Ensemble Kalman filter update step.

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] | Y[t-1], ...), this function assimilates obervation Y[t] to produce the updated ensemble sampled from P(X[t] | Y[t], ...).

Typically, with G some deterministic observation mapping, observation_fn(X) returns a normal distribution centered at G(X).

state Instance of EnsembleKalmanFilterState.
observation Tensor representing the observation for this timestep.
observation_fn callable returning an instance of tfd.MultivariateNormalLinearOperator along with an extra information to be returned in the EnsembleKalmanFilterState.
damping Floating-point Tensor representing how much to damp the update by. Used to mitigate filter divergence. Default value: 1.
low_rank_ensemble Whether to use a LinearOperatorLowRankUpdate (rather than a dense Tensor) to represent the observation covariance. The "low rank" is the ensemble size. This is useful only if (i) the ensemble size is much less than the number of observations, and (ii) the LinearOperator associated with the observation_fn has an efficient inverse
seed PRNG seed; see tfp.random.sanitize_seed for details.
name Python str name for ops created by this method. Default value: None (i.e., 'ensemble_kalman_filter_update').

next_state EnsembleKalmanFilterState representing particles at next timestep, after applying Kalman update equations.


[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.