Showing papers on "Particle filter published in 2001"

Sequential Monte Carlo methods in practice

Abstract: Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

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

Abstract: 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.

Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks.

Abstract: Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity. They have appeared in several fields under such names as "condensation", "sequential Monte Carlo" and "survival of the fittest". In this paper, we show how we can exploit the structure of the DBN to increase the efficiency of particle filtering, using a technique known as Rao-Blackwellisation. Essentially, this samples some of the variables, and marginalizes out the rest exactly, using the Kalman filter, HMM filter, junction tree algorithm, or any other finite dimensional optimal filter. We show that Rao-Blackwellised particle filters (RBPFs) lead to more accurate estimates than standard PFs. We demonstrate RBPFs on two problems, namely non-stationary online regression with radial basis function networks and robot localization and map building. We also discuss other potential application areas and provide references to some finite dimensional optimal filters.

Following a moving target—Monte Carlo inference for dynamic Bayesian models

Abstract: Markov chain Monte Carlo (MCMC) sampling is a numerically intensive simulation technique which has greatly improved the practicality of Bayesian inference and prediction. However, MCMC sampling is too slow to be of practical use in problems involving a large number of posterior (target) distributions, as in dynamic modelling and predictive model selection. Alternative simulation techniques for tracking moving target distributions, known as particle filters, which combine importance sampling, importance resampling and MCMC sampling, tend to suffer from a progressive degeneration as the target sequence evolves. We propose a new technique, based on these same simulation methodologies, which does not suffer from this progressive degeneration.

Particle filters for state estimation of jump Markov linear systems

Abstract: 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 simulation-based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed-lag 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 simulations are carried out to evaluate the performance of the proposed algorithms. The problems of on-line deconvolution of impulsive processes and of tracking a maneuvering target are considered. It is shown that our algorithms outperform the current methods.

BraMBLe: a Bayesian multiple-blob tracker

Abstract: Blob trackers have become increasingly powerful in recent years largely due to the adoption of statistical appearance models which allow effective background subtraction and robust tracking of deforming foreground objects. It has been standard, however, to treat background and foreground modelling as separate processes-background subtraction is followed by blob detection and tracking-which prevents a principled computation of image likelihoods. This paper presents two theoretical advances which address this limitation and lead to a robust multiple-person tracking system suitable for single-camera real-time surveillance applications. The first innovation is a multi-blob likelihood function which assigns directly comparable likelihoods to hypotheses containing different numbers of objects. This likelihood function has a rigorous mathematical basis: it is adapted from the theory of Bayesian correlation, but uses the assumption of a static camera to create a more specific background model while retaining a unified approach to background and foreground modelling. Second we introduce a Bayesian filter for tracking multiple objects when the number of objects present is unknown and varies over time. We show how a particle filter can be used to perform joint inference on both the number of objects present and their configurations. Finally we demonstrate that our system runs comfortably in real time on a modest workstation when the number of blobs in the scene is small.

Improving Regularised Particle Filters

Abstract: The optimal filter computes the posterior probability distribution of the state in a dynamical system, given noisy measurements, by iterative application of prediction steps according to the dynamics of the state, and correction steps taking the measurements into account. A new class of approximate nonlinear filter has been recently proposed, the idea being to produce a sample of independent random variables, called a particle system, (approximately) distributed according to this posterior probability distribution. The method is very easy to implement, even in high-dimensional problems, since it is sufficient in principle to simulate independent sample paths of the hidden dynamical system.

Tracking multiple moving targets with a mobile robot using particle filters and statistical data association

Abstract: One of the goals in the field of mobile robotics is the development of mobile platforms which operate in populated environments and offer various services to humans. For many tasks it is highly desirable that a robot can determine the positions of the humans in its surrounding. In this paper we present a method for tracking multiple moving objects with a mobile robot. We introduce a sample-based variant of joint probabilistic data association filters to track features originating from individual objects and to solve the correspondence problem between the detected features and the filters. In contrast to standard methods, occlusions are handled explicitly during data association. The technique has been implemented and tested on a real robot. Experiments carried out in a typical office environment show that the method is able to track multiple persons even when the trajectories of two people are crossing each other.

