Related papers: Error Analysis of the Stochastic Linear Feedback P…
Filtering for stochastic reaction networks (SRNs) is an important problem in systems/synthetic biology aiming to estimate the state of unobserved chemical species. A good solution to it can provide scientists valuable information about the…
We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…
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…
A decentralized approach for joint frequency and phase synchronization in distributed antenna arrays is presented. The nodes in the array share their frequencies and phases with their neighboring nodes to align these parameters across the…
Particle flow Gaussian particle flow (PFGPF) uses an invertible particle flow to generate a proposal density. It approximates the predictive and posterior distributions as Gaussian densities. In this paper, we use bank of PFGPF filters to…
In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we…
The random batch method (RBM) proposed in [Jin et al., J. Comput. Phys., 400(2020), 108877] for large interacting particle systems is an efficient with linear complexity in particle numbers and highly scalable algorithm for $N$-particle…
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…
This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter,…
Particle filters (PFs) form a class of Monte Carlo algorithms that propagate over time a set of $N\geq 1$ particles which can be used to estimate, in an online fashion, the sequence of filtering distributions $(\hat{\eta}_t)_{t\geq 1}$…
We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. Thus, the computational task is to estimate a time-evolving density $\rho(v, t)$ given noisy observations of the true density…
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…
This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling…
The frequency-domain Kalman filter (FKF) has been utilized in many audio signal processing applications due to its fast convergence speed and robustness. However, the performance of the FKF in under-modeling situations has not been…
This work studies the mean-square stability and stabilization problem for networked feedback systems. Data transmission delays in the network channels of the systems are considered. It is assumed that these delays are i.i.d. processes with…
Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…
A new formulation of the particle filter for nonlinear filtering is presented, based on concepts from optimal control, and from the mean-field game theory. The optimal control is chosen so that the posterior distribution of a particle…
The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble…
The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…