gives more accurate estimates than a 1-sided filter.
(Gelb, 1974)
Kalman filter vs. Kalman smoother
The 4-D Var
method is 2-sided, like a smoother.To do the backwards pass, you need an adjoint.But since one of the big advantages
of the EnKF is not needing an adjoint, you might as well use the varational
method at that point.There
_is_ the fixed-lag smoother; this does not require an adjoint since it
always moves forward in time, but requires more storage to store multiple
time steps in the state.