Extended Kalman filtering subject to random transmission delays: Dealing with packet disorders

This paper studies the extended Kalman filtering problem for a class of nonlinear discrete-time systems with random transmission delays (RTDs) and RTD-induced packet disorders. The relationship between the RTDs and the resulting packet disorders is discussed. The bounded RTDs, which take place in the sensor-to-filter channel, are modeled as independent and identically distributed random variables obeying a certain probability distribution. A novel filter structure is proposed that utilizes an integer-valued function of the mathematical expectation of the RTDs so as to compensate the RTD-induced effects. Under the proposed extended Kalman filter, an upper bound for the filtering error covariance is derived by solving two Riccati-like difference equations, and subsequently minimized (in the sense of trace) by appropriately designing the filter gains. A numerical simulation is provided to verify the validity of the developed filter design scheme.