Optimal estimation of dynamic systems

Title:

Personal Author:

Crassidis, John L.

Series:

Chapman & Hall/CRC applied mathematics & nonlinear science ; 24

Edition:

2nd ed.

Publication Information:

Boca Raton, F.L. : CRC Press, c2012

Physical Description:

xiv, 733 p. : ill. ; 25 cm.

ISBN:

9781439839850

Subject Term:

System analysis

Estimation theory

Added Author:

Junkins, John L

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010316427	QA402 C73 2012	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	33000000000758	QA402 C73 2012	Open Access Book	Book	Searching... Unknown

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.

Author Notes

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 NASA's 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.

Preface	p. xiii
1 Least Squares Approximation	p. 1
1.1 A Curve Fitting Example	p. 2
1.2 Linear Batch Estimation	p. 7
1.2.1 Linear Least Squares	p. 9
1.2.2 Weighted Least Squares	p. 14
1.2.3 Constrained Least Squares	p. 16
1.3 Linear Sequential Estimation	p. 19
1.4 Nonlinear Least Squares Estimation	p. 25
1.5 Basis Functions	p. 35
1.6 Advanced Topics	p. 40
1.6.1 Matrix Decompositions in Least Squares	p. 40
1.6.2 Kronecker Factorization and Least Squares	p. 43
1.6.3 Levenberg-Marquardt Method	p. 48
1.6.4 Projections in Least Squares	p. 50
1.7 Summary	p. 52
2 Probability Concepts in Least Squares	p. 63
2.1 Minimum Variance Estimation	p. 63
2.1.1 Estimation without a priori State Estimates	p. 64
2.1.2 Estimation with a priori State Estimates	p. 68
2.2 Unbiased Estimates	p. 74
2.3 Cramer-Rao Inequality	p. 76
2.4 Constrained Least Squares Covariance	p. 82
2.5 Maximum Likelihood Estimation	p. 84
2.6 Properties of Maximum Likelihood Estimation	p. 88
2.6.1 Invariance Principle	p. 88
2.6.2 Consistent Estimator	p. 88
2.6.3 Asymptotically Gaussian Property	p. 90
2.6.4 Asymptotically Efficient Property	p. 90
2.7 Bayesian Estimation	p. 91
2.7.1 MAP Estimation	p. 91
2.7.2 Minimum Risk Estimation	p. 95
2.8 Advanced Topics	p. 98
2.8.1 Nonuniqueness of the Weight Matrix	p. 98
2.8.2 Analysis of Covariance Errors	p. 101
2.8.3 Ridge Estimation	p. 103
2.8.4 Total Least Squares	p. 108
2.9 Summary	p. 119
3 Sequential State Estimation	p. 135
3.1 A Simple First-Order Filter Example	p. 136
3.2 Full-Order Estimators	p. 138
3.2.1 Discrete-Time Estimators	p. 142
3.3 The Discrete-Time Kalman Filter	p. 143
3.3.1 Kalman Filter Derivation	p. 144
3.3.2 Stability and Joseph's Form	p. 149
3.3.3 Information Filter and Sequential Processing	p. 151
3.3.4 Steady-State Kalman Filter	p. 153
3.3.5 Relationship to Least Squares Estimation	p. 156
3.3.6 Correlated Measurement and Process Noise	p. 158
3.3.7 Cramér-Rao Lower Bound	p. 159
3.3.8 Orthogonality Principle	p. 164
3.4 The Continuous-Time Kalman Filter	p. 168
3.4.1 Kalman Filter Derivation in Continuous Time	p. 168
3.4.2 Kalman Filter Derivation from Discrete Time	p. 171
