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Numerous fields of nonlinear physics, very different in nature, produce signals and images, that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding…
We consider nonlinear filters for diffusion processes when the observation and signal noises are small and of the same order. As the noise intensities approach zero, the nonlinear filter can be approximated by a certain variational problem…
In modern days, the ability to carry out computations in parallel is key to efficient implementations of computationally intensive algorithms. This paper investigates the applicability of the previously proposed Augmented Island Resampling…
In this paper, approximate Linear Minimum Variance (LMV) filters for continuous-discrete state space models are introduced. The filters are obtained by means of a recursive approximation to the predictions for the first two moments of the…
We introduce a modified algorithm to perform nonlinear filtering of a time series by locally linear phase space projections. Unlike previous implementations, the algorithm can be used not only for a posteriori processing but includes the…
Differentiable particle filters are an emerging class of models that combine sequential Monte Carlo techniques with the flexibility of neural networks to perform state space inference. This paper concerns the case where the system may…
The purpose of this paper is to describe the feedback particle filter algorithm for problems where there are a large number ($M$) of non-interacting agents (targets) with a large number ($M$) of non-agent specific observations…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
This work concerns the nonlinear filtering problem of multiscale McKean-Vlasov stochastic systems where the whole systems depend on distributions of fast components. First of all, we prove that the slow component of the original system…
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic…
We deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. Previous works by several authors have shown that the error structure of the method is characterized by…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
"Particle methods" are sequential Monte Carlo algorithms, typically involving importance sampling, that are used to estimate and sample from joint and marginal densities from a collection of a, presumably increasing, number of random…
Localization using time-difference of arrival (TDOA) has myriad applications, e.g., in passive surveillance systems and marine mammal research. In this paper, we present a Bayesian estimation method that can localize an unknown number of…
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…
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…
We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…
Particle probability hypothesis density filtering has become a promising means for multi-target tracking due to its capability of handling an unknown and time-varying number of targets in non-linear non-Gaussian system. However, its…