Optimal estimation of dynamic systems

Title:

Personal Author:

Crassidis, John L.

Publication Information:

Boca Raton : Chapman & Hall/CRC, 2004

ISBN:

9781584883913

Subject Term:

System analysis

Estimation theory

Added Author:

Junkins, John L.

Available:*

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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.

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. 15
1.3 Linear Sequential Estimation	p. 18
1.4 Nonlinear Least Squares Estimation	p. 24
1.5 Basis Functions	p. 34
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. 44
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 Maximum Likelihood Estimation	p. 75
2.4 Cramer-Rao Inequality	p. 81
2.5 Nonuniqueness of the Weight Matrix	p. 86
2.6 Bayesian Estimation	p. 89
2.7 Advanced Topics	p. 96
2.7.1 Analysis of Covariance Errors	p. 97
2.7.2 Ridge Estimation	p. 99
2.7.3 Total Least Squares	p. 103
2.8 Summary	p. 107
3 Review of Dynamical Systems	p. 119
3.1 Linear System Theory	p. 119
3.1.1 The State Space Approach	p. 120
3.1.2 Homogeneous Linear Dynamical Systems	p. 123
3.1.3 Forced Linear Dynamical Systems	p. 127
3.1.4 Linear State Variable Transformations	p. 129
3.2 Nonlinear Dynamical Systems	p. 132
3.3 Parametric Differentiation	p. 135
3.4 Observability	p. 137
3.5 Discrete-Time Systems	p. 140
3.6 Stability of Linear and Nonlinear Systems	p. 143
3.7 Attitude Kinematics and Rigid Body Dynamics	p. 149
3.7.1 Attitude Kinematics	p. 149
3.7.2 Rigid Body Dynamics	p. 155
3.8 Spacecraft Dynamics and Orbital Mechanics	p. 157
3.8.1 Spacecraft Dynamics	p. 157
3.8.2 Orbital Mechanics	p. 159
3.9 Aircraft Flight Dynamics	p. 164
3.10 Vibration	p. 168
3.11 Summary	p. 173
4 Parameter Estimation: Applications	p. 189
4.1 Global Positioning System Navigation	p. 189
4.2 Attitude Determination	p. 194
4.2.1 Vector Measurement Models	p. 194
4.2.2 Maximum Likelihood Estimation	p. 197
4.2.3 Optimal Quaternion Solution	p. 198
4.2.4 Information Matrix Analysis	p. 202
4.3 Orbit Determination	p. 205
4.4 Aircraft Parameter Identification	p. 213
4.5 Eigensystem Realization Algorithm	p. 219
4.6 Summary	p. 226
5 Sequential State Estimation	p. 243
5.1 A Simple First-Order Filter Example	p. 244
5.2 Full-Order Estimators	p. 246
5.2.1 Discrete-Time Estimators	p. 250
5.3 The Discrete-Time Kalman Filter	p. 251
5.3.1 Kalman Filter Derivation	p. 252
5.3.2 Stability and Joseph's Form	p. 256
5.3.3 Information Filter and Sequential Processing	p. 259
5.3.4 Steady-State Kalman Filter	p. 260
5.3.5 Correlated Measurement and Process Noise	p. 263
5.3.6 Orthogonality Principle	p. 265
5.4 The Continuous-Time Kalman Filter	p. 270
5.4.1 Kalman Filter Derivation in Continuous Time	p. 270
5.4.2 Kalman Filter Derivation from Discrete Time	p. 273
5.4.3 Stability	p. 277
5.4.4 Steady-State Kalman Filter	p. 277
5.4.5 Correlated Measurement and Process Noise	p. 282
5.5 The Continuous-Discrete Kalman Filter	p. 283
5.6 Extended Kalman Filter	p. 285
5.7 Advanced Topics	p. 292
