Semi-independent resampling for particle filtering

Among Sequential Monte Carlo (SMC) methods,Sampling Importance Resampling (SIR) algorithms are based on Importance Sampling (IS) and on some resampling-based)rejuvenation algorithm which aims at fighting against weight degeneracy. However %whichever the resampling technique used this mechanism tends to be insufficient when applied to informative or high-dimensional models. In this paper we revisit the rejuvenation mechanism and propose a class of parameterized SIR-based solutions which enable to adjust the tradeoff between computational cost and statistical performances

Independent Resampling Sequential Monte Carlo Algorithms

Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance Sampling with a bootstrap resampling step which aims at struggling against weights degeneracy. However, in some situations (informative measurements, high dimensional model), the resampling step can prove inefficient. In this paper, we revisit the fundamental resampling mechanism which leads us back to Rubin's static resampling mechanism. We propose an alternative rejuvenation scheme in which the resampled particles share the same marginal distribution as in the classical setup, but are now independent. This set of independent particles provides a new alternative to compute a moment of the target distribution and the resulting estimate is analyzed through a CLT. We next adapt our results to the dynamic case and propose a particle filtering algorithm based on independent resampling. This algorithm can be seen as a particular auxiliary particle filter algorithm with a relevant choice of the first-stage weights and instrumental distributions. Finally we validate our results via simulations which carefully take into account the computational budget

Estimating a CBRN atmospheric release in a complex environment using Gaussian Processes

International audienceIn this paper, we present a new methodology for the estimation and the prediction of the concentration of pollutant in a complex environment. We take benefit of a semi-parametric formulation of the problem to perform a faster and more efficient estimation of the pollutant cloud. In a first part, we present how we use the Gaussian process to model the interactions between position and time given the observations. Then, we introduce the expansion as a function of the observations through the time, and we construct an estimator of the time of release from it within change-point detection framework. Then, we use this time estimate to obtain the position (or more likely, a confidence region of the position) of the source. Several simulations are provided in a complex city scenario that demonstrate the accuracy of the proposed technique

Pilot-Aided Sequential Monte Carlo Estimation of Phase Distortions and Transmitted Symbols in Multicarrier Systems

We address the challenging problem of the joint estimation of transmitted symbols and phase distortions in standardized multicarrier systems, including pilot or virtual subcarriers. These subcarriers create time correlation on the useful transmitted OFDM signal that we propose to take into account by an autoregressive model. Because the phase distortions are nonlinear, we set the joint estimation algorithm on the framework of the Sequential Monte Carlo methods. Simulation results are provided in terms of bit error rate (BER) and mean square error (MSE); they highlight the efficiency and the robustness of the estimator.Peer Reviewe

Subgradient-Based Markov Chain Monte Carlo Particle Methods for Discrete-Time Nonlinear Filtering

This work shows how a carefully designed instrumental distribution can improve the performance of a Markov chain Monte Carlo (MCMC) filter for systems with a high state dimension. We propose a special subgradient-based kernel from which candidate moves are drawn. This facilitates the implementation of the filtering algorithm in high dimensional settings using a remarkably small number of particles. We demonstrate our approach in solving a nonlinear non-Gaussian high-dimensional problem in comparison with a recently developed block particle filter and over a dynamic compressed sensing (l1 constrained) algorithm. The results show high estimation accuracy

Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced. © 2013 Elsevier Inc. All rights reserved

Rare coding variants in PLCG2, ABI3, and TREM2 implicate microglial-mediated innate immunity in Alzheimer's disease

