Other eBook Options:

- Presents rigorous, detailed treatments of least squares and Kalman filtering
- Discusses several advanced estimation concepts, such as multiple-model adaptive estimation and unscented, particle, Gaussian sum, and ensemble filtering
- Applies estimation theory to actual dynamic systems, including flight paths, space orbits, and machine control
- Includes tables for all algorithms to enable quick access for programming purposes
- Integrates the required prerequisites (matrix properties, probability, statistics, and optimization methods) in the appendices
- Contains 350 analytical and computer-based problems
- Provides the MATLAB codes for all examples on the book’s website

**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.

**Least Squares Approximation**A Curve Fitting Example

Linear Batch Estimation

Linear Sequential Estimation

Nonlinear Least Squares Estimation

Basis Functions

Advanced Topics

**Probability Concepts in Least Squares**

Minimum Variance Estimation

Unbiased Estimates

Maximum Likelihood Estimation

Cramer-Rao Inequality

Constrained Least Squares Covariance

Maximum Likelihood Estimation

Properties of Maximum Likelihood Estimation

Bayesian Estimation

Advanced Topics

**Sequential State Estimation**

A Simple First-Order Filter Example

Full-Order Estimators

The Discrete-Time Kalman Filter

The Continuous-Time Kalman Filter

The Continuous-Discrete Kalman Filter

Extended Kalman Filter

Unscented Filtering

Constrained Filtering

**Advanced Topics in Sequential State Estimation**

Factorization Methods

Colored-Noise Kalman Filtering

Consistency of the Kalman Filter

Consider Kalman Filtering

Decentralized Filtering

Adaptive Filtering

Ensemble Kalman Filtering

Nonlinear Stochastic Filtering Theory

Gaussian Sum Filtering

Particle Filtering

Error Analysis

Robust Filtering

**Batch State Estimation**

Fixed-Interval Smoothing

Fixed-Point Smoothing

Fixed-Lag Smoothing

Advanced Topics

**Parameter Estimation: Applications**

Attitude Determination

Global Positioning System Navigation

Simultaneous Localization and Mapping

Orbit Determination

Aircraft Parameter Identification

Eigensystem Realization Algorithm

**Estimation of Dynamic Systems: Applications**

Attitude Estimation

Inertial Navigation with GPS

Orbit Estimation

Target Tracking of Aircraft

Smoothing with the Eigensystem Realization Algorithm

**Optimal Control and Estimation Theory**

Calculus of Variations

Optimization with Differential Equation Constraints

Pontryagin’s Optimal Control Necessary Conditions

Discrete-Time Control

Linear Regulator Problems

Linear Quadratic-Gaussian Controllers

Loop Transfer Recovery

Spacecraft Control Design

**Appendix A: Review of Dynamical Systems****Appendix B: Matrix Properties****Appendix C: Basic Probability Concepts****Appendix D: Parameter Optimization Methods****Appendix E: Computer Software**

Index

*A Summary appears at the end of each chapter.*

**Praise for the First Edition**A nice feature of this book is that it makes the effort to explain the underlying principles behind the formula for each algorithm; the relationship between different algorithms is equally well addressed. … The text is a good combination of theory and practice. It will be a valuable addition to references for academic researchers and industrial engineers working in the field of estimation. It will also serve as a useful reference for graduate courses in control and estimation.

—