Related papers: Error Analysis of the Stochastic Linear Feedback P…
The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…
Ensemble Kalman--Bucy filters (EnKBFs) are an important tool in Data Assimilation that aim to approximate the posterior distribution for continuous time filtering problems using an ensemble of interacting particles. In this work we extend a…
Several particle algorithms admit a Feynman-Kac representation such that the potential function may be expressed as a recursive function which depends on the complete state trajectory. An important example is the mixture Kalman filter, but…
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…
Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…
The Kalman filter is ubiquitous for state space models because of its desirable statistical properties, ease of implementation, and generally good performance. However, it can perform poorly in the presence of outliers, or measurements with…
We study a population of $N$ particles, which evolve according to a diffusion process and interact through a dynamical network. In turn, the evolution of the network is coupled to the particles' positions. In contrast with the mean-field…
Recurrent neural networks (RNNs) have been extraordinarily successful for prediction with sequential data. To tackle highly variable and noisy real-world data, we introduce Particle Filter Recurrent Neural Networks (PF-RNNs), a new RNN…
Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods face significant obstacles: Gaussian-based filters struggle…
This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and…
We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial…
This article examines large time behaviour of finite state mean-field interacting particle systems. Our first main result is a sharp estimate (in the exponential scale) on the time required for convergence of the empirical measure process…
We address the problem of observation noise misspecification in Bayesian filtering of dynamical systems via recent advances in generalised Bayesian inference. Mis-match in tail decay between the true data generating process and an assumed…
This paper addresses two interrelated problems of the nonlinear filtering mechanism and fast attitude filtering with the matrix Fisher distribution (MFD) on the special orthogonal group. By analyzing the distribution evolution along Bayes'…
In this work, we propose a Deep neural network-assisted Particle Filter-based (DePF) approach to address the Mobile User (MU) joint synchronization and localization (sync\&loc) problem in ultra dense networks. In particular, DePF deploys an…
A common assumption in signal processing is that underlying data numerically conforms to a Gaussian distribution. It is commonly utilized in signal processing to describe unknown additive noise in a system and is often justified by citing…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
We present Neural Bayesian Filtering (NBF), an algorithm for maintaining distributions over hidden states, called beliefs, in partially observable systems. NBF is trained to find a good latent representation of the beliefs induced by a…
Iterative algorithms based on thresholding, feedback and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and fast, particularly for large scale problems. The core algorithm is shown to converge in finitely…
This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to…