to be independent over the individual targets, leading to an efficient componentwise sampling strategy to construct new particles. We evaluate and compare the proposed methods on a challenging synthetic tracking problem.
Bayesian sequential inference for nonlinear multivariate diffusions
 Statistics and Computing
, 2006
"... In this paper, we adapt recently developed simulationbased sequential algorithms to the problem concerning the Bayesian analysis of discretely observed diffusion processes. The estimation framework involves the introduction of m −1 latent data points between every pair of observations. Sequential ..."
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Cited by 51 (6 self)
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In this paper, we adapt recently developed simulationbased sequential algorithms to the problem concerning the Bayesian analysis of discretely observed diffusion processes. The estimation framework involves the introduction of m −1 latent data points between every pair of observations. Sequential MCMC methods are then used to sample the posterior distribution of the latent data and the model parameters online. The method is applied to the estimation of parameters in a simple stochastic volatility model (SV) of the U.S. shortterm interest rate. We also provide a simulation study to validate our method, using synthetic data generated by the SV model with parameters calibrated to match weekly observations of the U.S. shortterm interest rate. 1
Tracking Through Singularities and Discontinuities By Random Sampling
 IN IEEE INTERNATIONAL CONFERENCE ON COMPUTER VISION
, 1999
"... Some issues in markerless tracking of human body motion are addressed. Extended Kalman filters have commonly been applied to kinematic variables, to combine predictions consistent with plausible motion, with the incoming stream of visual measurements. Kalman filtering is applicable only when the und ..."
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Cited by 51 (3 self)
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Some issues in markerless tracking of human body motion are addressed. Extended Kalman filters have commonly been applied to kinematic variables, to combine predictions consistent with plausible motion, with the incoming stream of visual measurements. Kalman filtering is applicable only when the underlying distribution is approximately Gaussian. Often, this assumption proves remarkably robust. There are two
Particle Methods for Bayesian Modelling and Enhancement of Speech Signals
, 2000
"... This paper applies timevarying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform online estimation ..."
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Cited by 49 (6 self)
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This paper applies timevarying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform online estimation of the clean speech and model parameters, and to determine the adequacy of the chosen statistical models. Ecient particle methods are developed to solve the optimal ltering and xedlag smoothing problems. The algorithms combine sequential importance sampling (SIS), a selection step and Markov chain Monte Carlo (MCMC) methods. They employ several variance reduction strategies to make the best use of the statistical structure of the model. It is also shown how model adequacy may be determined by combining the particle lter with frequentist methods. The modelling and enhancement performance of the models and estimation algorithms are evaluated in simulation studies on both synthetic and re...
Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation
, 2010
"... This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The nonGaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspe ..."
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Cited by 47 (10 self)
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This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The nonGaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these nonGaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in highdimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on secondorder moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and nonGaussian effects remain. They essentially originate in the nonlinear models and in the nonGaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are