Particle Filters for Mobile Robot Localization

Abstract: This chapter investigates the utility of particle filters in the context of mobile robotics. In particular, we report results of applying particle filters to the problem of mobile robot localization, which is the problem of estimating a robot’s pose relative to a map of its environment. The localization problem is a key one in mobile robotics, because it plays a fundamental role in various successful mobile robot systems; see e.g., (Cox and Wilfong 1990, Fukuda, Ito, Oota, Arai, Abe, Tanake and Tanaka 1993, Hinkel and Knieriemen 1988, Leonard, Durrant-Whyte and Cox 1992, Rencken 1993, Simmons, Goodwin, Haigh, Koenig and O’Sullivan 1997, Weis, Wetzler and von Puttkamer 1994) and various chapters in (Borenstein, Everett and Feng 1996) and (Kortenkamp, Bonasso and Murphy 1998). Occasionally, it has been referred to as “the most fundamental problem to providing a mobile robot with autonomous capabilities” (Cox 1991).

KLD-Sampling: Adaptive Particle Filters

Abstract: Over the last years, particle filters have been applied with great success to a variety of state estimation problems. We present a statistical approach to increasing the efficiency of particle filters by adapting the size of sample sets on-the-fly. The key idea of the KLD-sampling method is to bound the approximation error introduced by the sample-based representation of the particle filter. The name KLD-sampling is due to the fact that we measure the approximation error by the Kullback-Leibler distance. Our adaptation approach chooses a small number of samples if the density is focused on a small part of the state space, and it chooses a large number of samples if the state uncertainty is high. Both the implementation and computation overhead of this approach are small. Extensive experiments using mobile robot localization as a test application show that our approach yields drastic improvements over particle filters with fixed sample set sizes and over a previously introduced adaptation technique.

Better proposal distributions: object tracking using unscented particle filter

Abstract: Tracking objects involves the modeling of non-linear non-Gaussian systems. On one hand, variants of Kalman filters are limited by their Gaussian assumptions. On the other hand, conventional particle filter, e.g., CONDENSATION, uses transition prior as the proposal distribution. The transition prior does not take into account current observation data, and many particles can therefore be wasted in low likelihood area. To overcome these difficulties, unscented particle filter (UPF) has recently been proposed in the field of filtering theory. In this paper, we introduce the UPF framework into audio and visual tracking. The UPF uses the unscented Kalman filter to generate sophisticated proposal distributions that seamlessly integrate the current observation, thus greatly improving the tracking performance. To evaluate the efficacy of the UPF framework, we apply it in two real-world tracking applications. One is the audio-based speaker localization, and the other is the vision-based human tracking. The experimental results are compared against those of the widely used CONDENSATION approach and have demonstrated superior tracking performance.

Model-based 3D tracking of an articulated hand

Abstract: This paper presents a practical technique for model-based 3D hand tracking. An anatomically accurate hand model is built from truncated quadrics. This allows for the generation of 2D profiles of the model using elegant tools from projective geometry, and for an efficient method to handle self-occlusion. The pose of the hand model is estimated with an Unscented Kalman filter (UKF), which minimizes the geometric error between the profiles and edges extracted from the images. The use of the UKF permits higher frame rates than more sophisticated estimation methods such as particle filtering, whilst providing higher accuracy than the extended Kalman filter The system is easily scalable from single to multiple views, and from rigid to articulated models. First experiments on real data using one and two cameras demonstrate the quality of the proposed method for tracking a 7 DOF hand model.

