MATLAB Code Implementation for Kalman Filter

The Kalman filter is an optimal recursive algorithm for state estimation, widely used in signal processing and control systems. This MATLAB implementation example demonstrates the fundamental working principles of a one-dimensional Kalman filter. The Kalman filter implementation primarily consists of two phases: prediction phase and update phase. In MATLAB code, the prediction phase uses system dynamics to estimate the current state and error covariance, while the update phase corrects these predictions using new measurement data. Key parameters that must be defined in the MATLAB implementation include: state transition matrix (A), measurement matrix (H), process noise covariance (Q), and measurement noise covariance (R). During initialization in MATLAB code, programmers need to set the initial state estimate (x0) and initial error covariance matrix (P0). The prediction step utilizes the system dynamic model to project the state to the next time increment while calculating the predicted error covariance through matrix operations. The update step involves computing the Kalman gain (K) - a critical parameter that determines the relative reliability between predicted values and measured values - followed by state correction and covariance update calculations. For practical applications, MATLAB users can adjust the system model and noise parameters according to specific problem requirements. This basic implementation can be extended to various scenarios such as target tracking, navigation systems, and signal denoising. After understanding this example, learners can further explore extended Kalman filters (EKF) to handle nonlinear system problems through appropriate linearization techniques in MATLAB.