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58
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.
Statistical algorithms for models in state space using SstPack 2.2
 ECONOMETRICS JOURNAL (1999), VOLUME 2, PP. 113–166.
, 1999
"... This paper discusses and documents the algorithms of SsfPack 2.2. SsfPack is a suite of C routines for carrying out computations involving the statistical analysis of univariate and multivariate models in state space form. The emphasis is on documenting the link we have made to the Ox computing en ..."
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Cited by 201 (34 self)
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This paper discusses and documents the algorithms of SsfPack 2.2. SsfPack is a suite of C routines for carrying out computations involving the statistical analysis of univariate and multivariate models in state space form. The emphasis is on documenting the link we have made to the Ox computing environment. SsfPack allows for a full range of different state space forms: from a simple timeinvariant model to a complicated timevarying model. Functions can be used which put standard models such as ARMA and cubic spline models in state space form. Basic functions are available for filtering, moment smoothing and simulation smoothing. Readytouse functions are provided for standard tasks such as likelihood evaluation, forecasting and signal extraction. We show that SsfPack can be easily used for implementing, fitting and analysing Gaussian models relevant to many areas of econometrics and statistics. Some Gaussian illustrations are given.
proposal distributions: Object tracking using unscented particle filter
 in Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Kauai
, 2001
"... Tracking objects involves the modeling of nonlinear nonGaussian systems. On one hand, variants of Kalman filters are limited by their Gaussian assumptions. On the other hand, conventional particle filter, e.g., CONDENSATION, uses transition prior as the proposal distribution. The transition prior ..."
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Cited by 96 (3 self)
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Tracking objects involves the modeling of nonlinear nonGaussian systems. On one hand, variants of Kalman filters are limited by their Gaussian assumptions. On the other hand, conventional particle filter, e.g., CONDENSATION, uses transition prior as the proposal distribution. The transition prior does not take into account current observation data, and many particles can therefore be wasted in low likelihood area. To overcome these difficulties, unscented particle filter (UPF) has recently been proposed in the field of filtering theory. In this paper, we introduce the UPF framework into audio and visual tracking. The UPF uses the unscented Kalman filter to generate sophisticated proposal distributions that seamlessly integrate the current observation, thus greatly improving the tracking performance. To evaluate the efficacy of the UPF framework, we apply it in two realworld tracking applications. One is the audiobased speaker localization, and the other is the visionbased human tracking. The experimental results are compared against those of the widely used CONDENSATION approach and have demonstrated superior tracking performance. 1.
Maximum Likelihood For Blind Separation And Deconvolution Of Noisy Signals Using Mixture Models
, 1997
"... In this paper, an approximate maximum likelihood method for blind source separation and deconvolution of noisy signal is proposed. This technique relies upon a data augmentation scheme, where the (unobserved) input are viewed as the missing data. In the technique described in this contribution, the ..."
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Cited by 88 (3 self)
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In this paper, an approximate maximum likelihood method for blind source separation and deconvolution of noisy signal is proposed. This technique relies upon a data augmentation scheme, where the (unobserved) input are viewed as the missing data. In the technique described in this contribution, the input signal distribution is modeled by a mixture of Gaussian distributions, enabling the use of explicit formula for computing the posterior density and conditional expectation and thus avoiding MonteCarlo integrations. Because this technique is able to capture some salient features of the input signal distribution, it performs generally much better than thirdorder or fourthorder cumulant based techniques. 1. INTRODUCTION This contribution is devoted to blind source separation and blind deconvolution. In these models, the observed data fx(t)g (a m \Theta 1 vector) is assumed to be given by x(t) = L X k=0 A(k)s(t \Gamma k) + v(t) (1) where fs(t)g (n \Theta 1) is the (unobserved) inp...
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.
On the Mechanics of Forming and Estimating Dynamic Linear Economies
"... This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to sever ..."
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Cited by 86 (19 self)
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This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to several example economies.
Practical Filtering with Sequential Parameter Learning
, 2003
"... In this paper we develop a general simulationbased approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering ..."
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Cited by 40 (8 self)
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In this paper we develop a general simulationbased approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering distribution as a mixture of lagsmoothing distributions and to implement this sequentially. Our approach has a number of advantages over current methodologies. First, it allows for sequential parmeter learning where sequential importance sampling approaches have difficulties. Second
Likelihoodbased analysis for dynamic factor models
, 2008
"... We present new results for the likelihoodbased analysis of the dynamic factor model that possibly includes intercepts and explanatory variables. The latent factors are modeled by stochastic processes. The idiosyncratic disturbances are specified as autoregressive processes with mutually correlated ..."
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Cited by 38 (7 self)
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We present new results for the likelihoodbased analysis of the dynamic factor model that possibly includes intercepts and explanatory variables. The latent factors are modeled by stochastic processes. The idiosyncratic disturbances are specified as autoregressive processes with mutually correlated innovations. The new results lead to computationally efficient procedures for the estimation of the factors and parameter estimation by (quasi)maximum likelihood. An illustration is provided for the analysis of a large panel of macroeconomic time series
A SemiStructural Method to Estimate Potential Output: Combining Economic Theory with a TimeSeries Filter (The Bank of Canada’s New Quarterly Projection Model Part 4),” Bank of Canada
, 1996
"... The views expressed in this report are solely those of the author. No responsibility for them should be attributed to the Bank of Canada. ISSN 07137931 ISBN 0662251016 Printed in Canada on recycled paperACKNOWLEDGMENTS iii The work on this project has been a cooperative effort. The credit for t ..."
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Cited by 34 (0 self)
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The views expressed in this report are solely those of the author. No responsibility for them should be attributed to the Bank of Canada. ISSN 07137931 ISBN 0662251016 Printed in Canada on recycled paperACKNOWLEDGMENTS iii The work on this project has been a cooperative effort. The credit for the development of the extended multivariate filter rightly belongs to Doug Laxton, David Rose and Jean Xie, with considerable input from Bob Tetlow and the programming skills of Hope Pioro. Both Laxton and Xie left the Research Department after the initial development work was completed, at which time I became involved in the project. The implementation and documentation were completed by me.