The linear fitting Kalman filter for nonlinear tracking

Dynamic estimation in various synthetic aperture radar (SAR) applications often involves nonlinear models. The first-order Taylor approximation is usually used to linearize the nonlinear functions to perform estimation efficiently. However, the error generated by the first-order Taylor approximation cannot be negligible when dynamic systems are high nonlinearity or with large input errors. This paper proposes a linearization method by minimizing the difference between the nonlinear function and its linear approximation, and yields a better linear fitting function. A Kalman filter based on this principle is suggested. Simulation tests are conducted among the proposed linear fitting Kalman filter (LFKF), the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The results show that the LFKF obviously outperforms the EKF which uses the first-order Taylor approximation, and the LFKF can achieve similar estimation accuracy of the UKF with less computational cost.