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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 1137 (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 133 (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.
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 17 (6 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 9 (1 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 5 (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...
Wiener chaos and nonlinear filtering
 Appl. Math. Optim
"... Abstract. The paper discusses two algorithms for solving the Zakai equation in the timehomogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the CameronMartin version of the Wiener chaos expansion, so that the a ..."
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Cited by 2 (0 self)
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Abstract. The paper discusses two algorithms for solving the Zakai equation in the timehomogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the CameronMartin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For realtime applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. The paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noisecorrelated setting. The presentation includes the necessary background on the Wiener chaos
A Robust Particle Filter for State Estimation – with Convergence Results
"... Abstract — Particle filters are becoming increasingly important and useful for state estimation in nonlinear systems. Many filter versions have been suggested, and several results on convergence of filter properties have been reported. However, apparently a result on the convergence of the state est ..."
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Abstract — Particle filters are becoming increasingly important and useful for state estimation in nonlinear systems. Many filter versions have been suggested, and several results on convergence of filter properties have been reported. However, apparently a result on the convergence of the state estimate itself has been lacking. This contribution describes a general framework for particle filters for state estimation, as well as a robustified filter version. For this version a quite general convergence result is established. In particular, it is proved that the particle filter estimate convergences w.p.1 to the optimal estimate, as the number of particles tends to infinity. I.
A Forward Model of Optic Flow for Detecting External Forces
, 2007
"... Robot positioning is an important function of autonomous intelligent robots. However, the application of external forces to a robot can disrupt its normal operation and cause localisation errors. We present a novel approach for detecting external disturbances based on optic flow without the use of e ..."
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Robot positioning is an important function of autonomous intelligent robots. However, the application of external forces to a robot can disrupt its normal operation and cause localisation errors. We present a novel approach for detecting external disturbances based on optic flow without the use of egomotion information. Even though this research moderately validates the efficacy of the model we argue that its application is plausible to a large number of robotic systems.
AUTOMATIC CONTROL
, 2007
"... Technical reports from the Automatic Control group in Linköping are available from ..."
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Technical reports from the Automatic Control group in Linköping are available from