Extended Kalman Filter

The Kalman filter is a highly efficient recursive filter (autoregressive filter) capable of estimating the state of dynamic systems from a series of incomplete and noisy measurements. Named after its inventor Rudolf E. Kalman, this filtering method was originally designed for Gaussian-distributed systems. Later scholars developed various improvements, including the Extended Kalman Filter (EKF) which extends applicability to time-nonlinear dynamic systems through first-order Taylor series linearization.

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.