Extended Kalman Filter

The Extended Kalman Filter (EKF) is a widely-used state estimation algorithm suitable for both linear and nonlinear systems. By fusing measurement data with system models, it achieves more accurate state estimation. In practical applications, EKF is extensively employed in autonomous driving, robotics navigation, and signal processing. The core concept involves recursively updating state estimates through prediction and correction steps, continuously optimizing filtering results to enhance system robustness and accuracy. From an implementation perspective, the EKF algorithm typically involves initializing state vectors and covariance matrices, followed by executing two main phases: prediction (using system dynamics models) and update (incorporating measurement data). Key functions include Jacobian matrix calculations for linearizing nonlinear systems and Kalman gain computations for optimal weighting between predictions and measurements. Understanding and mastering the EKF algorithm is crucial for researchers and developers working in related fields, particularly for implementing real-time state tracking systems with nonlinear characteristics.