From the Linear Quadratic Regulator (LQR) to the (Deterministic) Kalman Filter in Two Easy Steps
This paper presents a two-step tutorial demonstrating how to derive the deterministic Kalman filter from the Linear Quadratic Regulator (LQR) by first converting the state estimation problem into a purely quadratic LQR formulation using homogeneous coordinates, and then partitioning the resulting solution to recover the traditional Kalman filter dynamics and Riccati equation.