Extended Kalman Filter (EKF) Computation in Kalman Filtering

This article focuses on the Extended Kalman Filter (EKF) within Kalman filter computations. The Kalman filter serves as a mathematical tool for estimating system states by combining sensor measurements with dynamic equations from system models. The EKF represents an extended version that handles nonlinear systems through linearization techniques, commonly implemented in control and navigation applications for state estimation. We will examine the EKF working mechanism, its practical applications, and its relationship with standard Kalman filters to enhance understanding and implementation. From a coding perspective, EKF implementation typically involves: 1) State prediction using nonlinear process models (often implemented through Euler integration or Runge-Kutta methods), 2) Linearization of system dynamics using Jacobian matrices for covariance propagation, and 3) Measurement update steps employing partial derivatives of observation functions. Key functions in EKF algorithms commonly include state transition modeling, covariance matrix operations, and innovation calculation for optimal state corrections.