Time-Varying Kalman Filter: Properties and Applications

This lecture covers the derivation and properties of the time-varying Kalman filter, focusing on state estimation in a linear Gaussian setting and the challenges of conditioning on measured outputs. The instructor explains the naive method and introduces the Kalman filter as a recursive way to compute desired quantities optimally. The lecture also discusses the generalization to systems with inputs and the importance of affine transformations of Gaussian random vectors. Key concepts include the prediction step, filtering step, and the optimality of the predictor and filter in a statistical sense.