Robust Filtering Problem For Uncertain Stochastic Systems

This paper considers two robust filtering problem of uncertain random systems.The first one is the robust filtering problem for uncertain random systems with time-correlated noise.The second one is the robust filtering problem for uncertain random systems with amplify-and-forward relays.Firstly,the robust filtering problem of uncertain random systems with time-correlated observation noise is discussed,in which time-correlated observation noise is described by a linear system model with white noise.To tackle the problem of time-correlated observation noise,a new observation equation is defined by using the observation difference method.Based on the new observation model,a robust optimal filter is designed.Secondly,the robust filtering problem of a class of uncertain random systems with amplify-and-forward relays is studied.The amplify-and-forward relay is located between the sensor and the remote filter,sending the received signal from the sensor to the filter.A set of random variables with a certain probability distribution is introduced to characterize the transmission power of sensors and relays.A robust optimal filter is designed by using the average transmission power in the presence of uncertain parameter matrices.Finally,the effectiveness of the proposed filter is verified by simulation examples.