An Introduction to the Extended Kalman Filter first presents a study wherein a two-stage approach for the estimation of a spacecraft's position and velocity using single station antenna tracking data is proposed. Since the Kalman filter and its variants are widely used for estimation in diverse domains, the authors also present a review of fault detection, diagnosis and fault tolerant control of descriptor/differential algebraic equation systems specifically focused on the Kalman filter and its variants. The closing contribution provides insight into the intrinsic convergence of the extended Kalman filter when operated in the stochastic frame for the class of systems and outputs considered.