Image segmentation by data driven Markov chain Monte Carlo

Abstract: This paper presents a computational paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian, statistical framework. The paper contributes to image segmentation in three aspects. Firstly, it designs effective and well balanced Markov Chain dynamics to explore the solution space and makes the split and merge process reversible at a middle level vision formulation. Thus it achieves globally optimal solution independent of initial segmentations. Secondly, instead of computing a single maximum a posteriori solution, it proposes a mathematical principle for computing multiple distinct solutions to incorporates intrinsic ambiguities in image segmentation. A k-adventurers algorithm is proposed for extracting distinct multiple solutions from the Markov chain sequence. Thirdly, it utilizes data-driven (bottom-up) techniques, such as clustering and edge detection, to compute importance proposal probabilities, which effectively drive the Markov chain dynamics and achieve tremendous speedup in comparison to traditional jump-diffusion method. Thus DDM-CMC paradigm provides a unifying framework where the role of existing segmentation algorithms, such as; edge detection, clustering, region growing, split-merge, SNAKEs, region competition, are revealed as either realizing Markov chain dynamics or computing importance proposal probabilities. We report some results on color and grey level image segmentation in this paper and refer to a detailed report and a web site for extensive discussion.

A particle filter for track-before-detect

Abstract: A Bayesian track-before-detect particle filter is proposed. The filter provides a sample based approximation to the distribution of the target state directly from pixel array data. The filter also provides a measure of the probability that a target is present.

Monte Carlo Experiments: Design and Implementation

Abstract: The use of Monte Carlo simulations for the empirical assessment of statistical estimators is becoming more common in structural equation modeling research. Yet, there is little guidance for the researcher interested in using the technique. In this article we illustrate both the design and implementation of Monte Carlo simulations. We present 9 steps in planning and performing a Monte Carlo analysis: (1) developing a theoretically derived research question of interest, (2) creating a valid model, (3) designing specific experimental conditions, (4) choosing values of population parameters, (5) choosing an appropriate software package, (6) executing the simulations, (7) file storage, (8) troubleshooting and verification, and (9) summarizing results. Throughout the article, we use as a running example a Monte Carlo simulation that we performed to illustrate many of the relevant points with concrete information and detail.

Nonlinear filtering for speaker tracking in noisy and reverberant environments

Abstract: This paper addresses the problem of speaker tracking in a noisy and reverberant environment using time delay of arrival (TDOA) measurements at spatially distributed microphone pairs The tracking problem is posed within a state-space estimation framework, and models are developed for the speaker motion and the likelihood of the speaker location in the light of the TDOA measurements The resulting state-space model is nonlinear and nonGaussian, and consequently no closed-form solutions exist for the filtering distributions required to perform tracking Here sequential Monte Carlo (SMC) methods are applied to approximate the true filtering distribution with a set of samples The resulting tracking algorithm requires no triangulation, is computationally efficient, and can straightforwardly be extended to track multiple speakers

People tracking using hybrid Monte Carlo filtering

Abstract: Particle filters are used for hidden state estimation with nonlinear dynamical systems. The inference of 3-D human motion is a natural application, given the nonlinear dynamics of the body and the nonlinear relation between states and image observations. However, the application of particle filters has been limited to cases where the number of state variables is relatively small, because the number of samples needed with high dimensional problems can be prohibitive. We describe a filter that uses hybrid Monte Carlo (HMC) to obtain samples in high dimensional spaces. It uses multiple Markov chains that use posterior gradients to rapidly explore the state space, yielding fair samples from the posterior. We find that the HMC filter is several thousand times faster than a conventional particle filter on a 28 D people tracking problem.

Real-Parameter Evolutionary Monte Carlo With Applications to Bayesian Mixture Models

Abstract: We propose an evolutionary Monte Carlo algorithm to sample from a target distribution with real-valued parameters The attractive features of the algorithm include the ability to learn from the samples obtained in previous steps and the ability to improve the mixing of a system by sampling along a temperature ladder The effectiveness of the algorithm is examined through three multimodal examples and Bayesian neural networks The numerical results confirm that the real-coded evolutionary algorithm is a promising general approach for simulation and optimization

Particle filtering based likelihood ratio approach to fault diagnosis in nonlinear stochastic systems

Abstract: This paper presents the development of a particle filtering (PF) based method for fault detection and isolation (FDI) in stochastic nonlinear dynamic systems. The FDI problem is formulated in the multiple model (MM) environment, then by combining the likelihood ratio (LR) test with the PF, a new FDI scheme is developed. The simulation results on a highly nonlinear system are provided which demonstrate the effectiveness of the proposed method.

