MATLAB Code Implementation of Kalman Filter with Custom Function

In my course design project, I developed a comprehensive MATLAB implementation of a Kalman filter algorithm. The main function is defined as [Y, PY, KC] = myKalman(x, A, B, Q, H, R, y0, P0). The Kalman filter algorithm operates by combining system model predictions with actual measurements through an optimal weighting mechanism, resulting in refined state estimates. The implementation follows the standard Kalman filter procedure with the following key components: - Parameter x represents the input measurement sequence that drives the filtering process - System matrices A (state transition) and B (control input) define the dynamic model - Q (process noise covariance) and R (measurement noise covariance) characterize system uncertainties - Observation matrix H maps state variables to measurements - Initial conditions y0 (initial state estimate) and P0 (initial error covariance) provide starting values The algorithm executes through two main phases: prediction (using prior state and covariance) and update (incorporating new measurements). The function returns: - Y: The sequence of optimal state estimates - PY: The corresponding error covariance matrices for each estimate - KC: Kalman gain matrices used in the correction step This implementation efficiently handles the recursive nature of Kalman filtering, making it suitable for real-time state estimation applications in control systems and signal processing.