Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

/pdf/sequential-monte-carlo-methods-in-practice-3kfxeebn8e.pdf

Sequential Monte Carlo methods in practice

Particle methods have been recently proposed to deal with the nonlinear filtering problem. These are Monte Carlo methods that can provide a nonparametric approximation to the signal conditional distribution even in nonlinear and non Gaussian cases, without depending on the state space dimension. We present a new version of regularized particle filter using a progressive correction (PC) principle which improves the approximation, in introducing a decreasing sequence of (fictitious) matrices for the observation noise. This method is applied to the multisensor tracking problem (radar and IR sensor) and compared to the classical regularized particle filter and the EKF.

Progressive correction for regularized particle filters

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the variational Gaussian process smoother with an exact solution computed using a hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while marginal variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother.

/pdf/evaluation-of-variational-and-markov-chain-monte-carlo-1o8smc1q2x.pdf

Evaluation of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems

This Ph.D. thesis is concerned with the development of algorithms for the detection and tracking of multiple targets using wireless sensor networks from the Bayesian standpoint. This is achieved by calculating the probability density function (PDF) of the multitarget state given the sensor measurements (posterior PDF) as it includes all the useful information to perform these tasks. The models of the target dynamics and the sensor measurements are usually nonlinear/non-Gaussian. Therefore, the posterior PDF cannot be calculated in closed form and approximations need to be made. Particle filters' approximations to the posterior PDF are convergent if the number of particles tends to infinity. However, in a practical situation, the computer power available is limited. As a result, the number of particles is bounded and particle filter performance is not guaranteed to be high. This decrease in performance due to the limited computational power is even more acute in a multiple target situation because of the high dimension of the state. 

Therefore, this thesis focuses on the development of particle filtering techniques with lower computational burden and higher performance than previously developed ones. Three different scenarios are considered: the detection and tracking of an unknown and variable number of targets using a sensor network, the tracking of targets when there is uncertainty in the sensor positions and the tracking of targets when a non-synchronised sensor network is used.

As regards the detection and tracking of an unknown and variable number of targets, a particle filter with two layers is proposed to detect targets and an efficient algorithm, called the parallel partition method, is developed to track the detected targets. Also, a technique to extract target labelling information when there are two targets is proposed. That is, the filter is able to decide which target is which and determine the probability of error.

The tracking of targets when there is uncertainty in the sensor positions is carried out by simultaneously localising the sensors and tracking the targets using simultaneous localisation and mapping (SLAM) techniques, traditionally used in the field of robotics. However, the multiple target nature of the problem implies that traditional SLAM techniques are not suitable and a new technique, which is based on the parallel partition method, is proposed to overcome the problems of conventional SLAM techniques. Additionally, the truncated Kalman filter also presented in this thesis is of great importance to estimate the positions of the sensors and is shown to be a very useful filtering technique that can be applied to a variety of filtering problems.

When the sensors are not synchronised, conventional particle filtering techniques have a large computational load. Therefore, in this thesis, the asynchronous particle filter is proposed to lower their computational burden while providing accurate estimates.

Detection and tracking of multiple targets using wireless sensor networks - Detección y seguimiento de múltiples blancos en redes inalámbricas de sensores

It has recently been proved by J.M.C. Clark et al. that the relative entropy (or Kullback-Leibler information distance) between two nonlinear filters with different initial conditions is a supermartingale, hence its expectation can only decrease with time. This result was obtained for a very general model, where the unknown state and observation processes form jointly a continuous-time Markov process. The purpose of this paper is (i) to extend this result to a large class of f-divergences, including the total variation distance, the Hellinger distance, and not only the Kullback-Leibler information distance, and (ii) to consider not only robustness w.r.t. the initial condition of the filter, but also w.r.t. perturbation of the state generator. On the other hand, the model considered here is much less general, and consists of a diffusion process observed in discrete-time.

https://www.irisa.fr/aspi/legland/pub/cdc99.pdf

Stability and approximation of nonlinear filters: an information theoretic approach

Statistical methods for general state-space models

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Statistical methods for general state-space models