Optimal Filtering for Stochastic Descriptor Systems with Delayed Measurements

This note deals with discrete-time stochastic descriptor systems with both instantaneous and delayed measurements. The condition of the estimability for such system is given. By introducing the reorganized measurement sequence, the optimal Kalman filter and corresponding filtering error covariance matrix are derived. The optimal filter is calculated without resorting to state augmentation which lessons the computation demand greatly. A numerical example is presented to illustrate the given algorithm.