Abstract-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.

A prevalent problem in statistical signal processing, applied statistics, and time series analysis is the calculation of the smoothed posterior distribution, which describes the uncertainty associated with a state, or a sequence of states, conditional on data from the past, the present, and the future. The aim of this paper is to provide a rigorous foundation for the calculation, or approximation, of such smoothed distributions, to facilitate a robust and efficient implementation. Through a cohesive and generic exposition of the scientific literature we offer several novel extensions such that one can perform smoothing in the most general case. Experimental results for: a Jump Markov Linear System; a comparison of particle smoothing methods; and parameter estimation using a particle implementation of the EM algorithm, are provided.

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Adverse drug reactions come at a considerable cost on society. Social media are a potentially invaluable reservoir of information for pharmacovigilance, yet their true value remains to be fully understood. In order to realize the benefits social media holds, a number of technical, regulatory and ethical challenges remain to be addressed. We outline these key challenges identifying relevant current research and present possible solutions.

In this paper we consider a nonlinear bearing-only target tracking problem using three different methods and compare their performances. The study is motivated by a ground surveillance problem where a target is tracked from an airborne sensor at an approximately known altitude using depression angle observations. Two nonlinear suboptimal estimators, namely, the extended Kalman Filter (EKF) and the pseudomeasurement tracking filter are applied in a 2-D bearing-only tracking scenario. The EKF is based on the linearization of the nonlinearities in the dynamic and/or the measurement equations. The pseudomeasurement tracking filter manipulates the original nonlinear measurement algebraically to obtain the linear-like structured measurement. Finally, the particle filter, which is a Monte Carlo integration based optimal nonlinear filter and has been presented in the literature as a better alternative to linearization via EKF, is used on the same problem. The performances of these three different techniques in terms of accuracy and computational load are presented in this paper. The results demonstrate the limitations of these algorithms on this deceptively simple tracking problem.

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Abstract-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.