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Ensemble Kalman filter prediction step.
tfp.experimental.sequential.ensemble_kalman_filter_predict(
state, transition_fn, seed=None, inflate_fn=None, name=None
)
The Ensemble Kalman Filter is a Monte Carlo version of the traditional Kalman Filter. See also [2]. It assumes the model
X[t] ~ transition_fn(X[t-1])
Y[t] ~ observation_fn(X[t])
Given the ensemble state.particles
sampled from P(X[t-1] | Y[t-1], ...)
,
this function produces the predicted (a.k.a. forecast or background) ensemble
sampled from P(X[t] | Y[t-1], ...)
. This is the predicted next state
before assimilating the observation Y[t]
.
Typically, with F
some deterministic mapping, transition_fn(X)
returns a
normal distribution centered at F(X)
.
Args | |
---|---|
state
|
Instance of EnsembleKalmanFilterState .
|
transition_fn
|
callable returning a (joint) distribution over the next
latent state, and any information in the extra state.
Each component should be an instance of
MultivariateNormalLinearOperator .
|
seed
|
PRNG seed; see tfp.random.sanitize_seed for details.
|
inflate_fn
|
Function that takes in the particles and returns a new set of
particles . Used for inflating the covariance of points. Note this
function should try to preserve the sample mean of the particles, and
scale up the sample covariance [3].
|
name
|
Python str name for ops created by this method.
Default value: None (i.e., 'ensemble_kalman_filter_predict' ).
|
Returns | |
---|---|
next_state
|
EnsembleKalmanFilterState representing particles after
applying transition_fn .
|
References
[1] Geir Evensen. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research, 1994.
[2] Matthias Katzfuss, Jonathan R. Stroud & Christopher K. Wikle Understanding the Ensemble Kalman Filter. The Americal Statistician, 2016.
[3] Jeffrey L. Anderson and Stephen L. Anderson. A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts. Monthly Weather Review, 1999.