Robust extended Kalman filter of discrete-time Markovian jump nonlinear system under uncertain noise

This paper examines the problem of robust extended Kalman filter design for discrete-time Markovian jump nonlinear systems with noise uncertainty. Because of the existence of stochastic Markovian switching, the state and measurement equations of underlying system are subject to uncertain noise whose covariance matrices are time-varying or un-measurable instead of stationary. First, based on the expression of filtering performance deviation, admissible uncertainty of noise covariance matrix is given. Secondly, two forms of noise uncertainty are taken into account: Non-Structural and Structural. It is proved by applying game theory that this filter design is a robust mini-max filter. A numerical example shows the validity of the method.