Optimal Estimation of Dynamic Systems (Advances in Applied Mathematics)
Optimal Estimation of Dynamic Systems, Second Edition highlights the importance of both physical and numerical modeling in solving dynamics-based estimation problems found in engineering systems. Accessible to engineering students, applied mathematicians, and practicing engineers, the text presents the central concepts and methods of optimal estimation theory and applies the methods to problems with varying degrees of analytical and numerical difficulty. Different approaches are often compared to show their absolute and relative utility. The authors also offer prototype algorithms to stimulate the development and proper use of efficient computer programs. MATLAB® codes for the examples are available on the book’s website.
New to the Second Edition
With more than 100 pages of new material, this reorganized edition expands upon the best-selling original to include comprehensive developments and updates. It incorporates new theoretical results, an entirely new chapter on advanced sequential state estimation, and additional examples and exercises.
An ideal self-study guide for practicing engineers as well as senior undergraduate and beginning graduate students, the book introduces the fundamentals of estimation and helps newcomers to understand the relationships between the estimation and modeling of dynamical systems. It also illustrates the application of the theory to real-world situations, such as spacecraft attitude determination, GPS navigation, orbit determination, and aircraft tracking.
Why Read This Book
You will learn how to turn physical models and noisy measurements into precise state and parameter estimates using principled optimal-estimation methods. This book emphasizes both the mathematical foundations and practical numerical algorithms (with prototype MATLAB code), making it ideal for applying Kalman filters, smoothers, and nonlinear estimators to real DSP, radar, navigation, and communications problems.
Who Will Benefit
Graduate students, researchers, and practicing engineers in signal processing, radar, communications, and control who need to design and implement optimal state estimators and sensor-fusion algorithms.
Level: Intermediate — Prerequisites: Undergraduate linear algebra, probability and stochastic processes, basic signals & systems or control theory, and familiarity with MATLAB or similar numerical computing environments.
Key Takeaways
- Derive and implement the discrete- and continuous-time Kalman filter and Rauch–Tung–Striebel smoothing algorithms.
- Apply batch and sequential least-squares estimation methods to state and parameter identification problems.
- Develop and compare practical nonlinear estimators (e.g., EKF and other nonlinear approaches) and understand their numerical issues.
- Quantify estimator performance using covariance analysis, observability concepts, and bounds such as the Cramér–Rao lower bound.
- Adapt estimation techniques to common engineering applications (navigation, radar, communications, and signal processing) and convert theory into working MATLAB code.
Topics Covered
- Introduction and Motivation: Modeling for Estimation
- Mathematical Preliminaries: Linear Algebra and Stochastic Processes
- Least-Squares and Batch Estimation
- Discrete-Time Optimal Linear Estimation (Kalman Filter)
- Continuous-Time Estimation and Hybrid Systems
- Smoothing and Fixed-Interval/Fixed-Lag Algorithms
- Numerical Implementation, Stability, and Tuning
- Nonlinear Estimation Techniques (EKF and related methods)
- Parameter Estimation and System Identification
- Adaptive and Robust Filtering Considerations
- Practical Applications: Navigation, Radar, and Communications
- MATLAB Algorithms and Example Implementations
Languages, Platforms & Tools
How It Compares
Complementary to Gelb's classical Applied Optimal Estimation and Dan Simon's Optimal State Estimation, Crassidis's book balances rigorous theory with modern numerical implementation and extensive MATLAB prototype code.
