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| Preface | |
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| Least Squares Approximation | |
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| A Curve Fitting Example | |
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| Linear Batch Estimation | |
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| Linear Least Squares | |
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| Weighted Least Squares | |
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| Constrained Least Squares | |
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| Linear Sequential Estimation | |
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| Nonlinear Least Squares Estimation | |
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| Basis Functions | |
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| Advanced Topics | |
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| Matrix Decompositions in Least Squares | |
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| Kronecker Factorization and Least Squares | |
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| Levenberg-Marquardt Method | |
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| Projections in Least Squares | |
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| Summary | |
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| Probability Concepts in Least Squares | |
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| Minimum Variance Estimation | |
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| Estimation without a priori State Estimates | |
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| Estimation with a priori State Estimates | |
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| Unbiased Estimates | |
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| Cramer-Rao Inequality | |
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| Constrained Least Squares Covariance | |
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| Maximum Likelihood Estimation | |
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| Properties of Maximum Likelihood Estimation | |
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| Invariance Principle | |
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| Consistent Estimator | |
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| Asymptotically Gaussian Property | |
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| Asymptotically Efficient Property | |
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| Bayesian Estimation | |
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| MAP Estimation | |
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| Minimum Risk Estimation | |
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| Advanced Topics | |
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| Nonuniqueness of the Weight Matrix | |
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| Analysis of Covariance Errors | |
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| Ridge Estimation | |
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| Total Least Squares | |
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| Summary | |
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| Sequential State Estimation | |
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| A Simple First-Order Filter Example | |
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| Full-Order Estimators | |
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| Discrete-Time Estimators | |
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| The Discrete-Time Kalman Filter | |
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| Kalman Filter Derivation | |
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| Stability and Joseph's Form | |
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| Information Filter and Sequential Processing | |
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| Steady-State Kalman Filter | |
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| Relationship to Least Squares Estimation | |
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| Correlated Measurement and Process Noise | |
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| Cram�r-Rao Lower Bound | |
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| Orthogonality Principle | |
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| The Continuous-Time Kalman Filter | |
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| Kalman Filter Derivation in Continuous Time | |
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| Kalman Filter Derivation from Discrete Time | |
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| Stability | |
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| Steady-State Kalman Filter | |
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| Correlated Measurement and Process Noise | |
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| The Continuous-Discrete Kalman Filter | |
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| Extended Kalman Filter | |
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| Unscented Filtering | |
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| Constrained Filtering | |
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| Summary | |
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| Advanced Topics in Sequential State Estimation | |
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| Factorization Methods | |
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| Colored-Noise Kalman Filtering | |
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| Consistency of the Kalman Filter | |
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| Consider Kalman Filtering | |
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| Consider Update Equations | |
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| Consider Propagation Equations | |
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| Decentralized Filtering | |
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| Covariance Intersection | |
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| Adaptive Filtering | |
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| Batch Processing for Filter Tuning | |
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| Multiple-Modeling Adaptive Estimation | |
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| Interacting Multiple-Model Estimation | |
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| Ensemble Kalman Filtering | |
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| Nonlinear Stochastic Filtering Theory | |
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| It� Stochastic Differential Equations | |
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| It� Formula | |
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| Fokker-Planck Equation | |
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| Kushner Equation | |
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| Gaussian Sum Filtering | |
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| Particle Filtering | |
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| Optimal Importance Density | |
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| Bootstrap Filter | |
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| Rao-Blackwellized Particle Filter | |
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| Navigation Using a Rao-Blackwellized Particle Filter | |
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| Error Analysis | |
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| Robust Filtering | |
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| Summary | |
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| Batch State Estimation | |
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| Fixed-Interval Smoothing | |
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| Discrete-Time Formulation | |
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| Continuous-Time Formulation | |
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| Nonlinear Smoothing | |
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| Fixed-Point Smoothing | |
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| Discrete-Time Formulation | |
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| Continuous-Time Formulation | |
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| Fixed-Lag Smoothing | |
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| Discrete-Time Formulation | |
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| Continuous-Time Formulation | |
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| Advanced Topics | |
