Robust time-varying Kalman predictor for uncertain singular system with missing measurement and colored noises

Abstract

For the linear stochastic singular system with missing measurement, colored noise and uncertain-variance noises, the robust Kalman prediction problem is addressed. Applying the singular value decomposition (SVD) method, the fictitious noise approach, the augmented state approach and difference transformation approach, the original singular system is transformed to new reduced-order standard system only with uncertain-variance fictitious noises. By the augmented state approach and difference transformation approach, the new augmented state space model with correlated white noise is presented. Applying the minimax robust estimation principle, the minmax robust time-varying Kalman predictor is presented. Its robustness is proved by the Lyapunov equation approach in the sense that its actual prediction error variance is guaranteed to have the corresponding minimal upper bound for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.