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E-raamat: Optimal Estimation of Dynamic Systems

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(State University of New York-Buffalo, USA), (Texas A&M University, College Station, USA)
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Crassidis (State U. of New York-Buffalo) and Junkins (Texas A&M U.-College Station) have substantially rewritten and expanded their 2004 text introducing the fundamentals of estimation to engineers, scientists, and applied mathematicians and to senior undergraduates and first-year graduates in those fields. They trace the development of central concepts and methods of optimal estimation theory, illustrate the application of the methods to problems with varying degrees of analytical and numerical difficulty, and present prototype algorithms at enough detail to stimulate efficient computer programs. Among their topics are probability concepts in least squares, sequential state estimation, batch state estimation, and optimal control and estimation theory. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)

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.

Arvustused

Praise for the First EditionA 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. AIAA Journal, Vol. 43, No. 1, January 2005

Preface xiii
1 Least Squares Approximation
1(62)
1.1 A Curve Fitting Example
2(5)
1.2 Linear Batch Estimation
7(12)
1.2.1 Linear Least Squares
9(5)
1.2.2 Weighted Least Squares
14(2)
1.2.3 Constrained Least Squares
16(3)
1.3 Linear Sequential Estimation
19(6)
1.4 Nonlinear Least Squares Estimation
25(10)
1.5 Basis Functions
35(5)
1.6 Advanced Topics
40(12)
1.6.1 Matrix Decompositions in Least Squares
40(3)
1.6.2 Kronecker Factorization and Least Squares
43(5)
1.6.3 Levenberg-Marquardt Method
48(2)
1.6.4 Projections in Least Squares
50(2)
1.7 Summary
52(11)
2 Probability Concepts in Least Squares
63(72)
2.1 Minimum Variance Estimation
63(11)
2.1.1 Estimation without a priori State Estimates
64(4)
2.1.2 Estimation with a priori State Estimates
68(6)
2.2 Unbiased Estimates
74(2)
2.3 Cramer-Rao Inequality
76(6)
2.4 Constrained Least Squares Covariance
82(2)
2.5 Maximum Likelihood Estimation
84(4)
2.6 Properties of Maximum Likelihood Estimation
88(3)
2.6.1 Invariance Principle
88(1)
2.6.2 Consistent Estimator
88(2)
2.6.3 Asymptotically Gaussian Property
90(1)
2.6.4 Asymptotically Efficient Property
90(1)
2.7 Bayesian Estimation
91(7)
2.7.1 MAP Estimation
91(4)
2.7.2 Minimum Risk Estimation
95(3)
2.8 Advanced Topics
98(21)
2.8.1 Nonuniqueness of the Weight Matrix
98(3)
2.8.2 Analysis of Covariance Errors
101(2)
2.8.3 Ridge Estimation
103(5)
2.8.4 Total Least Squares
108(11)
2.9 Summary
119(16)
3 Sequential State Estimation
135(84)
3.1 A Simple First-Order Filter Example
136(2)
3.2 Full-Order Estimators
138(5)
3.2.1 Discrete-Time Estimators
142(1)
3.3 The Discrete-Time Kalman Filter
143(25)
3.3.1 Kalman Filter Derivation
144(5)
3.3.2 Stability and Joseph's Form
149(2)
3.3.3 Information Filter and Sequential Processing
151(2)
3.3.4 Steady-State Kalman Filter
153(3)
3.3.5 Relationship to Least Squares Estimation
156(2)
3.3.6 Correlated Measurement and Process Noise
158(1)
3.3.7 Cramer-Rao Lower Bound
159(5)
3.3.8 Orthogonality Principle
164(4)
3.4 The Continuous-Time Kalman Filter
168(14)
3.4.1 Kalman Filter Derivation in Continuous Time
