Extended Kalman Filter (EKF)

Among various dynamic filtering algorithms, the Extended Kalman Filter (EKF) is widely used for handling nonlinear systems. As a real-time linearization algorithm based on Bayesian filtering theory, EKF provides effective state estimation and prediction for nonlinear dynamic systems. Compared to the traditional Kalman Filter, EKF addresses nonlinearity by performing online linearization through first-order Taylor series expansion. This approach approximates nonlinear equations as linear equations around the current operating point, enabling subsequent state estimation using standard Kalman Filter techniques. From an implementation perspective, EKF code typically involves calculating Jacobian matrices for system and measurement models, followed by standard prediction and update cycles with modified linearized matrices. The algorithm's core functions include state prediction using nonlinear models and covariance propagation through linearized transformations. Consequently, EKF finds extensive applications across various domains including robotic navigation, aerospace systems, autonomous vehicles, and other fields requiring real-time nonlinear state estimation.