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.

Mobile robot localization is the problem of determining a robot's pose from sensor data. This article presents a family of probabilistic localization algorithms known as Monte Carlo Localization (MCL). MCL algorithms represent a robot's belief by a set of weighted hypotheses (samples), which approximate the posterior under a common Bayesian formulation of the localization problem. Building on the basic MCL algorithm, this article develops a more robust algorithm called MixtureMCL, which integrates two complimentary ways of generating samples in the estimation. To apply this algorithm to mobile robots equipped with range finders, a kernel density tree is learned that permits fast sampling. Systematic empirical results illustrate the robustness and computational efficiency of the approach.

In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the determin-istic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of the analytic structure present in some important classes of state-space models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.

This paper presents a new algorithm for mobile robot localization, called Monte Carlo Localization (MCL). MCL is a version of Markov localization, a family of probabilistic approaches that have recently been applied with great practical success. However, previous approaches were either computationally cumbersome (such as grid-based approaches that represent the state space by high-resolution 3D grids), or had to resort to extremely coarse-grained resolutions. Our approach is computationally efficient while retaining the ability to represent (almost) arbitrary distributions. MCL applies sampling-based methods for approximating probability distributions, in a way that places computation " where needed." The number of samples is adapted on-line, thereby invoking large sample sets only when necessary. Empirical results illustrate that MCL yields improved accuracy while requiring an order of magnitude less computation when compared to previous approaches. It is also much easier to implement...

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This paper describes how to use partitioned sampling on articulated objects, obtaining results that would be impossible with standard sampling methods. Because partitioned sampling is the statistical analogue of a hierarchical search, it makes sense to use it on articulated objects, since links at the base of the object can be localised before moving on to search for subsequent links

This paper presents a statistical algorithm for collaborative mobile robot localization. Our approach uses a sample-based version of Markov localization, capable of localizing mobile robots in an any-time fashion. When teams of robots localize themselves in the same environment, probabilistic methods are employed to synchronize each robot's belief whenever one robot detects another. As a result, the robots localize themselves faster, maintain higher accuracy, and high-cost sensors are amortized across multiple robot platforms. The technique has been implemented and tested using two mobile robots equipped with cameras and laser range-finders for detecting other robots. The results, obtained with the real robots and in series of simulation runs, illustrate drastic improvements in localization speed and accuracy when compared to conventional single-robot localization. A further experiment demonstrates that under certain conditions, successful localization is only possible if teams of heterogeneous robots collaborate during localization.

In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling, and weighted resampling to complete the on-line "filtering" task. In this article we propose a special sequential Monte Carlo method, the mixture Kalman filter, which uses random mixture of normal distributions to represent a target distribution. It is designed for on-line estimation and prediction of conditional and partial conditional dynamic linear models, which are themselves a class of widely used nonlinear system and also serve to approximate many other nonlinear systems. Compared with a few available filtering methods including Monte Carlo ones, the efficiency gain provided by the mixture Kalman filter can be very substantial. Another contribution of this article is the formulation of many nonlinear systems into conditional or partial conditional linear form, to which the mixture Kalman filter can be...

To navigate reliably in indoor environments, a mobile robot must know where it is. This includes both the ability of globally localizing the robot from scratch, as well as tracking the robot's position once its location is known. Vision has long been advertised as providing a solution to these problems, but we still lack efficient solutions in unmodified environments. Many existing approaches require modification of the environment to function properly, and those that work within unmodified environments seldomly address the problem of global localization. In this paper we present a novel, vision-based localization method based on the CONDENSATION algorithm [17, 18], a Bayesian filtering method that uses a samplingbased density representation. We show how the CONDENSATION algorithm can be used in a novel way to track the position of the camera platform rather than tracking an object in the scene. In addition, it can also be used to globally localize the camera platform, given a visua...

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 28D people tracking problem.