|
|
| |
| Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation |
| |
Citation： |
David KELLY,Andrew M. STUART.Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation[J].Chinese Annals of Mathematics B,2019,40(5):811~842 |
| Page view： 572
Net amount： 436 |
Authors： |
David KELLY; Andrew M. STUART |
Foundation： |
This work was supported by EPSRC (EQUIPS Program Grant),
DARPA (contract W911NF-15-2-0121) and ONR (award N00014-17-1-2079). |
|
|
| Abstract： |
Data assimilation refers to the methodology of combining dynamical
models and observed data with the objective of improving state
estimation. Most data assimilation algorithms are viewed as
approximations of the Bayesian posterior (filtering distribution) on
the signal given the observations. Some of these approximations are
controlled, such as particle filters which may be refined to produce
the true filtering distribution in the large particle number limit,
and some are uncontrolled, such as ensemble Kalman filter methods
which do not recover the true filtering distribution in the large
ensemble limit. Other data assimilation algorithms, such as cycled
3DVAR methods, may be thought of as controlled estimators of the
state, in the small observational noise scenario, but are also
uncontrolled in general in relation to the true filtering
distribution. For particle filters and ensemble Kalman filters it is
of practical importance to understand how and why data assimilation
methods can be effective when used with a fixed small number of
particles, since for many large-scale applications it is not
practical to deploy algorithms close to the large particle limit
asymptotic. In this paper, the authors address this question for
particle filters and, in particular, study their accuracy (in the
small noise limit) and ergodicity (for noisy signal and observation)
without appealing to the large particle number limit. The authors
first overview the accuracy and minorization properties for the true
filtering distribution, working in the setting of conditional
Gaussianity for the dynamics-observation model. They then show that
these properties are inherited by optimal particle filters for any
fixed number of particles, and use the minorization to establish
ergodicity of the filters. For completeness we also prove large
particle number consistency results for the optimal particle
filters, by writing the update equations for the underlying
distributions as recursions. In addition to looking at the optimal
particle filter with standard resampling, they derive all the above
results for (what they term) the Gaussianized optimal particle
filter and show that the theoretical properties are favorable for
this method, when compared to the standard optimal particle filter. |
Keywords： |
Particle filters, Data assimilation, Ergodic theory |
Classification： |
60G35, 62M20, 37H99, 60F99 |
|
|
Download PDF Full-Text
|
|
|
|
