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.

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On-line, spatially localized information about internal network performance can greatly assist dynamic routing algorithms and traffic transmission protocols. However, it is impractical to measure network traffic at all points in the network. A promising alternative is to measure only at the edge of the network and infer internal behavior from these measurements. In this paper we concentrate on the estimation and localization of internal delays based on end-to-end delay measurements from a source to receivers. We propose a sequential Monte Carlo (SMC) procedure capable of tracking nonstationary network behavior and estimating time-varying, internal delay characteristics. Simulation experiments demonstrate the performance of the SMC approach. 1 Introduction In large-scale networks, end-systems cannot rely on the network itself to cooperate in characterizing its own behavior. This has prompted several groups to investigate methods for inferring internal network behavior based on...

Abstract—Particle filter is a powerful visual tracking tool based on sequential Monte Carlo framework, and it needs large numbers of samples to properly approximate the posterior density of the state evolution. However, its efficiency will degenerate if too many samples are applied. In this paper, an improved particle filter is proposed by integrating support vector regression into sequential Monte Carlo framework to enhance the performance of particle filter with small sample set. The proposed particle filter utilizes an SVR based re-weighting scheme to re-approximate the posterior density and avoid sample impoverishment. Firstly, a regression function is obtained by support vector regression method over the weighted sample set. Then, each sample is re-weighted via the regression function. Finally, ameliorative posterior density of the state is reapproximated to maintain the effectiveness and diversity of samples. Experimental results demonstrate that the proposed particle filter improves the efficiency of tracking system effectively and outperforms classical particle filter. Keywords-visual tracking; particle filter; support vector regression I.

We review the class of time-varying autoregressive (TVAR) models and a range of related recent developments of Bayesian time series modelling. Beginning with TVAR models in a Bayesian dynamic linear modelling framework, we review aspects of latent structure analysis, including time-domain decomposition methods that provide inferences on the structure underlying non-stationary time series, and that are now central tools in the time series analyst's toolkit. Recent model extensions that deal with model order uncertainty, and are enabled using efficient Markov Chain Monte Carlo simulation methods, are discussed, as are novel approaches to sequential filtering and smoothing using particulate filtering methods. We emphasize the relevance of TVAR modelling in a range of applied contexts, including biomedical signal processing and communications, and highlight some of the central developments via examples arising in studies of multiple electroencephalographic (EEG) traces in neurophysiology. We conclude with comments about current research frontiers.