Van Trees H.L., Bell K.L. (Eds.) Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking

Wiley-IEEE Press, 2007. — 959 p. — ISBN: 0470120959, 9780470120958.The first comprehensive development of Bayesian Bounds for parameter estimation and nonlinear filtering/tracking.
Bayesian estimation plays a central role in many signal processing problems encountered in radar, sonar, communications, seismology, and medical diagnosis. There are often highly nonlinear problems for which analytic evaluation of the exact performance is intractable. A widely used technique is to find bounds on the performance of any estimator and compare the performance of various estimators to these bounds.
This book provides a comprehensive overview of the state of the art in Bayesian Bounds. It addresses two related problems: the estimation of multiple parameters based on noisy measurements and the estimation of random processes, either continuous or discrete, based on noisy measurements.
An extensive introductory chapter provides an overview of Bayesian estimation and the interrelationship and applicability of the various Bayesian Bounds for both static parameters and random processes. It provides the context for the collection of papers that are included.
This book will serve as a comprehensive reference for engineers and statisticians interested in both theory and application. It is also suitable as a text for a graduate seminar or as a supplementary reference for an estimation theory course.Introduction (Harry L. Van Trees and Kristine L. Bell).
Bayesian Estimation: Static Parameters.
Maximum Likelihood and Maximum a Posteriori Estimation.
Covariance Inequality Bounds.
Ziv–Zakai Bounds.
Method of Interval Estimation.Bayesian Estimation: Random Processes.
Continuous-Time Processes and Continuous-Time Observations.
Continuous-Time Processes and Discrete-Time Observations.
Discrete-Time Processes and Discrete-Time Observations.
Linear AWGN Process and Observations.
Global Recursive Bayesian Bounds.Outline of the Book