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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 1977 (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.
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 239 (9 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.
Limit theorems for weighted samples with applications to Sequential Monte Carlo Methods. eprint arXiv:math.ST/0507042
, 2005
"... In the last decade, sequential MonteCarlo methods (SMC) emerged as a key tool in computational statistics (see for instance Doucet et al. (2001), Liu (2001), Künsch (2001)). These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighte ..."
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Cited by 54 (14 self)
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In the last decade, sequential MonteCarlo methods (SMC) emerged as a key tool in computational statistics (see for instance Doucet et al. (2001), Liu (2001), Künsch (2001)). These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted population of particles. These particles and weights are generated recursively according to elementary transformations: mutation and selection. Examples of applications include the sequential MonteCarlo techniques to solve optimal nonlinear filtering problems in statespace models, molecular simulation, genetic optimization, etc. Despite many theoretical advances (see for instance Gilks and Berzuini (2001), Künsch (2003), Del Moral (2004), Chopin (2004)), the asymptotic property of these approximations remains of course a question of central interest. In this paper, we analyze sequential Monte Carlo methods from an asymptotic perspective, that is, we establish law of large numbers and invariance principle as the number of particles gets large. We introduce the concepts of weighted sample consistency and asymptotic normality, and derive conditions under which the mutation and the selection procedure used in the sequential MonteCarlo buildup preserve these properties. To illustrate our findings, we analyze SMC algorithms to approximate the filtering distribution in statespace models. We show how our techniques allow to relax restrictive technical conditions used in previously reported works and provide grounds to analyze more sophisticated sequential sampling strategies. Short title: Limit theorems for SMC. 1
A basic convergence result for particle filtering
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2007
"... The basic nonlinear ltering problem for dynamical systems is considered. Approximating the optimal lter estimate by particle lter methods has become perhaps the most common and useful method in recent years. Many variants of particle lters have been suggested, and there is an extensive literature o ..."
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Cited by 29 (8 self)
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The basic nonlinear ltering problem for dynamical systems is considered. Approximating the optimal lter estimate by particle lter methods has become perhaps the most common and useful method in recent years. Many variants of particle lters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still, a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to in nity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result.
Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems
 Ann. Appl. Prob
, 1996
"... In the paper we study interacting particle approximations of discrete time and measure valued dynamical systems. Such systems have arisen in such diverse scientific disciplines as physics and signal processing. We give conditions for the socalled particle density profiles to converge to the desired ..."
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Cited by 23 (7 self)
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In the paper we study interacting particle approximations of discrete time and measure valued dynamical systems. Such systems have arisen in such diverse scientific disciplines as physics and signal processing. We give conditions for the socalled particle density profiles to converge to the desired distribution when the number of particles is growing. The strength of our approach is that is applicable to a large class of measure valued dynamical system arising in engineering and particularly in nonlinear filtering problems. Our second objective is to use these results to solve numerically the nonlinear filtering equation. Examples arising in fluid mechanics are also given. 1 Introduction 1.1 Measure valued processes Let (E; fi(E)) be a locally compact and separable metric space, endowed with a Borel oefield, state space. Denote by P(E) be the space of all probability measures on E with the weak topology. The aim of this work is the design of a stochastic particle system approach fo...
A Uniform Convergence Theorem for the Numerical Solving of the Nonlinear Filtering Problem
 Journal of Applied Probability
, 1998
"... The filtering problem concerns the estimation of a stochastic process X from its noisy partial information Y . With the notable exception of the linearGaussian situation general optimal filters have no finitely recursive solution. The aim of this work is the design of a Monte Carlo particle system ..."
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Cited by 12 (2 self)
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The filtering problem concerns the estimation of a stochastic process X from its noisy partial information Y . With the notable exception of the linearGaussian situation general optimal filters have no finitely recursive solution. The aim of this work is the design of a Monte Carlo particle system approach to solve discrete time and non linear filtering problems. The main result is a uniform convergence Theorem. We introduce a concept of regularity and we give a simple ergodic condition on the signal semigroup for the Monte Carlo particle filter to converge in law and uniformly with respect to time to the optimal filter, yielding what seems to be the first uniform convergence result for a particle approximation of the non linear filtering equation. 1 Introduction The basic model for the general Non Linear Filtering problem consists of a time inhomogeneous Markov process X and a non linear observation Y with observation noise V . Namely, let (X; Y ) be the Markov process taking value...
On the Convergence and the Applications of the Generalized Simulated Annealing
 SIAM J. Control Optim
"... The convergence of the generalized simulated annealing with timeinhomogeneous communication cost functions is discussed. This study is based on the use of LogSobolev inequalities and semigroup techniques in the spirit of a previous article by one of the authors. We also propose a natural test set a ..."
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Cited by 9 (0 self)
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The convergence of the generalized simulated annealing with timeinhomogeneous communication cost functions is discussed. This study is based on the use of LogSobolev inequalities and semigroup techniques in the spirit of a previous article by one of the authors. We also propose a natural test set approach to study the global minima of the virtual energy. The second part of the paper is devoted to the application of these results. First we propose two general Markovian models of genetic algorithms and we give a simple proof of the convergence toward the global minima of the fitness function. Finally we introduce a stochastic algorithm which converges to the set of the global minima of a given mean cost optimization problem. Introduction Let E a finite state space and q an irreducible Markov kernel. The main purpose of this paper is to study the limiting behavior of a large class of timeinhomogeneous Markov processes controlled by two parameters (fl; fi) 2 R 2 + and associated to a f...
Nonasymptotic Error Bounds for Sequential MCMC
 Methods in Multimodal Settings., in preparation
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Private Communications
, 2001
"... 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. The problem of identifying nonlinear system models arise in various applications in control and signal ..."
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Cited by 5 (0 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. The problem of identifying nonlinear system models arise in various applications in control and signal processing. In this context, one of the most successful and popular stastical identification approaches is Particle Filtering, otherwise known as Sequential Monte Carlo (SMC) methods. As compared to Extended Kalman Filter and Gaussian Sum Filter, this approach is computationally reliable for identification of highly nonlinear systems in terms of accuracy, and, at the same time chance of failure in difficult circumstances decreases. The numerical integration techniques, on the other hand, are only feasible in lowdimensional