Standard algorithms in tracking and other state-space models assume identical and synchronous sampling rates for the state and measurement processes. However, real trajectories of objects are typically characterized by prolonged smooth sections, with sharp, but infrequent, changes. Thus, a more parsimonious representation of a target trajectory may be obtained by direct modeling of maneuver times in the state process, independently from the observation times. This is achieved by assuming the state arrival times to follow a random process, typically specified as Markovian, so that state points may be allocated along the trajectory according to the degree of variation observed. The resulting variable dimension state inference problem is solved by developing an efficient variable rate particle filtering algorithm to recursively update the posterior distribution of the state sequence as new data becomes available. The methodology is quite general and can be applied across many models where dynamic model uncertainty occurs on-line. Specific models are proposed for the dynamics of a moving object under internal forcing, expressed in terms of the intrinsic dynamics of the object. The performance of the algorithms with these dynamical models is demonstrated on several challenging maneuvering target tracking problems in clutter.

In this paper, we propose an extension of the soft-gating approach for measurement-to-target assignment for multitarget tracking. Given the latest observation and a set of multitarget particles, the proposed method combines efficient m-best 2D data assignment and sampling methods to compute a feasible measurement-to-target assignment with an associated probability for each particle. The particles containing the multitarget states and the association vectors can then be used to recursively estimate the posterior distribution of the targets using sequential Monte Carlo methods. Computer simulations demonstrate the robustness and effectiveness of the proposed method for data association and multitarget tracking.

In this paper we present an extension to Monte Carlo localisation (MCL) to solve the global localisation problem. This extension is in the form of an efficient data-dependent proposal that can be used both for initialisation and re-initialisation after tracking failure or robot kidnapping. The proposal is a Gaussian mixture over a fixed grid of locations, each of which has a sensor structure similar to that of the robot. The robot measurements are matched to these structures to give the best-match orientation for each grid point. The mixture components are then centred on the grid locations and best-match orientations, with the component weights proportional to the best-match likelihoods. Empirical results illustrate that our MCL approach is more computationally efficient than standard MCL, and demonstrates faster recovery from localisation failures.

Most object tracking approaches either assume that the number of objects is constant, or that information about object existence is provided by some external source. Here, we show how object existence can be rigorously integrated within the Bayesian single and multiple object tracking framework. We provide a general treatment that impacts as little as possible on existing tracking algorithms, so that software can be reused, and that allows implementation with Kalman filters, extended Kalman filters, particle filters, etc. We apply the proposed framework to colour-based tracking of multiple objects.

We discuss modifications to tracking models, and sequential Monte Carlo algorithms for their estimation from sequential and batch data. New models for tracking are proposed which involve a dynamical model on both the hidden state value and its arrival times. In this way we aim to have a more flexible and parsimonious representation of time-varying state characteristics which is more amenable to estimation using Bayesian filtering. In order to perform inference in this scenario, new particle filters and smoothers are proposed for cases where the state process arrives at unknown times that are generally different from the observation arrival times.

The effectiveness of probabilistic tracking of objects in image sequences has been revolutionized by the development of particle filtering. Whereas Kalman filters are restricted to Gaussian distributions, particle filters can propagate more general distributions, albeit only approximately. This is of particular benefit in visual tracking because of the inherent ambiguity of the visual world that stems from its richness and complexity. One important advantage of the particle filtering framework is that it allows the information from different measurement sources to be fused in a principled manner. Although this fact has been acknowledged before, it has not been fully exploited within a visual tracking context. Here we introduce generic importance sampling mechanisms for data fusion and discuss them for fusing color with either stereo sound, for teleconferencing, or with motion, for surveillance with a still camera. We show how each of the three cues can be modeled by an appropriate data likelihood function, and how the intermittent cues (sound or motion) are best handled by generating proposal distributions from their likelihood functions. Finally, the effective fusion of the cues by particle filtering is demonstrated on real teleconference and surveillance data.

The likelihood models used in probabilistic visual tracking applications are often complex non-linear and/or non-Gaussian functions, leading to analytically intractable inference. Solutions then require numerical approximation techniques, of which the particle filter is a popular choice. Particle filters, however, degrade in performance as the dimensionality of the state space increases and the support of the likelihood decreases. As an alternative to particle filters this paper introduces a variational approximation to the tracking recursion. The variational inference is intractable in itself, and is combined with an efficient importance sampling procedure to obtain the required estimates. The algorithm is shown to compare favorably with particle filtering techniques on a synthetic example and two real tracking problems. The first involves the tracking of a designated object in a video sequence based on its color properties, whereas the second involves contour extraction in a single image.

