Linear Quadratic Gaussian Control: Kalman Filtering and LQG Control

This lecture covers innovation-based tests for Kalman filtering, LQG control, and the linearized Kalman filter. It discusses tests for confidence intervals, normalized innovation sequences, and the convergence of normalized approximations. Examples illustrate applying Kalman filtering to systems with Gaussian noise and modeling errors. The lecture also explores the performance of the time-varying Kalman filter under perfect system models and the implications of underestimating noise variance. It concludes with discussions on the extended Kalman filter, linearized Kalman predictor, and the challenges of accounting for nonlinear dynamics in Kalman filtering.