Related papers: Poisson's equation in nonlinear filtering

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…

We propose a method for optimal Bayesian filtering with deterministic particles. In order to avoid particle degeneration, the filter step is not performed at once. Instead, the particles progressively flow from prior to posterior. This is…

A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a second-order information functional with respect to the…

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

This work concerns the nonlinear filtering problem of multiscale McKean-Vlasov stochastic systems where the whole systems depend on distributions of fast components. First of all, we prove that the slow component of the original system…

The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle…

The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…

In recent work it is shown that importance sampling can be avoided in the particle filter through an innovation structure inspired by traditional nonlinear filtering combined with Mean-Field Game formalisms. The resulting feedback particle…

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior…

State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to…

We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…

This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…

Particle filters are applicable to a wide range of nonlinear, non-Gaussian state-space models and have already been applied to a variety of problems. However, there is a problem in the calculation of smoothed distributions, where particles…

Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…

Recent works on deep non-linear spatially selective filters demonstrate exceptional enhancement performance with computationally lightweight architectures for stationary speakers of known directions. However, to maintain this performance in…

Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating…

We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…

Particle filters flexibly represent multiple posterior modes nonparametrically, via a collection of weighted samples, but have classically been applied to tracking problems with known dynamics and observation likelihoods. Such generative…