Optimal linear estimation for systems with multiplicative noise uncertainties and multiple packet dropouts

This study is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with multiplicative noise uncertainties in state and measurement matrices and with multiple packet dropouts from a sensor to an estimator. Based on the projection theory, the optimal linear estimators including filter, predictor and smoother are derived in the linear minimum variance sense. In the absence of stochastic uncertainties and/or packet dropouts, the corresponding results can be obtained as the special cases of the proposed estimators. Steady-state property is also analysed. A sufficient condition for the existence of the steady-state estimators is obtained. They can be computed offline. So they have the reduced online computational cost. Simulation examples are given to demonstrate the effectiveness of the proposed estimators.