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"Tikhonov" EKI in the literature, is achieved by applying the standard algorithms to an augmented state.
Namely, for tikhonov parameter a, and a prior N(m,C) the typical update is computed with the change:
G(u) -> [G(u),u]'
y -> [y,m]'
Gamma -> [Gamma 0; 0 a*C]
Currently we leave such changes to be completed by the user. However we could produce an interface for this, if it is of interest.
Possible Solution
In one interface, the user provides additionally a Tikhonov constant a (default 1) and the prior distribution
This must take place at/before construction of EKP
The user will call update_ensemble!(...) with G(u) as usual
During update_ensemble! the augmentations are applied to states.
When performing this internally (vs leaving it to user) imlementations must take care of additional locations where there is misalignments of state.
compute_error! will need to include the prior term
adaptive scheduler computations may require the prior term
and possible index issues for update-groups
Finally one must note that
UKI, currently has an impose_prior flag, and EKS, GNKI hav prior contributions by definition. So one may need to reconcile consistency here (e.g., impose_prior = true is the same as the Tikhonov with a=1?)
The text was updated successfully, but these errors were encountered:
Issue
"Tikhonov" EKI in the literature, is achieved by applying the standard algorithms to an augmented state.
Namely, for tikhonov parameter
a
, and a priorN(m,C)
the typical update is computed with the change:G(u) -> [G(u),u]'
y -> [y,m]'
Gamma -> [Gamma 0; 0 a*C]
Currently we leave such changes to be completed by the user. However we could produce an interface for this, if it is of interest.
Possible Solution
a
(default 1) and the prior distributionWhen performing this internally (vs leaving it to user) imlementations must take care of additional locations where there is misalignments of state.
Finally one must note that
impose_prior
flag, and EKS, GNKI hav prior contributions by definition. So one may need to reconcile consistency here (e.g.,impose_prior = true
is the same as the Tikhonov witha=1
?)The text was updated successfully, but these errors were encountered: