Optimal time-varying Kalman filter for descriptor system with random one-step measurement delay

For the linear stochastic descriptor system with random one-step measurement delays, the optimal time-varying Kalman filtering is presented. The singular value decomposition (SVD) method, the derandomization approach and the augmented state approach are presented, which are applied to transform the descriptor system with random one-step measurement delay to the standard non-descriptor system with fictitious white noises. Applying the Kalman filtering and the relation of the new and original systems, the corresponding Kalman filter and filtering error variances are presented. A simulation example about circuits system verifies the correctness of the proposed results.