Related papers: Gain Function Approximation in the Feedback Partic…
This paper is concerned with the analysis of the kernel-based algorithm for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted…
In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical…
Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation of the FPF algorithm, the main challenge is to numerically…
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…
The feedback particle filter (FPF) is an innovative, control-oriented and resampling-free adaptation of the traditional particle filter (PF). In the FPF, individual particles are regulated via a feedback gain, and the corresponding gain…
Control-type particle filters have been receiving increasing attention over the last decade as a means of obtaining sample based approximations to the sequential Bayesian filtering problem in the nonlinear setting. Here we analyse one such…
The feedback particle filter (FPF) is a promising nonlinear filtering (NLF) method, but its practical implementation is hindered by the intractability of the gain function, which satisfies a boundary value problem (BVP). This paper proposes…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
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…
The feedback particle filter (FPF), a resampling-free algorithm proposed over a decade ago, modifies the particle filter (PF) by incorporating a feedback structure. Each particle in FPF is regulated via a feedback gain function (lacking a…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort is dedicated to the development of numerical methods for approximating the solution of the filtering…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
We study an approximation method for the one-dimensional nonlinear filtering problem, with discrete time and continuous time observation. We first present the method applied to the Fokker-Planck equation. The convergence of the…
Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin…
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…
Feedback particle filter (FPF) is an algorithm to numerically approximate the solution of the nonlinear filtering problem in continuous time. The algorithm implements a feedback control law for a system of particles such that the empirical…
Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…
Feedback particle filter (FPF) is a Monte-Carlo (MC) algorithm to approximate the solution of a stochastic filtering problem. In contrast to conventional particle filters, the Bayesian update step in FPF is implemented via a mean-field type…