Related papers: Poisson's equation in nonlinear filtering
Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…
We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given…
In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter…
In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a…
The problem of phase retrieval has many applications in the field of optical imaging. Motivated by imaging experiments with biological specimens, we primarily consider the setting of low-dose illumination where Poisson noise plays the…
We propose a recursive particle filter for high-dimensional problems that inherently never degenerates. The state estimate is represented by deterministic low-discrepancy particle sets. We focus on the measurement update step, where a…
In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms--also known as particle filters--relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be…
This paper presents a new derivation of the variational Poisson multi-Bernoulli (V-PMB) filter for multi-target estimation proposed in [#Williams15]. The proposed derivation is based on considering an augmented space that includes the set…
Resampling is a key component of sample-based recursive state estimation in particle filters. Recent work explores differentiable particle filters for end-to-end learning. However, resampling remains a challenge in these works, as it is…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…
We consider particle filters with weakly informative observations (or `potentials') relative to the latent state dynamics. The particular focus of this work is on particle filters to approximate time-discretisations of continuous-time…
In this paper, we develop a drift homotopy implicit particle filter method. The methodology of our approach is to adopt the concept of drift homotopy in the resampling procedure of the particle filter method for solving the nonlinear…
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
We introduce an auxiliary technique, called residual nudging, to the particle filter to enhance its performance in cases that it performs poorly. The main idea of residual nudging is to monitor, and if necessary, adjust the residual norm of…
A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…