Robust Kalman estimation under multi-step random measurement delays, missing measurements and uncertain-variance multiplicative and linearly correlated additive noises

The paper solves the robust Kalman estimation problem for a system with mixed uncertainties. The system noise variances are uncertain but bounded above. Some Bernoulli-distributed random variables with known probabilities are used to describe multi-step random measurement delays and missing measurements from sensor to estimator. A novel model transformation method is proposed based on the augmented method and Hadamard product to transform the original system into one with only uncertain fictitious noise variance. The robust time-varying Kalman estimators are designed in a unified form based on the minimax robust estimation principle. Its robustness is proved by generalised Lyapunov equation method and multiple matrix analysis methods, including the Gerŝgorin circle theorem, Hadamard product theorem, strict diagonal dominance, and matrix elementary transformation. The accuracy relation and the convergence in a realisation are proved, and then the robust steady-state Kalman estimator is designed. A simulation example shows the correctness and effectiveness of the proposed results.