Kalman Filter Implementation in GPS Receivers - Tested and Beginner-Friendly

In GPS receiver systems, the Kalman filter serves as a fundamental algorithm for achieving more precise position and velocity estimations. Our implementation has undergone rigorous testing and successfully produces functional results, making it particularly suitable for beginners entering the field of navigation algorithms. The Kalman filter algorithm combines prediction and correction phases: the prediction step uses system dynamics models to forecast state variables (position/velocity), while the correction step incorporates GPS measurements to refine these estimates. Key implementation components include state transition matrices, measurement models, and covariance matrices handling. It's important to note that the Kalman filter is not a trivial algorithm - it requires solid mathematical foundations in linear algebra and probability theory, along with practical programming experience for effective implementation. When learning and applying Kalman filtering, we recommend methodical practice and detailed research to truly grasp the algorithm's core principles and practical applications. The code demonstrates proper handling of process noise and measurement noise covariance matrices, which are critical for achieving optimal filter performance.