Results 1 - 10 of 243

A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

by M. Sanjeev Arulampalam, Simon Maskell, Neil Gordon - IEEE TRANSACTIONS ON SIGNAL PROCESSING , 2002
"... Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view o ..."
Abstract - Cited by 2006 (2 self) - Add to MetaCart
Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line 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/non-Gaussian 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 state-space 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

by Pierre Del Moral, Arnaud Doucet , 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 defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal ..."
Abstract - Cited by 303 (44 self) - Add to MetaCart
In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial 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 Feynman-Kac flow in distribution space. One interpretation of the Feynman-Kac flow corresponds to a nonlinear Markov kernel admitting a specified invariant distribution and is a natural nonlinear extension of the standard Metropolis-Hastings algorithm. Many theoretical results have already been established for such flows and their particle approximations. We demonstrate the use of these algorithms through simulation.

Particle Filters for Positioning, Navigation and Tracking

by Fredrik Gustafsson, Fredrik Gunnarsson, Niclas Bergman, Urban Forssell, Jonas Jansson, Rickard Karlsson, Per-Johan Nordlund , 2002
"... A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious with the part ..."
Abstract - Cited by 219 (23 self) - Add to MetaCart
A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low-dimensional. This is of utmost importance for highperformance real-time applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter based algorithms. Here the use of non-linear models and non-Gaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map, and a car's horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable to satellite navigation (as GPS), but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

A tutorial on particle filtering and smoothing: fifteen years later

by Arnaud Doucet, Adam M. Johansen - OXFORD HANDBOOK OF NONLINEAR FILTERING , 2011
"... Optimal estimation problems for non-linear non-Gaussian state-space 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 ..."
Abstract - Cited by 214 (15 self) - Add to MetaCart
Optimal estimation problems for non-linear non-Gaussian state-space 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, up-to-date survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
(Show Context)

The Unscented Particle Filter

by Rudolph van der Merwe, Arnaud Doucet, Nando de Freitas, Eric Wan , 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 ..."
Abstract - Cited by 211 (8 self) - Add to MetaCart
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.

Monte Carlo smoothing for non-linear time series

by Simon J. Godsill, Arnaud Doucet, Mike West - JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION , 2004
"... We develop methods for performing smoothing computations in general state-space 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 ..."
Abstract - Cited by 153 (16 self) - Add to MetaCart
We develop methods for performing smoothing computations in general state-space 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 backward-smoothing procedure which can be viewed as the non-linear, non-Gaussian counterpart of standard Kalman filter-based simulation smoothers in the linear Gaussian case. Convergence in the mean-squared 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 time-varying 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.
(Show Context)

Markov Chain Monte Carlo Data Association for Multi-Target Tracking Univ

by Songhwai Oh, Stuart Russell, Shankar Sastry, Monte Carlo , 2008
"... data association (MCMCDA) for solving data association prob-lems arising in multi-target tracking in a cluttered environment. When the number of targets is fixed, the single-scan version of MCMCDA approximates joint probabilistic data association (JPDA). Although the exact computation of association ..."
Abstract - Cited by 151 (25 self) - Add to MetaCart
data association (MCMCDA) for solving data association prob-lems arising in multi-target tracking in a cluttered environment. When the number of targets is fixed, the single-scan version of MCMCDA approximates joint probabilistic data association (JPDA). Although the exact computation of association probabili-ties in JPDA is NP-hard, we prove that the single-scan MCMCDA algorithm provides a fully polynomial randomized approximation scheme for JPDA. For general multi-target tracking problems, in which unknown numbers of targets appear and disappear at random times, we present a multi-scan MCMCDA algorithm that approximates the optimal Bayesian filter. We also present exten-sive simulation studies supporting theoretical results in this paper. Our simulation results also show that MCMCDA outperforms multiple hypothesis tracking (MHT) by a significant margin in terms of accuracy and efficiency under extreme conditions, such as a large number of targets in a dense environment, low detection probabilities, and high false alarm rates. Index Terms—Joint probabilistic data association (JPDA), Markov chain Monte Carlo data association (MCMCDA), mul-tiple hypothesis tracking (MHT). I.
(Show Context)

Central limit theorem for sequential monte carlo methods and its application to bayesian inference

by Nicolas Chopin - 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 ..."
Abstract - Cited by 142 (4 self) - Add to MetaCart
“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 resample-move 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

A Sequential Particle Filter Method for Static Models

by Nicolas Chopin , 2000
"... Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes, in order to consistently explore a sequence of multiple distributions of interest. The purpose of this article is to show that such methods can also offer an efficient estimation tool ..."
Abstract - Cited by 109 (4 self) - Add to MetaCart
Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes, in order to consistently explore a sequence of multiple distributions of interest. The purpose of this article is to show that such methods can also offer an efficient estimation tool in "static" setups; in this case, π(θ|y_1, ..., y_N) is the only posterior distribution of interest but the preliminary exploration of partial posteriors π(θ|y_1, ..., y_N) (n < N) makes computing time savings possible. A complete "black-box" algorithm is proposed for independent or Markov models. Our method is shown to possibly challenge other common estimation procedures, in terms of robustness and execution time, especially when the sample size is important. Two classes of examples are discussed and illustrated by numerical results: mixture models and discrete generalized linear models.

Tracking Multiple Objects with Particle Filtering

by C. Hue, J. -p. Le Cadre, P. Prez , 2000
"... We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the ..."
Abstract - Cited by 100 (4 self) - Add to MetaCart
We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies.
(Show Context)