相关论文: Stability and Convergence of Stochastic Particle F…

In this paper, we are interested in obtaining answers to the following questions for particle flow filters: Can we provide a theoretical guarantee that particle flow filters give correct results such as unbiased estimates? Are particle…

A key challenge when designing particle filters in high-dimensional state spaces is the construction of a proposal distribution that is close to the posterior distribution. Recent advances in particle flow filters provide a promising avenue…

A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…

Under multiplicative drift and other regularity conditions, it is established that the asymptotic variance associated with a particle filter approximation of the prediction filter is bounded uniformly in time, and the nonasymptotic,…

This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…

Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…

We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…

This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…

We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…

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…

Particle Flow Filters perform the measurement update by moving particles to a different location rather than modifying the particles' weight based on the likelihood. Their movement (flow) is dictated by a drift term, which continuously…

We present linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles two-way coupled to the fluid velocity field via Stokes drag (Saffman 1962). We extend…

We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general…

We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…

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…

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…

Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity,…