Improving Regularised Particle Filters
A new class of approximate nonlinear filter has been recently proposed, the idea being to produce a sample of independent random variables, called a particle system, (approximately) distributed according to this posterior probability distribution.
Exponential Forgetting and Geometric Ergodicity in Hidden Markov Models
It is proved that the prediction filter, and its gradient with respect to some parameter in the model, forget almost surely their initial condition exponentially fast, and the extended Markov chain is geometrically ergodic and has a unique invariant probability distribution.
STABILITY AND UNIFORM APPROXIMATION OF NONLINEAR FILTERS USING THE HILBERT METRIC AND APPLICATION TO PARTICLE FILTERS1
We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective…
Large sample asymptotics for the ensemble Kalman filter
The ensemble Kalman filter (EnKF) has been proposed as a Monte Carlo, derivative-free, alternative to the extended Kalman filter, and is now widely used in sequential data assimilation, where state…
Time discretization of continuous-time filters and smoothers for HMM parameter estimation
- M. James, V. Krishnamurthy, F. Gland
- Computer ScienceIEEE Transactions on Information Theory
- 1 March 1996
This paper presents two algorithms for parameter estimation of fast-sampled homogeneous Markov chains observed in white Gaussian noise, based on the robust discretization of continuous-time filters that were recently obtained by Elliott to estimate quantities used in the EM algorithm.
Genetic genealogical models in rare event analysis
We present in this article a genetic type interacting particle systems algorithm and a genealogical model for estimating a class of rare events arising in physics and network analysis. We represent…
Approximate nonlinear filtering by projection on exponential manifolds of densities
This paper introduces in detail a new systematic method to construct approximate finite-dimensional solutions for the nonlinear filtering problem. Once a finite-dimensional family is selected, the…
Basic Properties of the Projective Product with Application to Products of Column-Allowable Nonnegative Matrices
Basic properties of the projective product are used to obtain exponential bounds for the Lipschitz constant associated with the projectives product of column-allowable nonnegative matrices and for the associated linear tangent maps.
Nonlinear system fault detection and isolation based on bootstrap particle filters
- Qinghua Zhang, F. Campillo, F. Cérou, F. Gland
- EngineeringProceedings of the 44th IEEE Conference on…
- 12 December 2005
A particle filter based method for nonlinear system fault detection and isolation is proposed in this paper. It is applicable to quite general stochastic nonlinear dynamic systems in discrete time.…
Time-discretization of the Zakai equation for diffusion processes observed in correlated noise
A time discretization scheme is provided for the Zakai equation, a stochastic PDE which gives the conditional law of a diffusion process observed in white-noise, and an error estimate of order √β is proved for the overall numerical scheme.