168(3)
3.4.2 Kalman Filter Derivation from Discrete Time
171(4)
3.4.3 Stability
175(1)
3.4.4 Steady-State Kalman Filter
176(6)
3.4.5 Correlated Measurement and Process Noise
182(1)
3.5 The Continuous-Discrete Kalman Filter
182(2)
3.6 Extended Kalman Filter
184(8)
3.7 Unscented Filtering
192(7)
3.8 Constrained Filtering
199(3)
3.9 Summary
202(17)
4 Advanced Topics in Sequential State Estimation
219(106)
4.1 Factorization Methods
219(4)
4.2 Colored-Noise Kalman Filtering
223(5)
4.3 Consistency of the Kalman Filter
228(3)
4.4 Consider Kalman Filtering
231(7)
4.4.1 Consider Update Equations
232(2)
4.4.2 Consider Propagation Equations
234(4)
4.5 Decentralized Filtering
238(6)
4.5.1 Covariance Intersection
240(4)
4.6 Adaptive Filtering
244(13)
4.6.1 Batch Processing for Filter Tuning
244(5)
4.6.2 Multiple-Modeling Adaptive Estimation
249(3)
4.6.3 Interacting Multiple-Model Estimation
252(5)
4.7 Ensemble Kalman Filtering
257(3)
4.8 Nonlinear Stochastic Filtering Theory
260(10)
4.8.1 Ito Stochastic Differential Equations
263(2)
4.8.2 Ito Formula
265(2)
4.8.3 Fokker-Planck Equation
267(2)
4.8.4 Kushner Equation
269(1)
4.9 Gaussian Sum Filtering
270(3)
4.10 Particle Filtering
273(23)
4.10.1 Optimal Importance Density
277(2)
4.10.2 Bootstrap Filter
279(8)
4.10.3 Rao-Blackwellized Particle Filter
287(4)
4.10.4 Navigation Using a Rao-Blackwellized Particle Filter
291(5)
4.11 Error Analysis
296(2)
4.12 Robust Filtering
298(4)
4.13 Summary
302(23)
5 Batch State Estimation
325(66)
5.1 Fixed-Interval Smoothing
326(27)
5.1.1 Discrete-Time Formulation
327(12)
5.1.2 Continuous-Time Formulation
339(10)
5.1.3 Nonlinear Smoothing
349(4)
5.2 Fixed-Point Smoothing
353(7)
5.2.1 Discrete-Time Formulation
353(4)
5.2.2 Continuous-Time Formulation
357(3)
5.3 Fixed-Lag Smoothing
360(7)
5.3.1 Discrete-Time Formulation
360(3)
5.3.2 Continuous-Time Formulation
363(4)
5.4 Advanced Topics
367(15)
5.4.1 Estimation/Control Duality
367(8)
5.4.2 Innovations Process
375(7)
5.5 Summary
382(9)
6 Parameter Estimation: Applications
391(60)
6.1 Attitude Determination
391(12)
6.1.1 Vector Measurement Models
392(3)
6.1.2 Maximum Likelihood Estimation
395(1)
6.1.3 Optimal Quaternion Solution
396(4)
6.1.4 Information Matrix Analysis
400(3)
6.2 Global Positioning System Navigation
403(4)
6.3 Simultaneous Localization and Mapping
407(4)
6.3.1 3D Point Cloud Registration Using Linear Least Squares
408(3)
6.4 Orbit Determination
411(8)
6.5 Aircraft Parameter Identification
419(6)
6.6 Eigensystem Realization Algorithm
425(7)
6.7 Summary
432(19)
7 Estimation of Dynamic Systems: Applications
451(62)
7.1 Attitude Estimation
451(15)
7.1.1 Multiplicative Quaternion Formulation
452(5)
7.1.2 Discrete-Time Attitude Estimation
457(3)
7.1.3 Murrell's Version
460(3)
7.1.4 Farrenkopf's Steady-State Analysis
463(3)
7.2 Inertial Navigation with GPS
466(10)
7.2.1 Extended Kalman Filter Application to GPS/INS
467(9)
7.3 Orbit Estimation
476(3)
7.4 Target Tracking of Aircraft
479(16)
7.4.1 The α-β Filter
479(7)
7.4.2 The α-β-γ Filter
486(4)
7.4.3 Aircraft Parameter Estimation
490(5)
7.5 Smoothing with the Eigensystem Realization Algorithm
495(4)
7.6 Summary
499(14)
8 Optimal Control and Estimation Theory
513(62)
8.1 Calculus of Variations
514(5)
8.2 Optimization with Differential Equation Constraints
519(2)
8.3 Pontryagin's Optimal Control Necessary Conditions
521(7)
