Estimating a remote signal from the measurements of another observed signal is a classical problem in the systems theory with numerous applications in different real-life problems. Such a problem is usually named in the literature a signal filtering problem or signal estimation/observation problem. In this chapter, we will address the problem of optimal filtering for a general class of systems described by impulsive stochastic linear differential equations. The metric used as an optimality measure of the proposed estimation scheme belongs to the \(H_{2}\) -type norm setting. More specifically, we will consider the two \(H_{2}\) -type norms defined in Chap. 7 . Our aim is to find the state-space representation of a dynamical system named filter, which fed at its input with the measured signals, provides at its output a signal which is the best estimate (in the sense of \(H_{2}\) norm minimization) of the signal of interest. The dimension of the state space of the considered filter is not prefixed. The state-space representations of the \(H_2\) -optimal filters corresponding to the two different considered norms are obtained in Theorems 8.1 and 8.3, respectively. We show that the dimensions of the optimal filters are equal to the dimension of the system under consideration. The corresponding feedback gains of the optimal filters are constructed based on the stabilizing solution of an adequately defined system of forward jump matrix linear differential equations with Riccati-type jumping operators. We finally apply the obtained results to the case of sampled-data linear stochastic systems (Theorems 8.4 and 8.5).