An Example of Kalman Filter Design

This article presents the fundamental design principles of Kalman filters accompanied by a practical application case study with detailed explanations. The Kalman filter serves as a widely-used control system algorithm that predicts future states and estimates errors through recursive mathematical processing. It finds extensive applications across aerospace, automotive systems, financial modeling, and numerous engineering domains. We will thoroughly examine the mathematical foundations and design workflow of Kalman filters, supplemented with implementation insights including key functions like state prediction (using system dynamics matrices) and measurement update (incorporating Kalman gain calculations). The accompanying documentation provides step-by-step guidance on algorithm implementation, covering crucial aspects such as covariance matrix initialization, process noise calibration, and real-time update procedures to help readers effectively understand and apply this powerful estimation methodology.