Optimal time-varying Kalman filter and predictor for the descriptor system with multiplicative noise and colored noises

Abstract

For the linear stochastic descriptor system with multiplicative noise and colored additive noises, the optimal time-varying Kalman filtering is addressed. By the singular value decomposition (SVD) method and fictitious noise approach, the descriptor system with multiplicative noise is transformed to two reduced-order non-descriptor systems without multiplicative noise. By the augmented state approach and difference transformation approach, the new augmented state space model with correlated white noise is presented. For the obtained non-descriptor standard system with white fictitious noises, the Kalman filter and predictor of the reduced-order augmented state and white process noise is presented. Further, the optimal time-varying Kalman filter and predictor of original state for the descriptor system are obtained according to the relations of the new and original systems. One simulation example verifies the correctness and effectiveness of the proposed algorithm.