Applications of Extended Kalman Filtering

The Extended Kalman Filter (EKF) is a state estimation algorithm designed for nonlinear systems, widely applied in system tracking, navigation, robot localization, and sensor fusion. Unlike the traditional Kalman Filter, EKF handles nonlinear models through local linearization, enabling high-precision estimation in complex dynamic environments. In code implementation, EKF typically involves linearizing nonlinear state transition and observation functions using Jacobian matrices at each time step.

In target tracking problems, EKF is commonly used when dealing with nonlinear motion models or observation equations. For instance, in radar or visual tracking systems, state variables like target position and velocity are often described by nonlinear equations. EKF approximates nonlinear functions through first-order Taylor expansion, converting them into linear models for recursive computation within the Kalman filter framework. Algorithm implementation requires calculating partial derivatives of system models to construct linearized matrices for prediction and update cycles.

Another significant application of EKF is sensor fusion, such as integrating GPS and Inertial Measurement Unit (IMU) data for positioning. While GPS provides absolute position information (though susceptible to interference), IMU measures acceleration and angular velocity but suffers from cumulative errors. EKF dynamically adjusts sensor weights through covariance matrices, fusing multi-source data to enhance estimation robustness. Key functions in implementation include measurement prediction and Kalman gain calculation for optimal data fusion.

Although EKF offers computational efficiency, its performance may degrade in strongly nonlinear or high-noise environments due to linearization errors. In such cases, advanced methods like Unscented Kalman Filter (UKF) or Particle Filter (PF) might be considered. However, for moderately nonlinear problems in most engineering practices, EKF remains the preferred solution balancing accuracy and complexity, with implementations often involving iterative linearization and error covariance propagation.