Dynamical systems arise in engineering, physical sciences as well as in social sciences. If the state of a system is known, one also knows its properties, and may, e.g., stabilise the system and prevent it from blowing up, or predict its near future. However, the state of a system consists often on internal parameters which are not always accessible. Instead, often only an observation process Y , which is a transformation of the current state, is accessible. Furthermore, a system operates in real environments; hence, itself and its observation are affected by random noise and/or disturbances. So, in reality, the dynamics of the system and the observation are corrupted by noise. The problem of nonlinear filtering is estimating the state of the system X(t) at a given time t > 0 through the data of the observation Y until time t (i.e. {Y (s) : 0 ≤ s ≤ t}).Usually, one considers models where the state process and the observation