Statistical Orbit Determination
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Table of contents
- Cover
- Copyright Pageii
- Contentsiii
- Prefacexi
- Chapter 1. Orbit Determination Concepts1
- 1.1 Introduction1
- 1.2 Uniform Gravity Field Model3
- 1.3 Background and Overview13
- 1.4 Summary14
- 1.5 References15
- 1.6 Exercises16
- Chapter 2. The Orbit Problem17
- 2.1 Historical Background17
- 2.2 Problem of Two Bodies: General Properties19
- 2.3 Perturbed Motion44
- 2.4 Coordinate Systems and Time: Introduction71
- 2.5 Orbit Accuracy82
- 2.6 References84
- 2.7 Exercises87
- Chapter 3. Observations93
- 3.1 Introduction93
- 3.2 Observations94
- 3.3 Conceptual Measurement Systems99
- 3.4 Realization of Measurements110
- 3.5 Measurement Systems116
- 3.6 Differenced Measurements139
- 3.7 Satellite Positions147
- 3.8 Angles148
- 3.9 References149
- 3.10 Exercises151
- Chapter 4. Fundamentals of Orbit Determination159
- 4.1 Introduction159
- 4.2 Linearization of the Orbit Determination Process160
- 4.3 The Least Squares Solution173
- 4.4 The Minimum Variance Estimate183
- 4.5 Maximum Likelihood and Bayesian Estimation190
- 4.6 Computational Algorithm for the Batch Processor194
- 4.7 The Sequential Estimation Algorithm199
- 4.8 Example Problems211
- 4.9 State Noise Compensation Algorithm220
- 4.10 Information Filter233
- 4.11 Batch and Sequential Estimation237
- 4.12 Observability237
- 4.13 Error Sources241
- 4.14 Orbit Accuracy244
- 4.15 Smoothing246
- 4.16 The Probability Ellipsoid251
- 4.17 Combining Estimates258
- 4.18 References261
- 4.19 Exercises264
- Chapter 5. Square Root Solution Methods285
- 5.1 Introduction285
- 5.2 Cholesky Decomposition286
- 5.3 Least Squares Solution via Orthogonal Transformation290
- 5.4 Givens Transformations291
- 5.5 The Householder Transformation310
- 5.6 Numerical Examples318
- 5.7 Square Root Filter Algorithms330
- 5.8 Time Update of the Estimation Error Covariance Matrix343
- 5.9 Continuous State Error Covariance Propagation346
- 5.10 The Square Root Information Filter351
- 5.11 Process Noise Parameter Filtering/Smoothing Using a SRIF369
- 5.12 References380
- 5.13 Exercises381
- Chapter 6. Consider Covariance Analysis387
- 6.1 Introduction387
- 6.2 Bias in Linear Estimation Problems388
- 6.3 Formulation of the Consider Covariance Matrix389
- 6.4 The Sensitivity and Perturbation Matrices397
- 6.5 Inclusion of Time-Dependent Effects400
- 6.6 Propagation of the Error Covariance405
- 6.7 Sequential Consider Covariance Analysis407
- 6.8 Example: Freely Falling Point Mass410
- 6.9 Example: Spring-Mass Problem420
- 6.10 Errors in the Observation Noise and A Priori State Covariances425
- 6.11 Errors in Process Noise, Observation Noise, and State Covariance427
- 6.12 Covariance Analysis and Orthogonal Transformations430
- 6.13 References434
- 6.14 Exercises435
- Appendix A. Probability and Statistics439
- A.1 Introduction439
- A.2 Axioms of Probability440
- A.3 Conditional Probability443
- A.4 Probability Density and Distribution Functions443
- A.5 Expected Values445
- A.6 Examples and Discussion of Expectation446
- A.7 Moment Generating Functions448
- A.8 Some Important Continuous Distributions449
- A.9 Two Random Variables452
- A.10 Marginal Distributions453
- A.11 Independence of Random Variables454
- A.12 Conditional Probability454
- A.13 Expected Values of Bivariate Functions455
- A.14 The Variance-Covariance Matrix456
- A.15 Properties of the Correlation Coefficient458
- A.16 Properties of Covariance and Correlation460
- A.17 Bivariate Normal Distribution460
- A.18 Marginal Distributions461
- A.19 The Multivariate Normal Distribution462
- A.20 The Central Limit Theorem465
- A.21 Bayes Theorem465
- A.22 Stochastic Processes467
- A.23 References471
- Appendix B. Review of Matrix Concepts473
- B.1 Introduction473
- B.2 Rank475
- B.3 Quadratic Forms475
- B.4 Determinants476
- B.5 Matrix Trace477
- B.6 Eigenvalues and Eigenvectors478
- B.7 The Derivatives of Matrices and Vectors478
- B.8 Maxima and Minima480
- B.9 Useful Matrix Inversion Theorems481
- B.10 Reference483
- Appendix C. Equations of Motion485
- C.1 Lagrange Planetary Equations485
- C.2 Gaussian Form485
- C.3 References486
- Appendix D. Constants487
- D.1 Physical Constants487
- D.2 Earth Constants487
- D.3 Lunar, Solar, and Planetary Masses488
- D.4 References490
- Appendix E. Analytical Theory for Near-Circular Orbits493
- E.1 Description493
- E.2 Example497
- E.3 References497
- Appendix F. Example of State Noise and Dynamic Model Compensation499
- F.1 Introduction499
- F.2 State Noise Compensation501
- F.3 Dynamic Model Compensation505
- F.4 Reference509
- Appendix G. Solution of the Linearized Equations of Motion511
- G.1 Introduction511
- G.2 The State Transition Matrix513
- Appendix H. Transformation between ECI and ECF Coordinates517
- H.1 Introduction517
- H.2 Matrix P518
- H.3 Matrix N519
- H.4 Matrix S'519
- H.5 Matrix W521
- H.6 References521
- Bibliography Abbreviations523
- Bibliography525
- Author Index537
- Index541
This book presents fundmentals of orbit determination--from weighted least squares approaches (Gauss) to today's high-speed computer algorithms that provide accuracy within a few centimeters. Numerous examples and problems are provided to enhance readers' understanding of the material.
*Covers such topics as coordinate and time systems, square root filters, process noise techniques, and the use of fictitious parameters for absorbing un-modeled and incorrectly modeled forces acting on a satellite.
*Examples and exercises serve to illustrate the principles throughout each chapter.
*Detailed solutions to end-of-chapter exercises available to instructors.
*Covers such topics as coordinate and time systems, square root filters, process noise techniques, and the use of fictitious parameters for absorbing un-modeled and incorrectly modeled forces acting on a satellite.
*Examples and exercises serve to illustrate the principles throughout each chapter.
*Detailed solutions to end-of-chapter exercises available to instructors.