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| Estimation/Control Duality | |
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| Innovations Process | |
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| Summary | |
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| Parameter Estimation: Applications | |
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| Attitude Determination | |
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| Vector Measurement Models | |
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| Maximum Likelihood Estimation | |
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| Optimal Quaternion Solution | |
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| Information Matrix Analysis | |
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| Global Positioning System Navigation | |
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| Simultaneous Localization and Mapping | |
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| 3D Point Cloud Registration Using Linear Least Squares | |
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| Orbit Determination | |
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| Aircraft Parameter Identification | |
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| Eigensystem Realization Algorithm | |
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| Summary | |
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| Estimation of Dynamic Systems: Applications | |
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| Attitude Estimation | |
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| Multiplicative Quaternion Formulation | |
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| Discrete-Time Attitude Estimation | |
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| Murrell's Version | |
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| Farrenkopf's Steady-State Analysis | |
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| Inertial Navigation with GPS | |
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| Extended Kalman Filter Application to GPS/INS | |
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| Orbit Estimation | |
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| Target Tracking of Aircraft | |
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| The �-� Filter | |
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| The �-�-� Filter | |
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| Aircraft Parameter Estimation | |
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| Smoothing with the Eigensystem Realization Algorithm | |
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| Summary | |
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| Optimal Control and Estimation Theory | |
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| Calculus of Variations | |
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| Optimization with Differential Equation Constraints | |
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| Pontryagin's Optimal Control Necessary Conditions | |
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| Discrete-Time Control | |
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| Linear Regulator Problems | |
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| Continuous-Time Formulation | |
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| Discrete-Time Formulation | |
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| Linear Quadratic-Gaussian Controllers | |
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| Continuous-Time Formulation | |
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| Discrete-Time Formulation | |
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| Loop Transfer Recovery | |
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| Spacecraft Control Design | |
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| Summary | |
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| Review of Dynamic Systems | |
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| Linear System Theory | |
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| The State-Space Approach | |
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| Homogeneous Linear Dynamic Systems | |
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| Forced Linear Dynamic Systems | |
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| Linear State Variable Transformations | |
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| Nonlinear Dynamic Systems | |
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| Parametric Differentiation | |
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| Observability and Controllability | |
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| Discrete-Time Systems | |
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| Stability of Linear and Nonlinear Systems | |
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| Attitude Kinematics and Rigid Body Dynamics | |
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| Attitude Kinematics | |
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| Rigid Body Dynamics | |
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| Spacecraft Dynamics and Orbital Mechanics | |
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| Spacecraft Dynamics | |
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| Orbital Mechanics | |
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| Inertial Navigation Systems | |
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| Coordinate Definitions and Earth Model | |
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| GPS Satellites | |
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| Simulation of Sensors | |
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| INS Equations | |
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| Aircraft Flight Dynamics | |
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| Vibration | |
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| Summary | |
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| Matrix Properties | |
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| Basic Definitions of Matrices | |
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| Vectors | |
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| Matrix Norms and Definiteness | |
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| Matrix Decompositions | |
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| Matrix Calculus | |
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| Basic Probability Concepts | |
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| Functions of a Single Discrete-Valued Random Variable | |
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| Functions of Discrete-Valued Random Variables | |
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| Functions of Continuous Random Variables | |
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| Stochastic Processes | |
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| Gaussian Random Variables | |
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| Joint and Conditional Gaussian Case | |
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| Probability Inside a Quadratic Hypersurface | |
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| Chi-Square Random Variables | |
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| Wiener Process | |
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| Propagation of Functions through Various Models | |
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| Linear Matrix Models | |
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| Nonlinear Models | |
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| Scalar and Matrix Expectations | |
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| Random Sampling from a Covariance Matrix | |
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| Parameter Optimization Methods | |
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| Unconstrained Extrema | |
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| Equality Constrained Extrema | |
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| Nonlinear Unconstrained Optimization | |
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| Some Geometrical Insights | |
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| Methods of Gradients | |
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| Second-Order (Gauss-Newton) Algorithm | |
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| Computer Software | |
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| Index | |