Time-varying Kalman filter for descriptor system with random two-step measurement delays and colored process noises

This paper presents the time-varying Kalman filter of the linear stochastic descriptor system with random two-step measurement delays and colored process noise. In the soft sensor measurement, the Bernoulli random variables are used to show the random two-step measurement delay. And applying singular value decomposition (SVD) method, the descriptor system is transformed into two reduced-order subsystem. Combining the de-randomization method and state augmented approach, the standard state space model with invariant transition matrices is presented, where the process noise and the measurement noise are white correlated noises. Then, based on the Kalman filtering theory, the time-varying Kalman filter and filtering error variance are obtained. A simulation example about two-loop circuits system verifies the correctness of the proposed results.