Crassidis J.L. Optimal estimation of dynamic systems / J.L.Crassidis, J.L.Junkins. - 2nd ed. - Boca Raton: CRC Press, 2012. - 733 p.: ill. - (Chapman & Hall/CRC applied mathematics and nonlinear science series). - Incl. bibl. ref. - Ind.: p.727-733. - ISBN 978-1-4398-3985-0  Место хранения:   028 | Институт сильноточной электроники СО РАН | Томск | Библиотека

Оглавление / Contents

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