The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric estimation of the optimal importance sampling distribution (known as ‘‘nonparametric importance sampling’’) is a reasonable alternative to parametric approaches. In this article, nonparametric variants of both the self-normalized and the unnormalized importance sampling estimator are proposed and investigated. A common critique of nonparametric importance sampling is the increased computational burden compared with parametric methods. We solve this problem to a large degree by utilizing the linear blend frequency polygon estimator instead of a kernel estimator. Mean square error convergence properties are investigated, leading to recommendations for the efficient application of nonparametric importance sampling. Particularly, we show that nonparametric importance sampling asymptotically attains optimal importance sampling variance. The efficiency of nonparametric importance sampling algorithms relies heavily on the computational efficiency of the nonparametric estimator used. The linear blend frequency polygon outperforms kernel estimators in terms of certain criteria such as efficient sampling and evaluation. Furthermore, it is compatible with the inversion method for sample generation. This allows one to combine nonparametric importance sampling with other variance reduction techniques such as stratified sampling. Empirical evidence for the usefulness of the suggested algorithms is obtained by means of three benchmark integration problems. We show empirically that these methods may work in higher dimensions, at least up to dimension eight. As an application, we estimate the distribution of the queue length of a spam filter queuing system based on real data.

The original publication is available at www.springerlink.com. A vision system suitable for a smart meeting room able to analyse the activities of its occupants is described. Multiple people were tracked using a particle filter in which samples were iteratively reweighted using an approximate likelihood in each frame. Trackers were automatically initialised and constrained using simple contextual knowledge of the room layout. Person-person occlusion was handled using multiple cameras. The method was evaluated on video sequences of a six person meeting. The tracker was demonstrated to outperform standard sampling importance re-sampling. All meeting participants were successfully tracked and their actions were recognised throughout the meeting scenarios tested. 1

particle filters

We apply sequential Monte Carlo (SMC) to the detection of turning points in the business cycle and to the evaluation of statistics currently employed in business cycle analysis. The proposed nonlinear filtering method is very useful for sequentially estimating the latent variables and the parameters of nonlinear and non-Gaussian time-series models, such as the Markov-switching (MS) models employed in business cycle analysis. Moreover, we show how to combine SMC with Monte Carlo Markov Chain for estimating time series models with MS latent factors. We illustrate the effectiveness of the methodology and measure, in a full Bayesian and on-line context, the ability of a pool of MS models to identify turning points in the European economic activity. We also compare our results with existing business cycle datations and provide a sequential evaluation of the forecast accuracy of the competing MS models. An application on real time data is also provided.

In this thesis we consider sequential Monte Carlo methods for Bayesian inference about the hidden state of a time-discrete nonlinear and non-Gaussian state-space model. Sequential Monte Carlo methods generate random samples, called particles, whose associated empirical measure approximates the posterior distribution of the hidden state. We give an overview of the most important sequential Monte Carlo methods for filtering, smoothing, prediction and fixed parameter estimation. Convergence results such as the almost sure convergence and a central limit theorem will also be reviewed. Up to now there is a lack of methods for non-parametric estimation of the statespace model functions. We suggest novel approaches for non-parametric estimation of the transition function which are based on a sequential Monte Carlo method. Furthermore, we develop a novel generalisation of the standard sequential importance resampling algorithm tackling the problems of sample depletion in the tails of the posterior distribution and sensitivity against outliers. This method, called scaled sequential importance resampling, is based on the enlargement of the variance of the observation noise aiming at more even importance weights. We show how the reviewed convergence results can be extended to hold for this new method. The implementation of the Bayesian Filtering Toolbox (BFT) which was developed in the course of this thesis is described. It is a software package including most filtering algorithms discussed in this thesis. In a final chapter we apply the BFT to several benchmark problems and show the usefulness of the new methods for filtering and non-parametric estimation. Erklärung zur Diplomarbeit Hiermit versichere ich, dass ich die vorliegende Arbeit selbständig und ohne unerlaubte fremde Hilfe verfasst habe und dass alle wörtlich oder sinngemäß aus

Abstract — Sequential filtering provides a suitable framework for estimating and updating the unknown parameters of a system as data become available. The foundations of sequential Bayesian filtering with emphasis on practical issues are first reviewed covering both Kalman and particle filter approaches. Filtering is demonstrated to be a powerful estimation tool, employing prediction from previous estimates and updates stemming from physical and statistical models that relate acoustic measurements to the unknown parameters. Ocean acoustic applications are then reviewed focusing on source tracking, estimation of environmental parameters evolving in time or space, and frequency tracking. Spatial arrival time tracking is illustrated with Shallow Water 06 data. Index Terms — Sequential Monte Carlo methods, ocean acoustics, acoustic signal processing, acoustic tracking, extended

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This paper describes the application of Knowledge-Based System (KBS) to tracking. Section 2 paves the way to the new technology by discussing the following topics: historical survey of stochastic filtering theory; overview of tracking systems with some details on mono-sensor and multi-sensor tracking, evolution of filtering logics, evolution of correlation logics, and presentation of recent findings on non linear filtering (e.g.: unscented Kalman filter, particle filter) theory which go beyond the classical Kalman filtering. After this introduction to the current state of the art, Section 3 discusses the new technology referred to as “knowledgebased tracker”: a tracker that exploits a-priori knowledge (e.g.: map data) to gain improved performance. Three applications follow: the first refers to the A-SMGCS (Advanced Surface Movement Guidance and Control System) for traffic control on the surface of an airport (section 4); in this case the target tracker is enhanced by exploiting the knowledge of the aerodrome map with runways, taxiways etc. The sensor is a high resolution surface based radar. The theme of section 5 is the tracking of ground moving or stationary vehicles using an airborne GMTI radar. Here we need to take care of the constraints imposed by the terrain (for which only uncertain data might be available), road networks and regions that could be not-trafficable. These information, also in this case, lead to finite support for the distribution of the target state; the classical Kalman filter doesn’t work well and KBS tracker is needed. The last application (section 6) refers to tracking of