Kalman Filter MATLAB Implementation with Code Examples

We present a MATLAB implementation of the Kalman Filter algorithm, an optimal estimation technique that combines historical system states with current observations through weighted averaging to determine the most probable system state. This MATLAB-based solution employs efficient matrix operations to simplify computational complexity and includes extensive inline documentation for clear understanding and customization. The implementation demonstrates key algorithmic components including state prediction equations (x = F*x + B*u) and measurement update steps (K = P*H'/(H*P*H' + R)), where F represents the state transition matrix, B the control input matrix, and K the Kalman gain. The code structure allows for straightforward modification of system matrices (Q for process noise covariance, R for measurement noise covariance) to adapt to various application scenarios. Through proper configuration of initial state vectors and covariance matrices, users can efficiently apply this implementation to different dynamic systems while maintaining numerical stability.