Lecture
This lecture covers the linearized Kalman Filter and the extended Kalman Filter, with examples illustrating their application in nonlinear systems. The instructor explains the design of a Kalman Filter for time-varying systems and the challenges of accounting for nonlinear dynamics. The lecture also delves into the estimation of unknown parameters using the Extended Kalman Filter. Various steps of the Kalman Filter process, such as prediction and filtering, are detailed, along with the implications of using linearized models. The lecture concludes with a comparison between the linearized and extended Kalman Filters through examples of predator-prey systems, showcasing the filters' performance in tracking dynamics and estimating populations.