Kalman Filtering: State Estimation and Prediction

This lecture covers the time-varying Kalman filter, focusing on state estimation and prediction in a linear Gaussian setting. It explains the affine transformation of Gaussian random vectors, the Kalman predictor and filter, and the iterative procedure for computing desired quantities. The instructor discusses the optimality of the predictor and filter, the computation of covariance matrices, and the practical implementation of the Kalman filter. The lecture also addresses the challenges of growing dimensions in state estimation and provides insights into the recursive computation of estimates. Key concepts include conditioning on past measurements, the Kalman gain, and the statistical properties of the predictor and filter.