Related papers: Multilevel Particle Filters for the Non-Linear Fil…
We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…
We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…
Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity.…
Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF)…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…
In this paper we consider the continuous--time nonlinear filtering problem, which has an infinite--dimensional solution in general, as proved by Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for which the optimal…
We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
In this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous time state space model with discrete time observations by an algorithm that combines the Kalman filter and a particle…
Motivated by non-linear, non-Gaussian, distributed multi-sensor/agent navigation and tracking applications, we propose a multi-rate consensus/fusion based framework for distributed implementation of the particle filter (CF/DPF). The CF/DPF…
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
Spatio-temporal data sets are rapidly growing in size. For example, environmental variables are measured with ever-higher resolution by increasing numbers of automated sensors mounted on satellites and aircraft. Using such data, which are…
Our article deals with Bayesian inference for a general state space model with the simulated likelihood computed by the particle filter. We show empirically that the partially or fully adapted particle filters can be much more efficient…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…
This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key…
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…
We consider the problem of nonlinear filtering of one-dimensional diffusions from noisy measurements. The filter is said to lose lock if the estimation error exits a prescribed region. In the case of phase estimation this region is one…
Advances in compact sensing devices mounted on satellites have facilitated the collection of large spatio-temporal datasets with coordinates. Since such datasets are often incomplete and noisy, it is useful to create the prediction surface…