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| Titel |
The equivalent weights particle filter |
| VerfasserIn |
M. Ades, P. J. van Leeuwen |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250070357
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| Zusammenfassung |
| The majority of data assimilation schemes rely on linearity assumptions. However as the
resolution and complexity of both the numerical models and observations increases these
linearity assumptions become less appropriate. A need is arising for data assimilation
schemes, such as Particle filters, which are fully nonlinear. Particle filters aim to represent the
full probability density of the state of the system given the observations (the posterior) by an
ensemble of particles. The importance of each particle in determining the posterior is given
by the likelihood of that particle, or the distance between the particle and the observations. 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. Hence the ability of the particle filter to represent the full posterior is severely
diminished.
Proposal densities have been used in the past to bring the particles closer to the
observations, thus increasing their likelihood, and making their weights more equal.
However, even the so-called ’Optimal Proposal Density’, which draws samples from the
transition density given the future observations, suffers from wildly varying weights when the
number of independent observations is large. The recently proposed Implicit Particle Filter
falls in the same category.
Here we look at the effect of using proposal densities as part of a particle filter in a high
dimensional system, exploring the freedom of proposal density to not only bring the particles
close to the observations, but also to ensure that the final weights are equivalent. With the
majority of particles being both close to the observations and having equivalent significance,
the ability to represent a multi-modal posterior density with only a few particles starts to be
realised.
The success of the scheme is examined using the Barotropic Vorticity equation with a
state dimension of over 50,000 in a highly nonlinear regime. Specifically, we observe the
system every 50 time steps, while the decorrelation time of the dynamics is about 25
time steps, resulting in a very nonlinear data assimilation problem. We present a
thorough analysis of the performance of the new scheme in this geophysical model of
intermediate complexity. The spread of the ensemble and the marginal posterior
probability density functions are discussed, in particular as the number of state
variables observed is decreased, both uniformly and blacking out large patches of state
space. |
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