Design of the Simplest Kalman Filter

Designing the simplest Kalman filter in MATLAB is highly convenient and efficient. The Kalman filter design is based on a state-space model framework, with the primary objective of estimating system states through optimal recursive data processing. This filter finds applications across various domains including navigation systems, automatic control, and signal processing. The MATLAB implementation typically involves defining system matrices (A, B, C, D), process noise covariance (Q), and measurement noise covariance (R). Key functions like 'kalman' or manual implementation using prediction and update equations can be utilized. The algorithm operates through two main stages: time update (predicting state and covariance) and measurement update (correcting predictions with new measurements). By implementing this process in MATLAB, users can easily generate performance visualization graphs that display state estimation accuracy, innovation sequences, and covariance convergence. This practical approach significantly enhances understanding of Kalman filter working principles, algorithmic behavior, and real-world application scenarios through immediate visual feedback.