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211
A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
- 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 ..."
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Cited by 2006 (2 self)
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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.
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have bee ..."
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Cited by 770 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
A Boosted Particle Filter: Multitarget Detection and Tracking
- In ECCV
, 2004
"... The problem of tracking a varying number of non-rigid objects has two major di#culties. First, the observation models and target distributions can be highly non-linear and non-Gaussian. Second, the presence of a large, varying number of objects creates complex interactions with overlap and ambig ..."
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Cited by 308 (7 self)
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The problem of tracking a varying number of non-rigid objects has two major di#culties. First, the observation models and target distributions can be highly non-linear and non-Gaussian. Second, the presence of a large, varying number of objects creates complex interactions with overlap and ambiguities. To surmount these di#culties, we introduce a vision system that is capable of learning, detecting and tracking the objects of interest. The system is demonstrated in the context of tracking hockey players using video sequences. Our approach combines the strengths of two successful algorithms: mixture particle filters and Adaboost. The mixture particle filter [17] is ideally suited to multi-target tracking as it assigns a mixture component to each player. The crucial design issues in mixture particle filters are the choice of the proposal distribution and the treatment of objects leaving and entering the scene.
Nonparametric Belief Propagation
- IN CVPR
, 2002
"... In applications of graphical models arising in fields such as computer vision, the hidden variables of interest are most naturally specified by continuous, non--Gaussian distributions. However, due to the limitations of existing inf#6F6F3 algorithms, it is of#]k necessary tof#3# coarse, ..."
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Cited by 279 (25 self)
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In applications of graphical models arising in fields such as computer vision, the hidden variables of interest are most naturally specified by continuous, non--Gaussian distributions. However, due to the limitations of existing inf#6F6F3 algorithms, it is of#]k necessary tof#3# coarse, discrete approximations to such models. In this paper, we develop a nonparametric belief propagation (NBP) algorithm, which uses stochastic methods to propagate kernel--based approximations to the true continuous messages. Each NBP message update is based on an efficient sampling procedure which can accomodate an extremely broad class of potentialf#l3]k[[z3 allowing easy adaptation to new application areas. We validate our method using comparisons to continuous BP for Gaussian networks, and an application to the stereo vision problem.
FastSLAM 2.0: An improved particle filtering algorithm for simultaneous localization and mapping that provably converges
"... In [15], Montemerlo et al. proposed an algorithm called FastSLAM as an efficient and robust solution to the simultaneous localization and mapping problem. This paper describes a modified version of FastSLAM that overcomes important deficiencies of the original algorithm. We prove convergence of this ..."
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Cited by 225 (7 self)
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In [15], Montemerlo et al. proposed an algorithm called FastSLAM as an efficient and robust solution to the simultaneous localization and mapping problem. This paper describes a modified version of FastSLAM that overcomes important deficiencies of the original algorithm. We prove convergence of this new algorithm for linear SLAM problems and provide real-world experimental results that illustrate an order of magnitude improvement in accuracy over the original FastSLAM algorithm. 1
A tutorial on particle filtering and smoothing: fifteen years later
- 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 ..."
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Cited by 214 (15 self)
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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.
Improved techniques for grid mapping with rao-blackwellized particle filters
- IEEE Transactions on Robotics
, 2007
"... Abstract — Recently, Rao-Blackwellized particle filters have been introduced as an effective means to solve the simultaneous localization and mapping problem. This approach uses a particle filter in which each particle carries an individual map of the environment. Accordingly, a key question is how ..."
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Cited by 179 (20 self)
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Abstract — Recently, Rao-Blackwellized particle filters have been introduced as an effective means to solve the simultaneous localization and mapping problem. This approach uses a particle filter in which each particle carries an individual map of the environment. Accordingly, a key question is how to reduce the number of particles. In this paper, we present adaptive techniques for reducing this number in a Rao-Blackwellized particle filter for learning grid maps. We propose an approach to compute an accurate proposal distribution taking into account not only the movement of the robot but also the most recent observation. This drastically decreases the uncertainty about the robot’s pose in the prediction step of the filter. Furthermore, we present an approach to selectively carry out resampling operations which seriously reduces the problem of particle depletion. Experimental results carried out with real mobile robots in large-scale indoor as well as in outdoor environments illustrate the advantages of our methods over previous approaches. Index Terms — SLAM, Rao-Blackwellized particle filter, adaptive resampling, motion-model, improved proposal
The Unscented Kalman Filter for nonlinear estimation
, 2000
"... The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system, estimating parameters for nonlinear system identification (e.g., learning the weights of a ne ..."
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Cited by 171 (4 self)
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The Extended Kalman Filter (EKF) has become a standard technique used in a number of nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system, estimating parameters for nonlinear system identification (e.g., learning the weights of a neural network), and dual estimation (e.g., the Expectation Maximization (EM) algorithm) where both states and parameters are estimated simultaneously. This paper points out the flaws in using the EKF, and introduces an improvement, the Unscented Kalman Filter (UKF), proposed by Julier and Uhlman [5]. A central and vital operation performed in the Kalman Filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF, the state distribution is approximated
Improving grid-based slam with rao-blackwellized particle filters by adaptive proposals and selective resampling
- In Proc. of the IEEE Int. Conf. on Robotics & Automation (ICRA
, 2005
"... Abstract — Recently Rao-Blackwellized particle filters have been introduced as effective means to solve the simultaneous localization and mapping (SLAM) problem. This approach uses a particle filter in which each particle carries an individual map of the environment. Accordingly, a key question is h ..."
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Cited by 152 (22 self)
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Abstract — Recently Rao-Blackwellized particle filters have been introduced as effective means to solve the simultaneous localization and mapping (SLAM) problem. This approach uses a particle filter in which each particle carries an individual map of the environment. Accordingly, a key question is how to reduce the number of particles. In this paper we present adaptive techniques to reduce the number of particles in a Rao-Blackwellized particle filter for learning grid maps. We propose an approach to compute an accurate proposal distribution taking into account not only the movement of the robot but also the most recent observation. This drastically decrease the uncertainty about the robot’s pose in the prediction step of the filter. Furthermore, we present an approach to selectively carry out re-sampling operations which seriously reduces the problem of particle depletion. Experimental results carried out with mobile robots in large-scale indoor as well as in outdoor environments illustrate the advantages of our methods over previous approaches. I.
