Extended Kalman Filter Implementation in MATLAB

This article provides a comprehensive guide to implementing Extended Kalman Filter (EKF) in MATLAB. We begin by discussing the fundamental principles and working mechanism of the standard Kalman filter to establish a solid foundation for understanding EKF implementation. The implementation typically involves creating state transition and measurement functions, calculating Jacobian matrices for linearization, and iterating through prediction and correction steps.

Next, we present the mathematical model of Extended Kalman Filter and provide detailed MATLAB code examples with explanations of key functions such as ekf_predict() for state prediction and ekf_update() for measurement correction. The code demonstrates how to handle nonlinear systems by linearizing around the current estimate using partial derivatives. We include practical examples showing sensor data fusion and trajectory tracking scenarios.

We also explore common application scenarios including robotic control and navigation, autonomous vehicles, and target tracking systems. For each application, we explain how to adapt the EKF implementation by modifying the state vector design and measurement models. The MATLAB implementations show how to handle different sensor types like IMUs, GPS, and LiDAR data integration.

Finally, we summarize the key concepts covered and provide additional learning resources and references for further exploration. The article includes MATLAB best practices for EKF implementation such as handling numerical stability, tuning covariance matrices, and debugging common implementation issues.