5.7.1 Factorization Methods	p. 292
5.7.2 Colored-Noise Kalman Filtering	p. 297
5.7.3 Consistency of the Kalman Filter	p. 301
5.7.4 Adaptive Filtering	p. 304
5.7.5 Error Analysis	p. 308
5.7.6 Unscented Filtering	p. 310
5.7.7 Robust Filtering	p. 316
5.8 Summary	p. 320
6 Batch State Estimation	p. 343
6.1 Fixed-Interval Smoothing	p. 344
6.1.1 Discrete-Time Formulation	p. 344
6.1.2 Continuous-Time Formulation	p. 357
6.1.3 Nonlinear Smoothing	p. 367
6.2 Fixed-Point Smoothing	p. 370
6.2.1 Discrete-Time Formulation	p. 371
6.2.2 Continuous-Time Formulation	p. 376
6.3 Fixed-Lag Smoothing	p. 378
6.3.1 Discrete-Time Formulation	p. 379
6.3.2 Continuous-Time Formulation	p. 382
6.4 Advanced Topics	p. 385
6.4.1 Estimation/Control Duality	p. 385
6.4.2 Innovations Process	p. 394
6.5 Summary	p. 401
7 Estimation of Dynamic Systems: Applications	p. 411
7.1 GPS Position Estimation	p. 411
7.1.1 GPS Coordinate Transformations	p. 411
7.1.2 Extended Kalman Filter Application to GPS	p. 415
7.2 Attitude Estimation	p. 419
7.2.1 Multiplicative Quaternion Formulation	p. 419
7.2.2 Discrete-Time Attitude Estimation	p. 425
7.2.3 Murrell's Version	p. 427
7.2.4 Farrenkopf's Steady-State Analysis	p. 431
7.3 Orbit Estimation	p. 433
7.4 Target Tracking of Aircraft	p. 435
7.4.1 The [alpha]-[beta] Filter	p. 435
7.4.2 The [alpha]-[beta]-[gamma] Filter	p. 443
7.4.3 Aircraft Parameter Estimation	p. 447
7.5 Smoothing with the Eigensystem Realization Algorithm	p. 452
7.6 Summary	p. 456
8 Optimal Control and Estimation Theory	p. 471
8.1 Calculus of Variations	p. 472
8.2 Optimization with Differential Equation Constraints	p. 477
8.3 Pontryagin's Optimal Control Necessary Conditions	p. 479
8.4 Discrete-Time Control	p. 485
8.5 Linear Regulator Problems	p. 487
8.5.1 Continuous-Time Formulation	p. 488
8.5.2 Discrete-Time Formulation	p. 494
8.6 Linear Quadratic-Gaussian Controllers	p. 498
8.6.1 Continuous-Time Formulation	p. 499
8.6.2 Discrete-Time Formulation	p. 503
8.7 Loop Transfer Recovery	p. 506
8.8 Spacecraft Control Design	p. 511
8.9 Summary	p. 517
A Matrix Properties	p. 533
A.1 Basic Definitions of Matrices	p. 533
A.2 Vectors	p. 538
A.3 Matrix Norms and Definiteness	p. 542
A.4 Matrix Decompositions	p. 544
A.5 Matrix Calculus	p. 548
B Basic Probability Concepts	p. 553
B.1 Functions of a Single Discrete-Valued Random Variable	p. 553
B.2 Functions of Discrete-Valued Random Variables	p. 557
B.3 Functions of Continuous Random Variables	p. 559
B.4 Gaussian Random Variables	p. 561
B.5 Chi-Square Random Variables	p. 563
B.6 Propagation of Functions through Various Models	p. 565
B.6.1 Linear Matrix Models	p. 565
B.6.2 Nonlinear Models	p. 565
C Parameter Optimization Methods	p. 569
C.1 Unconstrained Extrema	p. 569
C.2 Equality Constrained Extrema	p. 571
C.3 Nonlinear Unconstrained Optimization	p. 576
C.3.1 Some Geometrical Insights	p. 577
C.3.2 Methods of Gradients	p. 578
C.3.3 Second-Order (Gauss-Newton) Algorithm	p. 580
D Computer Software	p. 585
Index	p. 587

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