ASPI :
Applications of interacting particle systems to statistics
Post-doctoral position opened in 2005 / 2006
Generalized particle filtering
Location : IRISA / INRIA Rennes
Duration : one year, starting September 2005 (or later)
Application deadline : April 22, 2005 (electronic
application file :
Word)
Team :
ASPI (Applications
of interacting particle systems to statistics)
Contact :
François Le Gland
(tél. : +33 (0)2 99 84 73 62,
e-mail : legland@irisa.fr)
Background :
probability numerics, statistics, particle filtering,
Monte Carlo methods, MATLAB or SCILAB programming
Subject :
Particle filtering is a numerical method for the approximation of the
optimal Bayesian filter in hidden Markov models (HMM), which has found
numerous applications in localization, navigation and tracking of
mobiles, either in defence areas (aircraft, surface ship, submarine,
missile, drone, etc.) or in civilian areas (automobile, cellular phone,
PDA, mobile robot, etc.).
It is commonly assumed that implementing a particle filter algorithms
requires being able to
- simulate independent realizations of the hidden state,
- and evaluate a likelihood function which quantifies
the consistency of each simulated state with the current observation.
The subject of this post-doc project is to bring original contributions
both to the theoretical level and to the applications level, that will
allow to get rid of this assumption and to extend significantly the
domain of application of particle filtering.
It is based on the idea of regularizing the observations, some special
cases of which have been considered by Del Moral-Jacod-Protter and
by Rossi. Ultimately, it is enough to
- jointly simulate independent realizations of the hidden
state and the observation,
- and validate each simulated pair (hidden state,
observation) against the current observation.
If a binary validation rule is used, it may very well happen that all
the simulated pairs are rejected, in which case the sequential particle
algorithm introduced by LeGland-Oudjane should be used, which
automatically keeps the particle system alive.
With this class of algorithms, it is no longer necessary to evaluate
a likelihood function, which opens the possibility to approximate the
optimal Bayesian filter in situations where
- no explicit expression is available for the likelihood function,
- there is no likelihood function (for instance because the observation
noise does not appear in an additive way),
- there is no noise on (some components of) the observation, which can
be interpreted as a posterior constraint on the hidden state, etc.
The objective of this post-doc project is to design algorithms based
on the generalized particle filtering idea, to study their mathematical
properties and to implement them in various applications pertaining
to localization, navigation and tracking of mobiles.
Bibliography :
- P. Del Moral, J. Jacod, Ph. Protter,
The Monte Carlo method for filtering with discrete-time
observations, Probability Theory and Related Fields,
120, 3, pp. 346-368, 2001.
- F. Le Gland, N. Oudjane,
Stability and uniform approximation of nonlinear filters
using the Hilbert metric, and application to particle filters,
The Annals of Applied Probability,
14, 1, pp. 144-187, Feb. 2004.
- V. Rossi,
Filtrage non-linéaire par noyaux de
convolution,
Thèse de Doctorat, ENSAM, Montpellier, Déc. 2004.
