Optimal filtering for multi-rate systems with one-step auto-correlated noises

The optimal filtering problem is addressed for multi-rate systems with one-step auto-correlated noises. The state is updated at the highest sampling rate and the sensor has a lower sampling rate. System noise and measurement noise are one-step auto-correlated, respectively. An optimal filter in the linear minimum variance sense is proposed via an innovation analysis approach. A simulation example is given to show the effectiveness of the proposed algorithms.