Optimal filtering for linear discrete state delay systems

This paper is concerned with the optimal filtering problem for linear discrete state delay systems. One might tend to consider the problem by using the state augmentation and standard Kalman Filtering methods. However, the former usually results in higher state dimensions and expensive computational cost, especially when the delay is large. Therefore, based on the minimum mean square error (MMSE) estimation principle, a new filter design method is proposed by using the projection theory and recursive projection formula in Hilbert space. The dimension of the designed filter is the same as the original systems. A simulation example is given to illustrate the effectiveness of the proposed approach.