3.4.3 Stability	p. 175
3.4.4 Steady-State Kalman Filter	p. 176
3.4.5 Correlated Measurement and Process Noise	p. 182
3.5 The Continuous-Discrete Kalman Filter	p. 182
3.6 Extended Kalman Filter	p. 184
3.7 Unscented Filtering	p. 192
3.8 Constrained Filtering	p. 199
3.9 Summary	p. 202
4 Advanced Topics in Sequential State Estimation	p. 219
4.1 Factorization Methods	p. 219
4.2 Colored-Noise Kalman Filtering	p. 223
4.3 Consistency of the Kalman Filter	p. 228
4.4 Consider Kalman Filtering	p. 231
4.4.1 Consider Update Equations	p. 232
4.4.2 Consider Propagation Equations	p. 234
4.5 Decentralized Filtering	p. 238
4.5.1 Covariance Intersection	p. 240
4.6 Adaptive Filtering	p. 244
4.6.1 Batch Processing for Filter Tuning	p. 244
4.6.2 Multiple-Modeling Adaptive Estimation	p. 249
4.6.3 Interacting Multiple-Model Estimation	p. 252
4.7 Ensemble Kalman Filtering	p. 257
4.8 Nonlinear Stochastic Filtering Theory	p. 260
4.8.1 Itô Stochastic Differential Equations	p. 263
4.8.2 Itô Formula	p. 265
4.8.3 Fokker-Planck Equation	p. 267
4.8.4 Kushner Equation	p. 269
4.9 Gaussian Sum Filtering	p. 270
4.10 Particle Filtering	p. 273
4.10.1 Optimal Importance Density	p. 277
4.10.2 Bootstrap Filter	p. 279
4.10.3 Rao-Blackwellized Particle Filter	p. 287
4.10.4 Navigation Using a Rao-Blackwellized Particle Filter	p. 291
4.11 Error Analysis	p. 296
4.12 Robust Filtering	p. 298
4.13 Summary	p. 302
5 Batch State Estimation	p. 325
5.1 Fixed-Interval Smoothing	p. 326
5.1.1 Discrete-Time Formulation	p. 327
5.1.2 Continuous-Time Formulation	p. 339
5.1.3 Nonlinear Smoothing	p. 349
5.2 Fixed-Point Smoothing	p. 353
5.2.1 Discrete-Time Formulation	p. 353
5.2.2 Continuous-Time Formulation	p. 357
5.3 Fixed-Lag Smoothing	p. 360
5.3.1 Discrete-Time Formulation	p. 360
5.3.2 Continuous-Time Formulation	p. 363
5.4 Advanced Topics	p. 367
5.4.1 Estimation/Control Duality	p. 367
5.4.2 Innovations Process	p. 375
5.5 Summary	p. 382
6 Parameter Estimation: Applications	p. 391
6.1 Attitude Determination	p. 391
6.1.1 Vector Measurement Models	p. 392
6.1.2 Maximum Likelihood Estimation	p. 395
6.1.3 Optimal Quaternion Solution	p. 396
6.1.4 Information Matrix Analysis	p. 400
6.2 Global Positioning System Navigation	p. 403
6.3 Simultaneous Localization and Mapping	p. 407
6.3.1 3D Point Cloud Registration Using Linear Least Squares	p. 408
6.4 Orbit Determination	p. 411
6.5 Aircraft Parameter Identification	p. 419
6.6 Eigensystem Realization Algorithm	p. 425
6.7 Summary	p. 432
7 Estimation of Dynamic Systems: Applications	p. 451
7.1 Attitude Estimation	p. 451
7.1.1 Multiplicative Quaternion Formulation	p. 452
7.1.2 Discrete-Time Attitude Estimation	p. 457
7.1.3 Murrell's Version	p. 460
7.1.4 Farrenkopf's Steady-State Analysis	p. 463
7.2 Inertial Navigation with GPS	p. 466
7.2.1 Extended Kalman Filter Application to GPS/INS	p. 467
7.3 Orbit Estimation	p. 476
7.4 Target Tracking of Aircraft	p. 179
7.4.1 The ¿-ß Filter	p. 479
