Lectures on Discrete Time Filtering

This book is based on a course given at the University of Southern California, at the University of Nice, and at Cheng Kung University in Taiwan. It discusses linear and nonlinear sequential filtering theory: that is, the problem of estimating the process underlying a stochastic signal. For the linear colored-noise problem, the theory is due to Kalman, and in the case of white noise it is the continuous Kalman-Bucy theory. The techniques considered have applications in fields as diverse as economics (e.g., prediction of the money supply), geophysics (e.g., processing of sonar signals), electrical engineering (e.g., detection of radar signals), and numerical analysis (e.g., in integration packages). The nonlinear theory is treated thoroughly, along with some novel synthesis methods for this computationally demanding problem. The author also discusses the Burg technique, and gives a detailed analysis of the matrix Riccati equation that is not available elsewhere.