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

In estimating posterior state distributions, the Extended Kalman Filter (EKF) utilizes only first-order derivatives from Taylor expansions of nonlinear functions while disregarding higher-order terms. This methodological limitation frequently introduces substantial estimation errors, compromising filtering algorithm performance and consequently degrading overall tracking system accuracy. To address these shortcomings, the Unscented Kalman Filter (UKF) has recently emerged as an advanced adaptive filtering technique. Diverging from EKF's linearization approach, UKF strategically designs minimal sigma points that propagate through nonlinear functions. The algorithm then computes how these transformed points capture the propagation of first- and second-order statistical moments for random vectors. By employing this sigma point transformation methodology—typically implemented through weighted statistical linear regression rather than analytical Jacobians—UKF achieves superior approximation of nonlinear state equation characteristics. This fundamental difference enables UKF to deliver enhanced estimation accuracy, making it particularly valuable for applications demanding precise state estimation. The core implementation involves: 1) Sigma point selection using scaling parameters to control approximation accuracy, 2) Nonlinear propagation through system models without derivative calculations, and 3) Statistical moment reconstruction from transformed points for covariance updates.