In this chapter we develop model-based processor for the dynamic estimation problem; that is, the estimation of processes that vary with time. Here the state-space representation is used as the basic model. First, the fitting of noisy discrete-time observation to a continuous-time state-space model is approached by block processing using minimum variance linear estimator. Then we develop the linear sequential continuous–discrete estimator, the so-called continuous–discrete Kalman filter, for estimating continuous-time states from noisy discrete observations. We discuss the operation of the filter as a predictor-corrector algorithm. This is followed by the derivation of the discrete Kalman filter for estimating the discrete-time states from discrete observations, as well as the development of the continuous Kalman filterContinuousKalman filter for estimating the continuous-time states from the continuous-time observations. The innovations sequence is also discussed in detail to point out various properties useful for tuning the Kalman filter, and some of the geometric concepts are developed. Finally, the stochastic controllability, stochastic observability, the stability of the Kalman filter and the statistical steady state is discussed. The corresponding steady-state Kalman filter is given, and the link between the Kalman filter and the Wiener filter is established.