In this note, we develop a real-time and accurate solution for nonlinear filtering problems based on the Gaussian distribution. Specifically, we present an explicit solution of the Duncan-Mortensen-Zakai equation of the Yau filtering system, which includes the linear filtering system and the exact filtering system. The solution is given in terms, of a solution of a system of ordinary differentia[ equations. In particular, our method can be implemented in hardware. The complexity of our algorithms is the same as those of Kalman-Bucy filters in the case of linear filtering systems.