When performing subspace modeling of data using principal component analysis (PCA) it may be desirable to constrain certain directions to be more meaningful in the context of the problem being investigated. This need arises due to the data often being approximately isotropic along the lesser principal components, making the choice of directions for these components more-or-less arbitrary. Furthermore, constraining may be imperative to ensure viable solutions in problems where the dimensionality of the data space is of the same order as the number of data points available. This paper adopts a Bayesian approach and augments the likelihood implied by probabilistic principal component analysis (PPCA) (Tipping and Bishop, 1999) with a prior designed to achieve the constraining effect. The subspace parameters are computed efficiently using the EM algorithm. The constrained modeling approach is illustrated on two pertinent problems, one from speech analysis, and one from computer vision.

In recent years particle filters have become a tremendously popular tool to perform tracking for nonlinear and/or nonGaussian models. This is due to their simplicity, generality and success over a wide range of challenging applications. Particle filters, and Monte Carlo methods in general, are however poor at consistently maintaining the multimodality of the target distributions that may arise due to ambiguity or the presence of multiple objects. To address this shortcoming this paper proposes to model the target distribution as a nonparametric mixture model, and presents the general tracking recursion in this case. It is shown how a Monte Carlo implementation of the general recursion leads to a mixture of particle filters that interact only in the computation of the mixture weights, thus leading to an efficient numerical algorithm, where all the results pertaining to standard particle filters apply. The ability of the new method to maintain posterior multimodality is illustrated on a synthetic example and a real world tracking problem involving the tracking of football players in a video sequence.

We propose a method for sequential Bayesian kernel regression. As is the case for the popular Relevance Vector Machine (RVM) [10, 11], the method automatically identifies the number and locations of the kernels. Our algorithm overcomes some of the computational difficulties related to batch methods for kernel regression. It is non-iterative, and requires only a single pass over the data. It is thus applicable to truly sequen- tial data sets and batch data sets alike. The algorithm is based on a generalisation of Importance Sampling, which allows the design of in- tuitively simple and efficient proposal distributions for the model param- eters. Comparative results on two standard data sets show our algorithm to compare favourably with existing batch estimation strategies.

This paper presents a strategy for rapid summarisation and browsing of video sequences. The input video is first transformed into a sequence of representative feature vectors. Using this representation a utility function is designed that assigns high reward to subsequences of keyframes that are maximally distinct and individually carry the most information. For a specified level of detail and endpoints the keyframe sequence that maximises this utility function can be obtained by a non-iterative Dynamic Programming procedure, thus allowing the user to efficiently zoom in on any part or all of the video sequence. For the sake of compactness and clarity the working of the algorithm is illustrated on a television commercial. 1

This paper applies time-varying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modeling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diffusion processes. The main aim of the paper is to perform on-line estimation of the clean speech and model parameters and to determine the adequacy of the chosen statistical models. Efficient particle methods are developed to solve the optimal filtering and fixed-lag smoothing problems. The algorithms combine sequential importance sampling (SIS), a selection step and Markov chain Monte Carlo (MCMC) methods. They employ several variance reduction strategies to make the best use of the statistical structure of the model. It is also shown how model adequacy may be determined by combining the particle filter with frequentist methods. The modeling and enhancement performance of the models and estimation algorithms are evaluated in simulation studies on both synthetic and real speech data sets.

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.

This paper applies time-varying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform on-line estimation of the clean speech and the model parameters, and to determine the adequacy of the chosen statistical models. An ecient simulation-based method is developed to solve the optimal ltering problem. The algorithm combines sequential importance sampling and a selection step, and employs several variance reduction strategies to make the best use of the statistical structure of the model. The modelling and enhancement performance of the model and algorithm are evaluated in simulation studies on real speech data sets. 1. INTRODUCTION For enhancement purposes, speech is commonly modelled as the output of an autoregressive (AR) process observed in additive white Gaussian noise (AWGN). The main sh...

This paper investigates a Bayesian approach to the enhancement of speech signals corrupted by additive white Gaussian noise. Parametric models for the speech and noise processes are constructed, leading to a posterior distribution for the model parameters and uncorrupted speech samples given the observed noisy speech samples. Being analytically intractable, inferences concerning these variables are performed using Markov chain Monte Carlo (MCMC) methods. The efficiency of the sampling scheme within this framework is further improved by employing state-space techniques based on the Kalman filter.