7.4.2 The ¿-ß-¿ Filter	p. 486
7.4.3 Aircraft Parameter Estimation	p. 490
7.5 Smoothing with the Eigensystem Realization Algorithm	p. 495
7.6 Summary	p. 499
8 Optimal Control and Estimation Theory	p. 513
8.1 Calculus of Variations	p. 514
8.2 Optimization with Differential Equation Constraints	p. 519
8.3 Pontryagin's Optimal Control Necessary Conditions	p. 521
8.4 Discrete-Time Control	p. 528
8.5 Linear Regulator Problems	p. 529
8.5.1 Continuous-Time Formulation	p. 530
8.5.2 Discrete-Time Formulation	p. 536
8.6 Linear Quadratic-Gaussian Controllers	p. 540
8.6.1 Continuous-Time Formulation	p. 541
8.6.2 Discrete-Time Formulation	p. 545
8.7 Loop Transfer Recovery	p. 548
8.8 Spacecraft Control Design	p. 553
8.9 Summary	p. 558
A Review of Dynamic Systems	p. 575
A.l Linear System Theory	p. 575
A.1.1 The State-Space Approach	p. 576
A.1.2 Homogeneous Linear Dynamic Systems	p. 579
A.1.3 Forced Linear Dynamic Systems	p. 583
A.1.4 Linear State Variable Transformations	p. 585
A.2 Nonlinear Dynamic Systems	p. 588
A.3 Parametric Differentiation	p. 591
A.4 Observability and Controllability	p. 593
A.5 Discrete-Time Systems	p. 597
A.6 Stability of Linear and Nonlinear Systems	p. 602
A.7 Attitude Kinematics and Rigid Body Dynamics	p. 608
A.7.1 Attitude Kinematics	p. 608
A.7.2 Rigid Body Dynamics	p. 614
A. 8 Spacecraft Dynamics and Orbital Mechanics	p. 617
A.8.1 Spacecraft Dynamics	p. 617
A.8.2 Orbital Mechanics	p. 619
A.9 Inertial Navigation Systems	p. 624
A.9.1 Coordinate Definitions and Earth Model	p. 624
A.9.2 GPS Satellites	p. 628
A.9.3 Simulation of Sensors	p. 630
A.9.4 INS Equations	p. 633
A.10 Aircraft Flight Dynamics	p. 635
A.11 Vibration	p. 638
A.12 Summary	p. 644
B Matrix Properties	p. 661
B.1 Basic Definitions of Matrices	p. 661
B.2 Vectors	p. 666
B.3 Matrix Norms and Definiteness	p. 670
B.4 Matrix Decompositions	p. 672
B.5 Matrix Calculus	p. 677
C Basic Probability Concepts	p. 681
C.l Functions of a Single Discrete-Valued Random Variable	p. 681
C.2 Functions of Discrete-Valued Random Variables	p. 685
C.3 Functions of Continuous Random Variables	p. 687
C.4 Stochastic Processes	p. 689
C.5 Gaussian Random Variables	p. 690
C.5.1 Joint and Conditional Gaussian Case	p. 691
C.5.2 Probability Inside a Quadratic Hypersurface	p. 692
C.6 Chi-Square Random Variables	p. 694
C.7 Wiener Process	p. 695
C.8 Propagation of Functions through Various Models	p. 700
C.8.1 Linear Matrix Models	p. 700
C.8.2 Nonlinear Models	p. 701
C.9 Scalar and Matrix Expectations	p. 703
C.10 Random Sampling from a Covariance Matrix	p. 704
D Parameter Optimization Methods	p. 709
D.l Unconstrained Extrema	p. 709
D.2 Equality Constrained Extrema	p. 711
D.3 Nonlinear Unconstrained Optimization	p. 716
D.3.1 Some Geometrical Insights	p. 717
D.3.2 Methods of Gradients	p. 718
D.3.3 Second-Order (Gauss-Newton) Algorithm	p. 720
E Computer Software	p. 725
Index	p. 727

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