Optimal estimation for systems with multiplicative noises, random delays and multiple packet dropouts

In this research, the optimal estimation for networked control system with multiplicative noises (MN), one-step random delays and multiple packet dropouts is studied. Both the sensor-to-estimator and controller-to-actuator channels are affected by MN. The one-step random delays and packet dropouts are characterised by a series of Bernoulli variables. By state augmentation, the random circumstances in channels are transformed into random parameters, and the optimal estimators are derived utilising projection theory. For systems without MN, random delays or packet dropouts, the corresponding estimators can be derived as particular cases of the proposed algorithm. Then a sufficient existence condition of steady-state estimators is derived. Some numerical examples are given to validate the proposed estimation algorithms.