EKF Utilizes Only First-Order Derivatives in Nonlinear Function Taylor Expansion

The Extended Kalman Filter (EKF) relies solely on first-order derivatives from Taylor expansions of nonlinear functions, omitting higher-order terms. This approximation often introduces significant errors in estimating posterior state distributions, degrading both filtering algorithm performance and overall tracking system accuracy. Recently, the Unscented Kalman Filter (UKF) has emerged as an adaptive filtering alternative. Unlike EKF, UKF employs carefully designed sigma points that propagate through nonlinear functions to capture first- and second-order statistical properties of random vectors. This approach better approximates nonlinear dynamics in state equations, yielding superior estimation precision compared to EKF implementations.