Stochastic stability of modified extended Kalman filter over fading channels with transmission failure and signal fluctuation

The observations of nonlinear systems, exposed to a fading channel, greatly suffer from both transmission failure and signal fluctuation. This paper focuses on the design-oriented analysis of nonlinear estimator based on a modified extended Kalman filter (MEKF) over fading wireless networks. Bernoulli process and Rayleigh fading are taken into consideration to model transmission failure and signal fluctuation, respectively. The offline sufficient conditions are established for the boundedness of the expectations of the prediction error covariance matrices sequence (PECMS) of the MEKF, which shows the existence of a crucial arrival rate. Furthermore, based on the derived upper bound of PECMS, further sufficient conditions are provided for mean-square bounded estimate error of the MEKF using the fixed-point theorem. Numerical examples are also given to verify the analytical results and demonstrate the feasibility of the proposed methods.