557 research outputs found
Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces
Nonlinear non-Gaussian state-space models arise in numerous applications in
statistics and signal processing. In this context, one of the most successful
and popular approximation techniques is the Sequential Monte Carlo (SMC)
algorithm, also known as particle filtering. Nevertheless, this method tends to
be inefficient when applied to high dimensional problems. In this paper, we
focus on another class of sequential inference methods, namely the Sequential
Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising
alternative to SMC methods. After providing a unifying framework for the class
of SMCMC approaches, we propose novel efficient strategies based on the
principle of Langevin diffusion and Hamiltonian dynamics in order to cope with
the increasing number of high-dimensional applications. Simulation results show
that the proposed algorithms achieve significantly better performance compared
to existing algorithms
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
Efficient Sequential Monte-Carlo Samplers for Bayesian Inference
In many problems, complex non-Gaussian and/or nonlinear models are required
to accurately describe a physical system of interest. In such cases, Monte
Carlo algorithms are remarkably flexible and extremely powerful approaches to
solve such inference problems. However, in the presence of a high-dimensional
and/or multimodal posterior distribution, it is widely documented that standard
Monte-Carlo techniques could lead to poor performance. In this paper, the study
is focused on a Sequential Monte-Carlo (SMC) sampler framework, a more robust
and efficient Monte Carlo algorithm. Although this approach presents many
advantages over traditional Monte-Carlo methods, the potential of this emergent
technique is however largely underexploited in signal processing. In this work,
we aim at proposing some novel strategies that will improve the efficiency and
facilitate practical implementation of the SMC sampler specifically for signal
processing applications. Firstly, we propose an automatic and adaptive strategy
that selects the sequence of distributions within the SMC sampler that
minimizes the asymptotic variance of the estimator of the posterior
normalization constant. This is critical for performing model selection in
modelling applications in Bayesian signal processing. The second original
contribution we present improves the global efficiency of the SMC sampler by
introducing a novel correction mechanism that allows the use of the particles
generated through all the iterations of the algorithm (instead of only
particles from the last iteration). This is a significant contribution as it
removes the need to discard a large portion of the samples obtained, as is
standard in standard SMC methods. This will improve estimation performance in
practical settings where computational budget is important to consider.Comment: arXiv admin note: text overlap with arXiv:1303.3123 by other author
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
Sequential Markov Chain Monte Carlo for multi-target tracking with correlated RSS measurements
In this paper, we present a Bayesian approach to accurately track multiple objects based on Received Signal Strength (RSS) measurements. This work shows that taking into account the spatial correlations of the observations caused by the random shadowing effect can induce significant tracking performance improvements, especially in very noisy scenarios. Additionally, the superiority of the proposed Sequential Markov Chain Monte Carlo (SMCMC) method over the more common Sequential Importance Resampling (SIR) technique is empirically demonstrated through numerical simulations in which multiple targets have to be tracked
Gradient based sequential Markov chain Monte Carlo for multitarget tracking with correlated measurements
Measurements in wireless sensor networks (WSNs) are often correlated both in space and in time. This paper focuses on tracking multiple targets in WSNs by taking into consideration these measurement correlations. A sequential Markov Chain Monte Carlo (SMCMC) approach is proposed in which a Metropolis within Gibbs refinement step and a likelihood gradient proposal are introduced. This SMCMC filter is applied to case studies with cellular network received signal strength data in which the shadowing component correlations in space and time are estimated. The efficiency of the SMCMC approach compared to particle filtering, as well as the gradient proposal compared to a basic prior proposal, are demonstrated through numerical simulations. The accuracy improvement with the gradient-based SMCMC is above 90% when using a low number of particles. Thanks to its sequential nature, the proposed approach can be applied to various WSN applications, including traffic mobility monitoring and prediction
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