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. We establish stability and accuracy of the filter by studying this for the stochastic PDE describing the observer. For stability one has to show that solutions of the observer starting from different initial conditions converge exponentially fast towards each other. This would also imply that the random attractor of the observer is at most a single random point. Accuracy means that any solution of the observer converges exponentially fast to a small neighbourhood of the unknown solution u(t). In terms of random attractors one has to verify that the whole attractor is close to u(t). Joint work with Andrew Stuart, Kody Law, and Konstantinos Zygalakis