Improvement Strategies for Monte Carlo Particle Filters

Abstract: The particle filtering field has seen an upsurge in interest over recent years, and accompanying this upsurge several enhancements to the basic techniques have been suggested in the literature. In this paper we collect a group of these developments that seem to be particularly important for time series applications and give a broad discussion of the methods, showing the relationships between them. We firstly present a general importance sampling framework for the filtering/smoothing problem and show how the standard techniques can be obtained from this general approach. In particular, we show that the auxiliary particle filtering methods of (Pitt and Shephard: this volume) fall into the same general class of algorithms as the standard bootstrap filter of (Gordon et al. 1993). We then develop the ideas further and describe the role of MCMC resampling as proposed by (Gilks and Berzuini: this volume) and (MacEachern, Clyde and Liu 1999). Finally, we present a generalisation of our own in which MCMC resampling ideas are used to traverse a sequence of ‘bridging’ densities which lie between the prediction density and the filtering density. In this way it is hoped to reduce the variability of the importance weights by attempting a series of smaller, more manageable moves at each time step.

Automatic partitioning of high dimensional search spaces associated with articulated body motion capture

Abstract: Particle filters have proven to be an effective tool for visual tracking in non-Gaussian, cluttered environments. Conventional particle filters, however, do not scale to the problem of human motion capture (HMC) because of the large number of degrees of freedom involved. Annealed Particle Filtering (APF), introduced by J. Deutscher et al. (2000), tackled this by layering the search space and was shown to be a very effective tool for HMC. We improve upon and extend the APF in two ways. First we develop a hierarchical search strategy which automatically partitions the search space without any explicit representation of the partitions. Then we introduce a crossover operator (similar to that found in genetic algorithms) which improves the ability of the tracker to search different partitions in parallel. We present results for a simple example to demonstrate the new algorithm's implementation and then apply it to the considerably more complex problem of human motion capture with 34 degrees of freedom.

Maximum a posteriori sequence estimation using Monte Carlo particle filters

Abstract: We develop methods for performing maximum a posteriori (MAP) sequence estimation in non-linear non-Gaussian dynamic models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. MAP sequence estimation is then performed using a classical dynamic programming technique applied to the discretised version of the state space. In contrast with standard approaches to the problem which essentially compare only the trajectories generated directly during the filtering stage, our method efficiently computes the optimal trajectory over all combinations of the filtered states. A particular strength of the method is that MAP sequence estimation is performed sequentially in one single forwards pass through the data without the requirement of an additional backward sweep. An application to estimation of a non-linear time series model and to spectral estimation for time-varying autoregressions is described.

A co-inference approach to robust visual tracking

Abstract: Visual tracking could be treated as a parameter estimation problem of target representation based on observations in image sequences. A richer target representations would incur better chances of successful tracking in cluttered and dynamic environments. However, the dimensionality of target's state space also increases making tracking a formidable estimation problem. In this paper, the problem of tracking and integrating multiple cues is formulated in a probabilistic framework; and represented by factorized graphical model. Structured variational analysis of such graphical model factorizes different modalities and suggests a co-inference process among these modalities. A sequential Monte Carlo algorithm is proposed to give an efficient approximation of the co-inference based on the importance sampling technique. This algorithm is implemented in real-time at around 30 Hz. Specifically, tracking both position, shape and color distribution of a target is investigated in this paper. Our extensive experiments show that the proposed algorithm performs robustly in a large variety of trucking scenarios. The approach presented in this paper has the potential to solve other sensor fusion problems.

