227 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
Riemann-Langevin Particle Filtering in Track-Before-Detect
Track-before-detect (TBD) is a powerful approach that consists in providing
the tracker with sensor measurements directly without pre-detection. Due to the
measurement model non-linearities, online state estimation in TBD is most
commonly solved via particle filtering. Existing particle filters for TBD do
not incorporate measurement information in their proposal distribution. The
Langevin Monte Carlo (LMC) is a sampling method whose proposal is able to
exploit all available knowledge of the posterior (that is, both prior and
measurement information). This letter synthesizes recent advances in LMC-based
filtering to describe the Riemann-Langevin particle filter and introduces its
novel application to TBD. The benefits of our approach are illustrated in a
challenging low-noise scenario.Comment: Minor grammatical update
Invertible Particle Flow-based Sequential MCMC with extension to Gaussian Mixture noise models
Sequential state estimation in non-linear and non-Gaussian state spaces has a
wide range of applications in statistics and signal processing. One of the most
effective non-linear filtering approaches, particle filtering, suffers from
weight degeneracy in high-dimensional filtering scenarios. Several avenues have
been pursued to address high-dimensionality. Among these, particle flow
particle filters construct effective proposal distributions by using invertible
flow to migrate particles continuously from the prior distribution to the
posterior, and sequential Markov chain Monte Carlo (SMCMC) methods use a
Metropolis-Hastings (MH) accept-reject approach to improve filtering
performance. In this paper, we propose to combine the strengths of invertible
particle flow and SMCMC by constructing a composite Metropolis-Hastings (MH)
kernel within the SMCMC framework using invertible particle flow. In addition,
we propose a Gaussian mixture model (GMM)-based particle flow algorithm to
construct effective MH kernels for multi-modal distributions. Simulation
results show that for high-dimensional state estimation example problems the
proposed kernels significantly increase the acceptance rate with minimal
additional computational overhead and improve estimation accuracy compared with
state-of-the-art filtering algorithms
Accelerating MCMC Algorithms
Markov chain Monte Carlo algorithms are used to simulate from complex
statistical distributions by way of a local exploration of these distributions.
This local feature avoids heavy requests on understanding the nature of the
target, but it also potentially induces a lengthy exploration of this target,
with a requirement on the number of simulations that grows with the dimension
of the problem and with the complexity of the data behind it. Several
techniques are available towards accelerating the convergence of these Monte
Carlo algorithms, either at the exploration level (as in tempering, Hamiltonian
Monte Carlo and partly deterministic methods) or at the exploitation level
(with Rao-Blackwellisation and scalable methods).Comment: This is a survey paper, submitted WIREs Computational Statistics, to
with 6 figure
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
- …