We consider a noisy observer
for an unknown solution u(t) of a deterministic model.
The observer is a stochastic model similar to the original one,
and it arises as a limit of frequent observations in filtering.
Here noisy observations of the low Fourier modes of u(t)
together with knowledge of the deterministic model are used to track
the unknown solution u(t).
In this talk
as an example we discuss the simple 3DVAR-filter and the deterministic
2D-Navier Stokes equation.