A Nonlinear Filter of EKF Type Using Formal Linearization of Polynomials for Both State and Measurement Equations

A nonlinear filter is presented by using a formal linearization method and the Extended Kalman Filter (EKF) approach in this paper. Defining a linearization function that consists of polynomials, a given nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function. Introducing a new augmented measurement vector that consists of polynomials of measurement data for a given measurement equation, this equation is also transformed into an augmented linear one with respect to the linearization function in the same way. As a result, the EKF theory can be applied to these augmented linearized systems and a nonlinear filter is synthesized. In order to show the performance of the method, numerical experiments are carried out by comparing with the EKF as a conventional method.