Kalman Filter: Minimal Variance Estimator

This lecture covers the Kalman filter as a minimal variance estimator, the innovation sequence, and the update difference Riccati equation for filtering. It also discusses the generalization to systems with inputs, tuning the Kalman gain, and the duality relations between FH-LQ regulator and Kalman predictor. The lecture further explores the innovation sequence, statistics of the innovation, and its correlation properties, providing examples of its application in estimating the position and velocity of a vehicle using GPS measurements.