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141
A tutorial on particle filters for online nonlinear/nonGaussian Bayesian tracking
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2002
"... Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and nonGaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data online as it arrives, both from the point of view o ..."
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Cited by 1159 (2 self)
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Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and nonGaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data online as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/nonGaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or “particle”) representations of probability densities, which can be applied to any statespace model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.
Sequential Monte Carlo Samplers
, 2002
"... In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal ..."
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Cited by 147 (25 self)
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In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal which is a distribution of interest. To sample from these distributions, we use sequential Monte Carlo methods. We show that these methods can be interpreted as interacting particle approximations of a nonlinear FeynmanKac ow in distribution space. One interpretation of the FeynmanKac ow corresponds to a nonlinear Markov kernel admitting a speci ed invariant distribution and is a natural nonlinear extension of the standard MetropolisHastings algorithm. Many theoretical results have already been established for such ows and their particle approximations. We demonstrate the use of these algorithms through simulation.
Convergence of Sequential Monte Carlo Methods
 SEQUENTIAL MONTE CARLO METHODS IN PRACTICE
, 2000
"... Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data arise in many applications in statistics and related fields. Recently, a large number of algorithms and applications based on sequential Monte Carlo methods (also known as particle filter ..."
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Cited by 143 (11 self)
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Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data arise in many applications in statistics and related fields. Recently, a large number of algorithms and applications based on sequential Monte Carlo methods (also known as particle filtering methods) have appeared in the literature to solve this class of problems; see (Doucet, de Freitas & Gordon, 2001) for a survey. However, few of these methods have been proved to converge rigorously. The purpose of this paper is to address this issue. We present a general sequential Monte Carlo (SMC) method which includes most of the important features present in current SMC methods. This method generalizes and encompasses many recent algorithms. Under mild regularity conditions, we obtain rigorous convergence results for this general SMC method and therefore give theoretical backing for the validity of all the algorithms that can be obtained as particular cases of it.
A Survey of Convergence Results on Particle Filtering Methods for Practitioners
, 2002
"... Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closedform expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the o ..."
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Cited by 139 (4 self)
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Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closedform expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to solve the optimal filtering problem numerically. The posterior distribution of the state is approximated by a large set of Diracdelta masses (samples/particles) that evolve randomly in time according to the dynamics of the model and the observations. The particles are interacting; thus, classical limit theorems relying on statistically independent samples do not apply. In this paper, our aim is to present a survey of recent convergence results on this class of methods to make them accessible to practitioners.
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 121 (10 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
Adapting the Sample Size in Particle Filters Through KLDSampling
 International Journal of Robotics Research
, 2003
"... Over the last years, particle filters have been applied with great success to a variety of state estimation problems. In this paper we present a statistical approach to increasing the efficiency of particle filters by adapting the size of sample sets during the estimation process. ..."
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Cited by 97 (8 self)
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Over the last years, particle filters have been applied with great success to a variety of state estimation problems. In this paper we present a statistical approach to increasing the efficiency of particle filters by adapting the size of sample sets during the estimation process.
Monte Carlo smoothing for nonlinear time series
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2004
"... We develop methods for performing smoothing computations in general statespace models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are pr ..."
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Cited by 94 (14 self)
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We develop methods for performing smoothing computations in general statespace models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are presented for generation of sample realizations of historical state sequences. This is carried out in a forwardfiltering backwardsmoothing procedure which can be viewed as the nonlinear, nonGaussian counterpart of standard Kalman filterbased simulation smoothers in the linear Gaussian case. Convergence in the meansquared error sense of the smoothed trajectories is proved, showing the validity of our proposed method. The methods are tested in a substantial application for the processing of speech signals represented by a timevarying autoregression and parameterised in terms of timevarying partial correlation coe#cients, comparing the results of our algorithm with those from a simple smoother based upon the filtered trajectories.
A tutorial on particle filtering and smoothing: fifteen years later
 OXFORD HANDBOOK OF NONLINEAR FILTERING
, 2011
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. r ..."
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Cited by 72 (9 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
Central limit theorem for sequential monte carlo methods and its application to bayesian inference
 Ann. Statist
"... “particle filters, ” refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (πt). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result ..."
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Cited by 64 (2 self)
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“particle filters, ” refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (πt). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result holds under minimal assumptions on the distributions πt, and applies in a general framework which encompasses most of the sequential Monte Carlo methods that have been considered in the literature, including the resamplemove algorithm of Gilks and Berzuini [J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001) 127–146] and the residual resampling scheme. The corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter. We study, in particular, in some typical examples of Bayesian applications, whether and at which rate these asymptotic variances diverge in time, in order to assess the long term reliability of the considered algorithm. 1. Introduction. Sequential Monte Carlo methods form an emerging