This book provides an introduction to the fundamentals of estimation for engineers, scientists, and applied mathematicians. It is a follow-up to the first estimation book written by the second author in 1978, expanding upon previous treatments to provide more comprehensive developments and updates, including new theoretical results. The level of the presentation is accessible to senior undergraduate and first-year graduate students and is well-suited as a self-study guide for practicing professionals. The primary motivation is to minimize the painful process of digesting and applying the theory by emphasizing the interrelationships between estimation and modeling of dynamic systems. The book is based on the authors' experiences with practical problems in spacecraft attitude determination and control, aircraft navigation and tracking, orbit determination, powered rocket trajectories, photogrammetry applications, and identification of vibratory systems. The text has evolved from lecture notes for short courses and seminars given to professionals at various private laboratories and government agencies, and in conjunction with courses taught at the University at Buffalo and Texas A&M University. The structure of a typical estimation problem is introduced, with the goal of determining "best" estimates of poorly known parameters so that the mathematical model provides an "optimal estimate" of the system's actual behavior. Any systematic method that seeks to solve such problems is generally referred to as an estimation process. The degree of difficulty associated with solving such problems ranges from near-trivial to impossible, depending on the nature of the mathematical model and the statistical properties of the measurement errors. The book has three main objectives: to document the development of the central concepts and methods of optimal estimation theory in a manner accessible to engineering students, applied mathematicians, and practicing engineers; to illustrate the application of the methods to problems of varying degrees of analytical and numerical difficulty; and to present prototype algorithms that stimulate the development of efficient computer programs and intelligent use of programs. The text includes a variety of examples from diverse fields, such as determining the damping properties of a fluid-filled damper as a function of temperature, identification of aircraft dynamic and static aerodynamic coefficients, orbit and attitude determination, position determination using triangulation, and modal identification of vibratory systems. Even modern control strategies, such as certain adaptive controllers, use the least squares approximation to update model parameters in the control system. The book covers the theory and application of least squares approximation, including curve fitting, parameter identification, and system model realization. It also discusses probability concepts in least squares, review of dynamical systems, parameter estimation applications, sequential state estimation, batch state estimation, and estimation of dynamic systems. The text also includes a chapter on optimal control and estimation theory, as well as appendices on matrix properties, basic probability concepts, parameter optimization methods, and computer software.This book provides an introduction to the fundamentals of estimation for engineers, scientists, and applied mathematicians. It is a follow-up to the first estimation book written by the second author in 1978, expanding upon previous treatments to provide more comprehensive developments and updates, including new theoretical results. The level of the presentation is accessible to senior undergraduate and first-year graduate students and is well-suited as a self-study guide for practicing professionals. The primary motivation is to minimize the painful process of digesting and applying the theory by emphasizing the interrelationships between estimation and modeling of dynamic systems. The book is based on the authors' experiences with practical problems in spacecraft attitude determination and control, aircraft navigation and tracking, orbit determination, powered rocket trajectories, photogrammetry applications, and identification of vibratory systems. The text has evolved from lecture notes for short courses and seminars given to professionals at various private laboratories and government agencies, and in conjunction with courses taught at the University at Buffalo and Texas A&M University. The structure of a typical estimation problem is introduced, with the goal of determining "best" estimates of poorly known parameters so that the mathematical model provides an "optimal estimate" of the system's actual behavior. Any systematic method that seeks to solve such problems is generally referred to as an estimation process. The degree of difficulty associated with solving such problems ranges from near-trivial to impossible, depending on the nature of the mathematical model and the statistical properties of the measurement errors. The book has three main objectives: to document the development of the central concepts and methods of optimal estimation theory in a manner accessible to engineering students, applied mathematicians, and practicing engineers; to illustrate the application of the methods to problems of varying degrees of analytical and numerical difficulty; and to present prototype algorithms that stimulate the development of efficient computer programs and intelligent use of programs. The text includes a variety of examples from diverse fields, such as determining the damping properties of a fluid-filled damper as a function of temperature, identification of aircraft dynamic and static aerodynamic coefficients, orbit and attitude determination, position determination using triangulation, and modal identification of vibratory systems. Even modern control strategies, such as certain adaptive controllers, use the least squares approximation to update model parameters in the control system. The book covers the theory and application of least squares approximation, including curve fitting, parameter identification, and system model realization. It also discusses probability concepts in least squares, review of dynamical systems, parameter estimation applications, sequential state estimation, batch state estimation, and estimation of dynamic systems. The text also includes a chapter on optimal control and estimation theory, as well as appendices on matrix properties, basic probability concepts, parameter optimization methods, and computer software.