Nonlinear filtering with adaptive estimation of state transfer matrix for nonlinear systems with multiplicative noise

State estimation for systems with unknown state transfer matrix and multiplicative noise is very classical and important in signal processing and target tracking. Aiming at the problem, an adaptive estimation algorithm which can deal with unknown state transfer matrix and multiplicative noise has been presented by Dongsheng Chu for linear systems under without considering multiplicative noise in [1]. This work is very interesting and significative. A direct problem is how to design the adaptive estimation algorithm for nonlinear systems based on the current work. For this, this paper considers the estimator design of nonlinear systems with unknown state transfer matrix and multiplicative noise by using the extended Kalman filter (EKF). The purpose is to want to make clear the difference of estimators design between the linear system and the nonlinear system. Accordingly, it can provide the base to design adaptive unscented Kalman filter with unknown state transfer matrix and multiplicative noise. The result shows that there is difference between adaptive algorithms for linear and nonlinear systems, but the derive processes are similar.