We identified rare coding variants associated with Alzheimer’s disease (AD) in a 3-stage case-control study of 85,133 subjects. In stage 1, 34,174 samples were genotyped using a whole-exome microarray. In stage 2, we tested associated variants (P<1×10-4) in 35,962 independent samples using de novo genotyping and imputed genotypes. In stage 3, an additional 14,997 samples were used to test the most significant stage 2 associations (P<5×10-8) using imputed genotypes. We observed 3 novel genome-wide significant (GWS) AD associated non-synonymous variants; a protective variant in PLCG2 (rs72824905/p.P522R, P=5.38×10-10, OR=0.68, MAFcases=0.0059, MAFcontrols=0.0093), a risk variant in ABI3 (rs616338/p.S209F, P=4.56×10-10, OR=1.43, MAFcases=0.011, MAFcontrols=0.008), and a novel GWS variant in TREM2 (rs143332484/p.R62H, P=1.55×10-14, OR=1.67, MAFcases=0.0143, MAFcontrols=0.0089), a known AD susceptibility gene. These protein-coding changes are in genes highly expressed in microglia and highlight an immune-related protein-protein interaction network enriched for previously identified AD risk genes. These genetic findings provide additional evidence that the microglia-mediated innate immune response contributes directly to AD development

Méthodes séquentielles de Monte-Carlo pour les systèmes multiporteuses en présence de distorsions de phase

Thèse de doctorat en Electronique, Université de Valenciennes et du Hainaut-Cambrésis, 14 maiMulticarrier transmission systems have aroused great interest in recent years as a potential solution to the problem of transmitting high data rate over a frequency selective fading channel. Nowadays, multicarrier modulation is being selected as the transmission scheme for the majority of new communication systems. However, multicarrier systems are very sensitive to phase noise and carrier frequency offset caused by the oscillator instabilities. In this thesis, a general receiver for compensating the phase distortions effects in multicarrier systems is proposed. Our approach to this non-linear problem is based on Bayesian inference using sequential Monte Carlo filtering also referred to as particle filtering. First, the problem of channel estimation in the presence of phase noise and carrier frequency offset is addressed. Then, a particle filter is proposed to include the joint signal, phase noise and carrier frequency offset estimation. The proposed sequential Monte Carlo filters are efficiently implemented by combining sequential importance sampling, a selection scheme, a variance reduction technique and especially a new on-line parameter estimation based on parallel stochastic expectation maximization algorithms. Moreover in order to improve the estimation accuracy, an original autoregressive modeling of the time-domain multicarrier signal including either pilot or null-subcarriers is also proposed. Extensive simulation study is provided to illustrate the efficiency and the robustness of the proposed algorithms in comparison with those of existing schemesDans le contexte d’une demande croissante de débits de communications de plus en plus élevés, les systèmes multiporteuses ont suscité un grand intérêt dans la communauté scientifique depuis ces dernières années et sont désormais employées dans de nombreux systèmes de communication. Malheureusement, ce type de système est extrêmement sensible aux distorsions de phase, comme le bruit de phase et le décalage fréquentiel de la porteuse, engendrées par l’instabilité des oscillateurs locaux. Le but de cette thèse est donc de concevoir un récepteur capable de compenser ces perturbations. Notre approche à ce problème non-linéaire est basée sur l’inférence Bayésienne et plus particulièrement sur les méthodes séquentielles de Monte-Carlo, appelées également filtrage particulaire. En premier lieu, nous proposons un estimateur conjoint du canal et des distorsions de phase grâce à une séquence d’apprentissage. Ensuite, nous traitons le problème de l’estimation des données en présence de distorsions de phase. Les filtres particulaires proposés sont implémentés efficacement en combinant le principe d’échantillonnage par importance, un schéma de sélection, une technique de réduction de variance d’estimée et surtout un nouvel estimateur “on-line” de paramètres utilisant des algorithmes d’espérance-maximisation stochastique parallèles. De plus, dans le but toujours d’augmenter l’efficacité et la robustesse de nos estimateurs, nous proposons une modélisation originale du signal multiporteuses dans le domaine temporel par un processus autorégréssif dans le cas où des porteuses nulles ou pilotes sont présente

A Robust High-Dimensional Bayesian Filter: the Stochastic GH-GEnKF

International audienc