Optimal Estimation of Dynamic Systems (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)

Most newcomers to the field of linear stochastic estimation go through a difficult process in understanding and applying the theory.This book minimizes the process while introducing the fundamentals of optimal estimation. Optimal Estimation of Dynamic Systems explores topics that are important in the field of control where the signals received are used to determine highly sensitive processes such as the flight path of a plane, the orbit of a space vehicle, or the control of a machine. The authors use dynamic models from mechanical and aerospace engineering to provide immediate results of estimation concepts with a minimal reliance on mathematical skills. The book documents the development of the central concepts and methods of optimal estimation theory in a manner accessible to engineering students, applied mathematicians, and practicing engineers. It includes rigorous theoretial derivations and a significant amount of qualitiative discussion and judgements. It also presents prototype algorithms, giving detail and discussion to stimulate development of efficient computer programs and intelligent use of them. This book illustrates the application of optimal estimation methods to problems with varying degrees of analytical and numercial difficulty. It compares various approaches to help develop a feel for the absolute and relative utility of different methods, and provides many applications in the fields of aerospace, mechanical, and electrical engineering.

LEAST SQUARES APPROXIMATION
A Curve Fitting Example
Linear Batch Estimation
Linear Least Squares
Weighted Least Squares
Constrained Least Squares
Linear Sequential Estimation
Nonlinear Least Squares Estimation
Basis Functions
Advanced Topics
Matrix Decompositions in Least Squares
Kronecker Factorization and Least Squares
Levenberg-Marquardt Method
Projections in Least Squares
Summary

PROBABILITY CONCEPTS IN LEAST SQUARES
Minimum Variance Estimation
Estimation without a Prior State Estimates
Estimation with a Prior State Estimates
Unbiased Estimates
Maximum Likelihood Estimation
Cramer-Rao Inequality
Nonuniqueness of the Weight Matrix
Bayesian Estimation
Advanced Topics
Analysis of Covariance Errors
Ridge Estimation
Total Least Squares
Summary

REVIEW OF DYNAMICAL SYSTEMS
Linear System Theory
The State Space Approach
Homogeneous Linear Dynamical Systems
Forced Linear Dynamical Systems
Linear State Variable Transformations
Nonlinear Dynamical Systems
Parametric Differentiation
Observability
Discrete-Time Systems
Stability of Linear and Nonlinear Systems
Attitude Kinematics and Rigid Body Dynamics
Attitude Kinematics
Rigid Body Dynamics
Spacecraft Dynamics and Orbital Mechanics
Spacecraft Dynamics
Orbital Mechanics
Aircraft Flight Dynamics
Vibration
Summary

PARAMETER ESTIMATION: APPLICATIONS
Global Positioning System Navigation
Attitude Determination
Vector Measurement Models
Maximum Likelihood Estimation
Optimal Quaternion Solution
Information Matrix Analysis
Orbit Determination
Aircraft Parameter Identification
Eigen-system Realization Algorithm
Summary

SEQUENTIAL STATE ESTIMATION
A Simple First-Order Filter Example
Full-Order Estimators
Discrete-Time Estimators
The Discrete-Time Kalman Filter
Kalman Filter Derivation
Stability and Joseph's Form
Information Filter and Sequential Processing
Steady-State Kalman Filter
Correlated Measurement and Process Noise
Orthogonality Principle
The Continuous-Time Kalman Filter
Kalman Filter Derivation in Continuous Time
Kalman Filter Derivation from Discrete Time
Stability
Steady-State Kalman Filter
Correlated Measurement and Process Noise
The Continuous-Discrete Kalman Filter
Extended Kalman Filter
Advanced Topics
Factorization Methods
Colored-Noise Kalman Filtering
Consistency of the Kalman Filter
Adaptive Filtering
Error Analysis
Unscented Filtering
Robust Filtering
Summary

BATCH STATE ESTIMATION
Fixed-Interval Smoothing
Discrete-Time Formulation
Continuous-Time Formulation
Nonlinear Smoothing
Fixed-Point Smoothing
Discrete-Time Formulation
Continuous-Time Formulation
Fixed-Lag Smoothing
Discrete-Time Formulation
Continuous-Time Formulation
Advanced Topics
Estimation/Control Duality
Innovations Process
Summary

ESTIMATION OF DYNAMIC SYSTEMS: APPLICATIONS
GPS Position Estimation
GPS Coordinate Transformations
Extended Kalman Filter Application to GPS
Attitude Estimation
Multiplicative Quaternion Formulation
Discrete-Time Attitude Estimation
Murrell's Version
Farrenkopf's Steady-State Analysis
Orbit Estimation
Target Tracking of Aircraft
The a-b Filter
The a-b-g Filter
Aircraft Parameter Estimation
Smoothing with the Eigen-system Realization Algorithm
Summary

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
Continuous-Time Formulation
Discrete-Time Formulation
Linear Quadratic-Gaussian Controllers
Continuous-Time Formulation
Discrete-Time Formulation
Loop Transfer Recovery
Spacecraft Control Design
Summary

APPENDIX A MATRIX PROPERTIES
Basic Definitions of Matrices
Vectors
Matrix Norms and Definiteness
Matrix Decompositions
Matrix Calculus

APPENDIX B BASIC PROBABILITY CONCEPTS
Functions of a Single Discrete-Valued Random Variable
Functions of Discrete-Valued Random Variables
Functions of Continuous Random Variables
Gaussian Random Variables
Chi-Square Random Variables
Propagation of Functions through Various Models
Linear Matrix Models
Nonlinear Models

APPENDIX C PARAMETER OPTIMIZATION METHODS
C.1 Unconstrained Extrema
C.2 Equality Constrained Extrema
C.3 Nonlinear Unconstrained Optimization
C.3.1 Some Geometrical Insights
C.3.2 Methods of Gradients
C.3.3 Second-Order (Gauss-Newton) Algorithm

APPENDIX D COMPUTER SOFTWARE

Index