Construction of the Kalman Filter Algorithm on the Model Reduction

In this paper we derive a state variable estimation method of discrete stochastic dynamical systems. It aims to obtain accurate estimation with short computing time. Therefore, the point of this paper is to discuss a construction of Kalman filter algorithm on the reduced model. First, we construct a reduced model by using balanced truncation method. Further, we apply state variable estimation steps of discrete stochastic dynamical systems by using Kalman filter on the reduced model. Thus, Kalman filter algorithm will be constructed on the reduced model.