MATLAB Source Code Implementation of Kalman Filter Algorithm

Kalman filtering is a recursive state estimation algorithm widely used for estimating the state of dynamic systems from noisy observational data. MATLAB implementation typically involves two main phases: state prediction and measurement update. First, you need to define the system's state-space model parameters, including the state transition matrix, control input matrix (if applicable), measurement matrix, and covariance matrices for process noise and measurement noise. These parameters fundamentally determine the Kalman filter's behavior and performance characteristics. In MATLAB code, these are typically defined as matrix variables like F (state transition), H (measurement), Q (process noise covariance), and R (measurement noise covariance). During the prediction phase, the algorithm projects the current state estimate forward in time using the system model. This step calculates the a priori state estimate and error covariance using the state transition equations. The MATLAB implementation typically uses matrix multiplication operations like x_pred = F * x_prev for state prediction and P_pred = F * P_prev * F' + Q for covariance prediction. In the update phase, the algorithm incorporates actual measurement data to refine the predictions. By computing the Kalman gain, the system optimally balances the confidence between predicted values and measured values, resulting in more accurate state estimates. The MATLAB code implementation involves calculating the Kalman gain K = P_pred * H' * inv(H * P_pred * H' + R), then updating the state estimate x_updated = x_pred + K * (z - H * x_pred) and covariance P_updated = (I - K * H) * P_pred. MATLAB's strength in matrix operations enables efficient handling of the matrix calculations inherent in Kalman filtering. A typical implementation uses loop structures to iteratively process time-series data, with each iteration executing both prediction and update steps. The code often includes initialization of state vectors, covariance matrices, and a main processing loop that handles measurement data sequentially. This filtering method finds extensive applications in navigation systems, target tracking, signal processing, and is particularly suitable for linear Gaussian systems. For nonlinear systems, variants like Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKT) can be implemented using similar MATLAB programming approaches with appropriate linearization techniques.