Robust Recursive Filtering for Stochastic Systems With Time-Correlated Fading Channels

This article is concerned with the robust recursive filtering (RF) problem for a class of stochastic uncertain systems subject to time-correlated fading channels. The measurement received by the sensor is transmitted to the remote filter through the time-correlated fading channel where the channel coefficient evolves according to a certain dynamics and hence exhibits a time-correlated nature. The parameter uncertainties of the system are described by norm-bounded unknown matrices. By introducing a class of auxiliary variables, an augmented system is constructed to reflect the dynamics of the fading coefficient and state simultaneously. Then, a recursive filter is designed which is capable of online computation. Furthermore, an upper bound is guaranteed for the filtering error covariance (FEC) for the possible parameter uncertainties as well as the time-correlated fading channels. With the help of the completing-the-squares technique, filter gains are parameterized by minimizing the obtained upper bound. Finally, two examples are employed to verify the effectiveness of the proposed robust RF method.