Applied Optimal Estimation (Mit Press)
This is the first book on the optimal estimation that places its major emphasis on practical applications, treating the subject more from an engineering than a mathematical orientation. Even so, theoretical and mathematical concepts are introduced and developed sufficiently to make the book a self-contained source of instruction for readers without prior knowledge of the basic principles of the field. The work is the product of the technical staff of the The Analytic Sciences Corporation (TASC), an organization whose success has resulted largely from its applications of optimal estimation techniques to a wide variety of real situations involving large-scale systemsArthur Gelb writes in the Foreword that "It is our intent throughout to provide a simple and interesting picture of the central issues underlying modern estimation theory and practice. Heuristic, rather than theoretically elegant, arguments are used extensively, with emphasis on physical insights and key questions of practical importance."Numerous illustrative examples, many based on actual applications, have been interspersed throughout the text to lead the student to a concrete understanding of the theoretical material. The inclusion of problems with "built-in" answers at the end of each of the nine chapters further enhances the self-study potential of the text.After a brief historical prelude, the book introduces the mathematics underlying random process theory and state-space characterization of linear dynamic systems. The theory and practice of optimal estimation is them presented, including filtering, smoothing, and prediction. Both linear and non-linear systems, and continuous- and discrete-time cases, are covered in considerable detail. New results are described concerning the application of covariance analysis to non-linear systems and the connection between observers and optimal estimators. The final chapters treat such practical and often pivotal issues as suboptimal structure, and computer loading considerations.This book is an outgrowth of a course given by TASC at a number of US Government facilities. Virtually all of the members of the TASC technical staff have, at one time and in one way or another, contributed to the material contained in the work
Why Read This Book
You should read this book if you need a practical, engineering-focused guide to Kalman filtering and optimal estimation: it blends enough theory to be self-contained while emphasizing implementation, tuning, and real-world examples. You will get concrete techniques for implementing filters and smoothers, diagnosing numerical problems, and applying estimation to tracking and navigation systems.
Who Will Benefit
Engineers and practitioners in radar, communications, and signal processing who implement state‑space estimators or design tracking/navigation systems and need practical guidance on Kalman filters and smoothers.
Level: Intermediate — Prerequisites: Comfort with linear algebra (matrices and basic matrix calculus), basic probability/statistics, and state‑space/linear systems concepts; some exposure to discrete-time systems is helpful.
Key Takeaways
- Implement discrete and continuous Kalman filters and several smoothing algorithms (e.g., RTS smoother).
- Design and tune filter covariance models and process/measurement noise assumptions for real applications.
- Diagnose and mitigate numerical and stability issues in estimator implementations (e.g., covariance collapse, roundoff).
- Apply optimal estimation methods to practical tracking, navigation, and sensor‑fusion problems.
- Extend core linear estimation ideas to handle model uncertainties, time‑varying systems, and batch estimation (least‑squares).
Topics Covered
- Introduction and overview of optimal estimation
- Least squares and linear estimation fundamentals
- State‑space models and formulation of the estimation problem
- Discrete‑time Kalman filter: derivation and properties
- Continuous‑time filtering and discrete/continuous relationships
- Smoothing algorithms (fixed‑interval, fixed‑lag, RTS smoother)
- Filter tuning, initialization, and covariance modeling
- Numerical methods, stability, and implementation issues
- Extensions: time‑varying systems, parameter estimation and batch methods
- Applications: tracking, navigation, radar and aerospace examples
- Appendices: matrix algebra, probability background, implementation notes
Languages, Platforms & Tools
How It Compares
A classic engineering complement to later texts like Grewal & Andrews' Kalman Filtering (which is more up-to-date with MATLAB examples) and Simon's Optimal State Estimation (which consolidates modern nonlinear and implementational topics); Gelb/TASC is more historic and example-driven but less focused on modern nonlinear methods.
