This paper discusses two algorithms of extended unbiased FIR (EFIR) filtering of nonlinear discrete-time state-space models used in tracking and state estimation. The basic algorithm employs the extended nonlinear state and observation equations. The modified algorithm utilizes the nonlinear-to-linear conversion of the observation equation which is provided using a batch EFIR filter having small memory. Unlike the extended Kalman filter (EKF), both EFIR algorithms ignore the noise statistics and demonstrate better robustness against temporary model uncertainties. These algorithms require an optimal horizon in order to minimize the mean square error. Applications are given for robot indoor self-localization utilizing radio frequency identification tags.