8.4 Discrete-Time Control
528(1)
8.5 Linear Regulator Problems
529(11)
8.5.1 Continuous-Time Formulation
530(6)
8.5.2 Discrete-Time Formulation
536(4)
8.6 Linear Quadratic-Gaussian Controllers
540(8)
8.6.1 Continuous-Time Formulation
541(4)
8.6.2 Discrete-Time Formulation
545(3)
8.7 Loop Transfer Recovery
548(5)
8.8 Spacecraft Control Design
553(5)
8.9 Summary
558(17)
A Review of Dynamic Systems
575(86)
A.1 Linear System Theory
575(13)
A.1.1 The State-Space Approach
576(3)
A.1.2 Homogeneous Linear Dynamic Systems
579(4)
A.1.3 Forced Linear Dynamic Systems
583(2)
A.1.4 Linear State Variable Transformations
585(3)
A.2 Nonlinear Dynamic Systems
588(3)
A.3 Parametric Differentiation
591(2)
A.4 Observability and Controllability
593(4)
A.5 Discrete-Time Systems
597(5)
A.6 Stability of Linear and Nonlinear Systems
602(6)
A.7 Attitude Kinematics and Rigid Body Dynamics
608(9)
A.7.1 Attitude Kinematics
608(6)
A.7.2 Rigid Body Dynamics
614(3)
A.8 Spacecraft Dynamics and Orbital Mechanics
617(7)
A.8.1 Spacecraft Dynamics
617(2)
A.8.2 Orbital Mechanics
619(5)
A.9 Inertial Navigation Systems
624(11)
A.9.1 Coordinate Definitions and Earth Model
624(4)
A.9.2 GPS Satellites
628(2)
A.9.3 Simulation of Sensors
630(3)
A.9.4 INS Equations
633(2)
A.10 Aircraft Flight Dynamics
635(3)
A.11 Vibration
638(6)
A.12 Summary
644(17)
B Matrix Properties
661(20)
B.1 Basic Definitions of Matrices
661(5)
B.2 Vectors
666(4)
B.3 Matrix Norms and Definiteness
670(2)
B.4 Matrix Decompositions
672(5)
B.5 Matrix Calculus
677(4)
C Basic Probability Concepts
681(28)
C.1 Functions of a Single Discrete-Valued Random Variable
681(4)
C.2 Functions of Discrete-Valued Random Variables
685(2)
C.3 Functions of Continuous Random Variables
687(2)
C.4 Stochastic Processes
689(1)
C.5 Gaussian Random Variables
690(4)
C.5.1 Joint and Conditional Gaussian Case
691(1)
C.5.2 Probability Inside a Quadratic Hypersurface
692(2)
C.6 Chi-Square Random Variables
694(1)
C.7 Wiener Process
695(5)
C.8 Propagation of Functions through Various Models
700(3)
C.8.1 Linear Matrix Models
700(1)
C.8.2 Nonlinear Models
701(2)
C.9 Scalar and Matrix Expectations
703(1)
C.10 Random Sampling from a Covariance Matrix
704(5)
D Parameter Optimization Methods
709(16)
D.1 Unconstrained Extrema
709(2)
D.2 Equality Constrained Extrema
711(5)
D.3 Nonlinear Unconstrained Optimization
716(9)
D.3.1 Some Geometrical Insights
717(1)
D.3.2 Methods of Gradients
718(2)
D.3.3 Second-Order (Gauss-Newton) Algorithm
720(5)
E Computer Software
725(2)
Index 727
John L. Crassidis, Ph.D., is a professor of mechanical and aerospace engineering and the associate director of the Center for Multisource Information Fusion at the University at Buffalo, State University of New York. He previously worked at Texas A&M University, the Catholic University of America, and NASAs Goddard Space Flight Center, where he contributed to attitude determination and control schemes for numerous spacecraft missions.

John L. Junkins, Ph.D., is a distinguished professor of aerospace engineering and the founder and director of the Center for Mechanics and Control at Texas A&M University. In addition to his historical contributions in analytical dynamics and spacecraft GNC, Dr. Junkins and his team have designed, developed, and demonstrated several new electro-optical sensing technologies.
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