OPTIMAL ESTIMATION of DYNAMIC SYSTEMS

Transcription

1 CHAPMAN & HALL/CRC APPLIED MATHEMATICS -. AND NONLINEAR SCIENCE SERIES OPTIMAL ESTIMATION of DYNAMIC SYSTEMS John L Crassidis and John L. Junkins CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C.

2 Contents 1 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 52 2 Probability Concepts in Least Squares Minimum Variance Estimation Estimation without a priori State Estimates Estimation with a priori 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 127 XI

3 Xll 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 159,. 3.9 Aircraft Flight Dynamics Vibration Summary 173 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 Eigensystem Realization Algorithm Summary 226 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 282

4 Xlll 5.5 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-p Filter The a-p-y Filter Aircraft Parameter Estimation Smoothing with the Eigensystem Realization Algorithm Summary 456

5 XIV 8 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 517 A Matrix Properties 533 A.I Basic Definitions of Matrices 533 A.2 Vectors 538 A.3 Matrix Norms and Definiteness 542 A.4 Matrix Decompositions 544 A.5 Matrix Calculus 548 B Basic Probability Concepts 553 B.I Functions of a Single Discrete-Valued Random Variable 553 B.2 Functions of Discrete-Valued Random Variables 557 B.3 Functions of Continuous Random Variables 559 B.4 Gaussian Random Variables 561 B.5 Chi-Square Random Variables 563 B.6 Propagation of Functions through Various Models 565 B.6.1 Linear Matrix Models 565 B.6.2 Nonlinear Models 565 C Parameter Optimization Methods 569 C. 1 Unconstrained Extrema 569 C.2 Equality Constrained Extrema 571 C.3 Nonlinear Unconstrained Optimization 576 C.3.1 Some Geometrical Insights 577 C.3.2 Methods of Gradients 578 C.3.3 Second-Order (Gauss-Newton) Algorithm 580 D Computer Software 585 Index 587