The Kalman Filter: Efficient Recursive Estimation for Linear Dynamic Systems

The Kalman filter is an efficient recursive algorithm that estimates the state of a linear dynamic system from noisy measurements. Widely implemented in various engineering fields including radar systems, computer vision, and control theory, it serves as a fundamental solution to the Linear Quadratic Gaussian (LQG) control problem alongside Linear Quadratic Regulator (LQR). Implementation typically involves prediction and update steps using state transition matrices and measurement models.