 |
| Titel |
Efficient Particle Smoothers for large-dimensional problems |
| VerfasserIn |
Melanie Ades, Peter Jan van Leeuwen |
| Konferenz |
EGU General Assembly 2011
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250048378
|
|
|
|
|
|
| Zusammenfassung |
| With ever increasing model resolution and more complicated observations the data-assimilation
(or inverse) problem becomes more and more nonlinear. This calls for fully nonlinear
data-assimilation methods, such as particle filters and smoothers. Filters are optimal for
forecasting, but to study the dynamics of the real world, or to improve models, smoothers are
more appropriate. In this talk a particle smoother will be demonstrated that is applicable to
large-dimansional geophysical problems.
In Particle smoothers (and filters) the importance of each particle in estimating the
posterior density is dominated by the likelihood of that particle. In high-dimensional
systems with a large number of independent observations the likelihood can differ
substantially between particles resulting in only a few having statistical significance.
A standard procedure to try and increase the number of particles contributing to
the posterior is to use resampling, in which particles with very little input to the
posterior are abandoned and replaced with multiple copies of particles with a greater
statistical significance. As a consequence the trajectories of particles are no longer
continuous beyond the period between observations and hence the title Particle
Filter.
The idea of using the proposal density within the particle filter to provide a continuous
guidance towards a future observation has already been discussed in the literature. Using the
proposal density the aim is to increase the likelihood of all particles by ensuring
they end up significantly close to the observation. However the proposal density is
not restricted to continuous guidance but offers a much greater freedom in how
we treat the particles. In particular it can be used to ensure that the majority of
particles have an approximately equal significance in the posterior density and
hence remove the need for resampling. Without resampling the trajectories of the
particles become continuous over the whole time period leading to a fully nonlinear
smoother.
We will show how such a particle smoother is derived, and discuss the application of the
Particle smoother to the barotropic vorticity equations, both in the regime with periodic
trajectories and in the chaotic regime, with state dimensions of a few thousands and
more, using only tens of particles, showing that the degeneracy problem in particle
filtering/smoothing is something of the past. |
|
|
|
|
|
|