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.

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.

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.

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.

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.

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

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.

The ability to learn a consistent model of its environment is a prerequisite for autonomous mobile robots. A particularly challenging problem in acquiring environment maps is that of closing loops; loops in the environment create challenging data association problems [9]. This paper presents a novel algorithm that combines RaoBlackwellized particle filtering and scan matching. In our approach scan matching is used for minimizing odometric errors during mapping. A probabilistic model of the residual errors of scan matching process is then used for the resampling steps. This way the number of samples required is seriously reduced. Simultaneously we reduce the particle depletion problem that typically prevents the robot from closing large loops. We present extensive experiments that illustrate the superior performance of our approach compared to previous approaches.

Localization and mapping in unknown environments becomes more difficult as the complexity of the environment increases. With conventional techniques, the cost of maintaining estimates rises rapidly with the number of landmarks mapped. We present a monocular SLAM system that employs a particle filter and top-down search to allow realtime performance while mapping large numbers of landmarks. To our knowledge, we are the first to apply this FastSLAM-type particle filter to single-camera SLAM. We also introduce a novel partial initialization procedure that efficiently determines the depth of new landmarks. Moreover, we use information available in observations of new landmarks to improve camera pose estimates. Results show the system operating in real-time on a standard workstation while mapping hundreds of landmarks. 1.

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