Optimal Linear Estimators for Discrete-time Systems with One-step Random Delays and Multiple Packet Dropouts

A novel model is developed to describe possible one-step random delay and multiple packet dropouts by two Bernoulli distributed random variables. Based on the developed model, the optimal linear estimators including filter, predictor and smoother for the state are presented in the linear minimum variance sense. The solution to the optimal filter is given in terms of a Riccati equation and a Lyapunov equation. The stability of the filter is analyzed. A sufficient condition for the existence of the steady-state filter is given.