Extended modal Kalman filter

In this paper, based on Modal series, a new filter is proposed for a nonlinear system state estimation. Modal series is a new method to obtain a closed-form approximate solution of a nonlinear differential equation. Up to now, this series is only obtained in the neighborhood of an equilibrium point. In the proposed method, this series is attained in the neighborhood of the current estimated state vector that is named as Stochastic Extended Modal Series (SEMS). Based on SEMS and proper approximations, the proposed nonlinear filter is converted to a series of linear filters, and the extracted filter is named as Extended Modal Kalman Filter (EMKF). The performance of EMKF is analytically compared with that of Extended Kalman Filter (EKF), and its applicability presented with some simulations. Finally, it is proved that the EKF is a special case of EMKF.