Particle Filters — A Theoretical Perspective

Abstract: The purpose of this chapter is to present a rigorous mathematical treatment of the convergence of particle filters In general, we follow the notation and settings suggested by the editors, any extra notation being defined in the next section Section 231 contains the main results of the paper: Theorems 231 and 232 provide necessary and sufficient conditions for the convergence of the particle filter to the posterior distribution of the signal As an application of these results, we prove the convergence of a certain class of particle filters This class includes several known filters (such as those presented in (Carpenter, Clifford and Fearnhead 1999b, Crisan, Del Moral and Lyons 1999, Gordon et al 1993), but is by no means the most general one Finally, we discuss some of the issues that are relevant in applications and which arise from the theoretical analysis of these methods

Learning image statistics for Bayesian tracking

Abstract: This paper describes a framework for learning probabilistic models of objects and scenes and for exploiting these models for tracking complex, deformable, or articulated objects in image sequences. We focus on the probabilistic tracking of people and learn models of how they appear and move in images. In particular we learn the likelihood of observing various spatial and temporal filter responses corresponding to edges, ridges, and motion differences given a model of the person. Similarly, we learn probability distributions over filter responses for general scenes that define a likelihood of observing the filter responses for arbitrary backgrounds. We then derive a probabilistic model for tracking that exploits the ratio between the likelihood that image pixels corresponding to the foreground (person) were generated by an actual person or by some unknown background. The paper extends previous work on learning image statistics and combines it with Bayesian tracking using particle filtering. By combining multiple image cues, and by using learned likelihood models, we demonstrate improved robustness and accuracy when tracking complex objects such as people in monocular image sequences with cluttered scene and a moving camera.

Sequential Monte Carlo fusion of sound and vision for speaker tracking

Abstract: Video telephony could be considerably enhanced by provision of a tracking system that allows freedom of movement to the speaker while maintaining a well-framed image, for transmission over limited bandwidth. Already commercial multi-microphone systems exist which track speaker direction in order to reject background noise. Stereo sound and vision are complementary modalities in that sound is good for initialisation (where vision is expensive) whereas vision is good for localisation (where sound is less precise). Using generative probabilistic models and particle filtering, we show that stereo sound and vision can indeed be fused effectively, to make a system more capable than with either modality on its own.

Particle filter based detection for tracking

Abstract: We present a new method to perform detection and tracking of a possible target in noise. We perform tracking not on the basis of the standard measurements but on the raw radar video data. Detection then is based upon the a posteriori information, i.e., the probability density of the state given these past measurements (in this case video data). This way of data processing/tracking is also referred to as track before detect (TBD) for obvious reasons. An advantage of this method over classical tracking is that in this TBD approach the decision whether a target is present or not is based on integrated and kinematically correlated energy. This method is better suited for tracking weak targets in noise than the classical method. As this problem statement leads to a nonlinear non-Gaussian filtering problem classical filtering methods (e.g. Kalman filtering) will result in poor performance. A particle filter is used to deal with the nonlinearities and the non-Gaussian nature of the noise. The same particle filter output is also used to perform detection based on a likelihood ratio test.

Tracking of Multi-state Hand Models Using Particle Filtering and a Hierarchy of Multi-scale Image Features

Abstract: This paper presents an approach for simultaneous tracking and recognition of hierarchical object representations in terms of multiscale image features. A scale-invariant dissimilarity measure is proposed for comparing scale-space features at different positions and scales. Based on this measure, the likelihood of hierarchical, parameterized models can be evaluated in such a way that maximization of the measure over different models and their parameters allows for both model selection and parameter estimation. Then, within the framework of particle filtering, we consider the area of hand gesture analysis, and present a method for simultaneous tracking and recognition of hand models under variations in the position, orientation, size and posture of the hand. In this way, qualitative hand states and quantitative hand motions can be captured, and be used for controlling different types of computerised equipment.

Sequential Monte Carlo Methods for Optimal Filtering

Abstract: Estimating the state of a nonlinear dynamic model sequentially in time is of paramount importance in applied science. Except in a few simple cases, there is no closed-form solution to this problem. It is therefore necessary to adopt numerical techniques in order to compute reasonable approximations. Sequential Monte Carlo (SMC) methods are powerful tools that allow us to accomplish this goal.