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.

Localization is the process of updating the pose of a robot in an environment, based on sensor readings. In this experimental study, we compare two recent methods for localization of indoor mobile robots: Markov localization, which uses a probability distribution across a grid of robot poses; and scan matching, which uses Kalman filtering techniques based on matching sensor scans. Both these techniques are dense matching methods, that is, they match dense sets of environment features to an a priori map. To arrive at results for a range of situations, we utilize several different types of environments, and add noise to both the dead-reckoning and the sensors. Analysis shows that, roughly, the scan-matching techniques are more efficient and accurate, but Markov localization is better able to cope with large amounts of noise. These results suggest hybrid methods that are efficient, accurate and robust to noise. 1.

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.

Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data arise in many applications in statistics and related fields. Recently, a large number of algorithms and applications based on sequential Monte Carlo methods (also known as particle filtering methods) have appeared in the literature to solve this class of problems; see (Doucet, de Freitas & Gordon, 2001) for a survey. However, few of these methods have been proved to converge rigorously. The purpose of this paper is to address this issue. We present a general sequential Monte Carlo (SMC) method which includes most of the important features present in current SMC methods. This method generalizes and encompasses many recent algorithms. Under mild regularity conditions, we obtain rigorous convergence results for this general SMC method and therefore give theoretical backing for the validity of all the algorithms that can be obtained as particular cases of it. Keywords: Bayesian...

One of the goals in the field of mobile robotics is the development of mobile platforms which operate in populated environments. For many tasks it is therefore highly desirable that a robot can track the positions of the humans in its surrounding. In this paper we introduce sample-based joint probabilistic data association filters as a new algorithm to track multiple moving objects. Our method applies Bayesian filtering to adapt the tracking process to the number of objects in the perceptual range of the robot. The approach has been implemented and tested on a real robot using laser-range data. We present experiments illustrating that our algorithm is able to robustly keep track of multiple persons. The experiments furthermore show that the approach outperforms other techniques developed so far.

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.

Over the last years, particle filters have been applied with great success to a variety of state estimation problems. In this paper we present a statistical approach to increasing the efficiency of particle filters by adapting the size of sample sets during the estimation process.

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Automatic health monitoring helps enable independent living for the elderly by providing specific information to caregivers. This goal, called aging in place,is increasingly important as an unprecedented portion of the population enters old age. I introduce the simultaneous tracking and activity recognition (STAR) problem,whose solution provides this key information. I propose using data from many minimally invasive sensors commonly found in home security systems to provide simultaneous room-level tracking and recognition of many of the activities of daily living (ADLs). ADLs have been chosen by physicians to gauge the severity of cognitive and physical ailments. I describe a Rao-Blackwellised particle filter for room level tracking, rudimentary activity recognition, and data association, as well as a Monte Carlo EM approach for online parameter learning. I demonstrate results from experiments in an instrumented home and on simulated data. Proposed extensions improve the approach and add more complex activity recognition. We discuss how to integrate a growing vocabulary of activities into the tracker.

Abstract. In this paper, we describe an automated method for fast, ground-based acquisition of large-scale 3D city models. Our experimental set up consists of a truck equipped with one camera and two fast, inexpensive 2D laser scanners, being driven on city streets under normal traffic conditions. One scanner is mounted vertically to capture building facades, and the other one is mounted horizontally. Successive horizontal scans are matched with each other in order to determine an estimate of the vehicle’s motion, and relative motion estimates are concatenated to form an initial path. Assuming that features such as buildings are visible from both ground-based and airborne view, this initial path is globally corrected by Monte-Carlo Localization techniques. Specifically, the final global pose is obtained by utilizing an aerial photograph or a Digital Surface Model as a global map, to which the ground-based horizontal laser scans are matched. A fairly accurate, textured 3D cof the downtown Berkeley area has been acquired in a matter of minutes, limited only by traffic conditions during the data acquisition phase. Subsequent automated processing time to accurately localize the acquisition vehicle is 235 minutes for a 37 minutes or 10.2 km drive, i.e. 23 minutes per kilometer. Keywords: laser scanning, navigation, self-localization, mobile robots, 3D modeling, Monte-Carlo localization 1.