A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We deliver a guideline on how they should be used and under what circumstance each method is most suitable. Through the analysis of differences and connections, we consolidate these methods into a generic algorithm by combining desirable features. In addition, we propose a general use of Rao-Blackwellization to improve performances. Examples from econometrics and engineering are presented to demonstrate the importance of Rao-Blackwellization and to compare different Monte Carlo procedures. Keywords: Blind deconvolution; Bootstrap filter; Gibbs sampling; Hidden Markov model; Kalman filter; Markov...

. Tracking research has diverged into two camps; low-level approaches which are typically fast and robust but provide little fine-scale information, and high-level approaches which track complex deformations in high-dimensional spaces but must trade off speed against robustness. Real-time high-level systems perform poorly in clutter and initialisation for most high-level systems is either performed manually or by a separate module. This paper presents a new technique to combine low- and high-level information in a consistent probabilistic framework, using the statistical technique of importance sampling combined with the Condensation algorithm. The general framework, which we term Icondensation, is described, and a hand tracker is demonstrated which combines colour blob-tracking with a contour model. The resulting tracker is robust to rapid motion, heavy clutter and hand-coloured distractors, and re-initialises automatically. The system runs comfortably in real time on an...

The Kalman filter provides an effective solution to the linear-Gaussian filtering problem. However, where there is nonlinearity, either in the model specification or the observation process, other methods are required. We consider methods known generically as particle filters, which include the condensation algorithm and the Bayesian bootstrap or sampling importance resampling (SIR) filter. These filters

We present a method for recovering 3D human body motion from monocular video sequences based on a robust image matching metric, incorporation of joint limits and non-self-intersection constraints, and a new sample-and-refine search strategy guided by rescaled cost-function covariances. Monocular 3D body tracking is challenging: besides the difficulty of matching an imperfect, highly flexible, self-occluding model to cluttered image features, realistic body models have at least 30 joint parameters subject to highly nonlinear physical constraints, and at least a third of these degrees of freedom are nearly unobservable in any given monocular image. For image matching we use a carefully designed robust cost metric combining robust optical flow, edge energy, and motion boundaries. The nonlinearities and matching ambiguities make the parameter-space cost surface multi-modal, ill-conditioned and highly nonlinear, so searching it is difficult. We discuss the limitations of CONDENSATION-like samplers, and describe a novel hybrid search algorithm that combines inflated-covariance-scaled sampling and robust continuous optimization subject to physical constraints and model priors. Our experiments on challenging monocular sequences show that robust cost modeling, joint and selfintersection constraints, and informed sampling are all essential for reliable monocular 3D motion estimation.

Robust real-time tracking of non-rigid objects is a challenging task. Particle filtering has proven very successful for non-linear and nonGaussian estimation problems. The article presents the integration of color distributions into particle filtering, which has typically been used in combination with edge-based image features. Color distributions are applied, as they are robust to partial occlusion, are rotation and scale invariant and computationally efficient. As the color of an object can vary over time dependent on the illumination, the visual angle and the camera parameters, the target model is adapted during temporally stable image observations. An initialization based on an appearance condition is introduced since tracked objects may disappear and reappear. Comparisons with the mean shift tracker and a combination between the mean shift tracker and Kalman filtering show the advantages and limitations of the new approach.

The problem of tracking multiple targets with multiple sensors in the presence of interfering measurements is considered. A new hybrid bootstrap filter is proposed. The bootstrap filter is an approach where random samples are used to represent the target posterior distributions. By using this approach, we circumvent the usual problem of an exponentially increasing number of association hypotheses as well as allowing the use of any nonlinear/non-Gaussian system and/or measurement models. I. INTRODUCTION This paper concerns the problem of tracking multiple targets using the information from multiple sensors. The sensors produce measurements as a result of random noise, clutter, countermeasures and interference, in addition to those from the required targets. Hence, it is usually not possible to distinguish with certainty the origin of the sensor measurements. In the Bayesian approach to target tracking, the aim is to construct the probability density function (pdf) of the targets conditi...

Abstract—Sequential Bayesian estimation for nonlinear dynamic state-space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations. This paper introduces a new filter called the Gaussian particle filter1. It is based on the particle filtering concept, and it approximates the posterior distributions by single Gaussians, similar to Gaussian filters like the extended Kalman filter and its variants. It is shown that under the Gaussianity assumption, the Gaussian particle filter is asymptotically optimal in the number of particles and, hence, has much-improved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Simulation results are presented to demonstrate the versatility and improved performance of the Gaussian particle filter over conventional Gaussian filters and the lower complexity than known particle filters. The use of the Gaussian particle filter as a building block of more complex filters is addressed in a companion paper. Index Terms—Dynamic state space models, extended Kalman filter, Gaussian mixture, Gaussian mixture filter, Gaussian particle filter, Gaussian sum filter, Gaussian sum particle filter, Monte Carlo filters, nonlinear non-Gaussian stochastic systems, particle filters, sequential Bayesian estimation, sequential sampling methods, unscented Kalman filter. I.

This thesis establishes a stochastic framework for tracking curves in visual clutter, using a Bayesian random-sampling algorithm. The approach is rooted in ideas from statistics, control theory and computer vision. The problem is to track outlines and features of foreground objects, modelled as curves, as they move in substantial clutter, and to do it at, or close to, video frame-rate. The algorithm, named Condensation, for Conditional density propagation, has recently been derived independently by several researchers, and is generating signi cant interest in the statistics and signal processing communities. This thesis contributes to the literature on Condensation-like lters by presenting some novel applications of and extensions to the basic algorithm, and contributes to the visual motion estimation literature by demonstrating high tracking performance in cluttered environments. Despite its power the Condensation algorithm has a remarkably simple form and this allows the use of non-linear motion models which combine characteristics of discrete Hidden Markov Models with the continuous Auto-Regressive Process motion models traditionally used in Kalman lters. These mixed discrete-continuous models have promising applications to the emerging eld of perception of action. This thesis also implements two algorithms to smooth the output of the Condensation lter which improves the accuracy of motion estimation in a batch-mode procedure after tracking is complete.

Color can provide an efficient visual feature for tracking nonrigid objects in real-time. However, the color of an object can vary over time dependent on the illumination, the visual angle and the camera parameters. To handle these appearance changes a color-based target model must be adapted during temporally stable image observations.

The paper is concerned with approximations to nonlinear filtering problems that are of interest over a very long time interval. Since the optimal filter can rarely be constructed, one needs to compute with numerically feasible approximations. The signal model can be a jump-diffusion, reflected or not. The observations can be taken either in discrete or continuous time. The cost of interest is the pathwise error per unit time over a long time interval. In a previous paper of the authors [2], it was shown, under quite reasonable conditions on the approximating filter and on the signal and noise processes that (as time, bandwidth, process and filter approximation, etc.) go to their limit in any way at all, the limit of the pathwise average costs per unit time is just what one would get if the approximating processes were replaced by their ideal values and the optimal filter were used. When suitable approximating filters cannot be readily constructed due to excessive computational requirem...