This book provides an introductory, yet comprehensive, treatment of both Wiener and Kalman filtering, along with a development of least-squares estimation, maximum likelihood estimation, and maximum a posteriori estimation based on discrete-time measurements. A good deal of emphasis is placed in the text on showing how these different approaches to estimation fit together to form a systematic development of optimal estimation. Included in the text is a chapter on nonlinear filtering, focusing on the extended Kalman filter (EKF) and a new measurement update that uses the Levenburg-Marquardt algorithm to obtain more accurate results in comparison to the EKF measurement update. Applications of nonlinear filtering are also considered, including the identification of nonlinear systems modeled by neural networks, FM demodulation, target tracking based on polar-coordinate measurements, and multiple target tracking.