Optimal Linear Filters for Discrete-Time Systems With Randomly Delayed and Lost Measurements With/Without Time Stamps

A novel model is developed to describe possible random delays and losses of measurements transmitted from a sensor to a filter by a group of Bernoulli distributed random variables. Based on the new developed model, an optimal linear filter dependent on the probabilities is presented in the linear minimum variance sense by the innovation analysis approach when packets are not time-stamped. The solution to the optimal linear filter is given in terms of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state filter is given. At last, the optimal filter is given by Kalman filter when packets are time-stamped.