Optimal Linear Estimators for Systems With Random Sensor Delays, Multiple Packet Dropouts and Uncertain Observations

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random sensor delays, packet dropouts and uncertain observations. We develop a unified model to describe the mixed uncertainties of random delays, packet dropouts and uncertain observations by three Bernoulli distributed random variables with known distributions. Based on the proposed model, the optimal linear estimators that only depend on probabilities are developed via an innovation analysis approach. Their solutions are given in terms of a Riccati equation and a Lyapunov equation. They can deal with the optimal linear filtering, prediction and smoothing for systems with random sensor delays, packet dropouts and uncertain observations in a unified framework. Simulation results show the effectiveness of the proposed optimal linear estimators.