ABSTRACT
This chapter helps the reader to learn least-squares estimation, maximum likelihood estimation, and four versions of Kalman filter, namely, scalar static Kalman filter; linear multivariable dynamic Kalman filter; extended Kalman filter (EKF), which is applicable in nonlinear situations; and unscented Kalman filter, which is also applicable in nonlinear situations and has advantages over the EKF because it directly takes into account the propagation of random characteristics through system nonlinearities. It presents some basics of probability and statistics. The chapter outlines reliability considerations and associated probability models of multicomponent systems. To the randomness in the measurement process, the analytical representation of the measured quantity itself contains some random component. Specifically, there is randomness in the model. The model may include the relationship between the measured quantity and the estimated quantity in addition to the analytical representation of the process that generates the data.
