Minimum variance estimation for linear uncertain systems with one-step correlated noises and incomplete measurements

This paper deals with state estimation problem for linear uncertain systems with correlated noises and incomplete measurements. Multiplicative noises enter into state and measurement equations to account for the stochastic uncertainties. And one-step autocorrelated and cross-correlated process noises and measurement noises are taken into consideration. Using the latest received measurement to compensate lost packets, the modified multi-step random delays and packet dropout model is adopted in the present paper. By augmenting system states, measurements and new defined variables, the original system is transformed into the stochastic parameter one. On this basis, the optimal linear estimators in the minimum variance sense are designed via projection theory. They depend on the variances of multiplicative noises, the one-step correlation coefficient matrices together with the probabilities of delays and packet losses. The sufficient condition on the existence of steady-state estimators is then given. Finally, simulation results illustrate the performance of the developed algorithms.