Contents
1 Introduction 1
1.1 Jet Transport Technique 1
1.2 Organization of the Book 5
References 7
2 The Implementation of Jet Transport Software 11
2.1 Polynomial Storage 11
2.2 Polynomial Algebra 14
2.2.1 Basic Polynomial Operations 15
2.2.2 Differential Polynomial Algebra 20
2.2.3 Polynomial Approximation to Univariate Functions 21
2.2.4 Polynomial Approximation to a Multi-variable Function 26
2.2.5 Numerical Simulations 27
2.3 Flow Propagation 29
2.3.1 Parameterization Method 31
2.3.2 Runge-Kutta Methods 33
2.3.3 Semi-analytical Polynomial Propagation 35
2.3.4 Polynomial Evaluation 36
2.3.5 Numerical Simulations 38
References 43
3 Analysis of Orbit Uncertainty Propagation Using Jet Transport 45
3.1 Executive Summary 45
3.2 Dynamical Models 47
3.2.1 Cartesian Dynamic Model 47
3.2.2 Cylindrical Coordinates 48
3.2.3 GEO Dynamical Model 48
3.2.4 Coordinate Transformations 50
3.3 Analysis of Dominant Perturbation Accelerations 51
3.3.1 Perturbation Modelling 51
3.3.2 Perturbation Analysis 53
3.4 Geostationary Orbit Propagation 55
3.4.1 Selection of Fixed Step Integrator 55
3.4.2 Polynomial-based Orbit Propagation 55
3.4.3 Comparison with Different Coordinate Representations 61
References 62
4 Jet Transport Application to Particle Filter for Attitude Estimation of Tumbling Space Objects 65
4.1 Executive Summary 65
4.2 Basic Dynamical Models 67
4.3 Quaternion Particle Filter 69
4.4 Jet Transport Particle Filter 72
4.5 Simulation Studies 74
4.5.1 Simulation Scenarios 74
4.5.2 Simulation Results 77
References 82
5 Jet Transport-based High Order Kalman Filter for Joint Orbit
and Parameter Estimation 85
5.1 Executive Summary 85
5.2 Augmented High Order Extended Kalman Filter 86
5.3 Joint Orbit and Parameter Estimation 91
5.3.1 Equations of Motion 91
5.3.2 Measurement Model 91
5.3.3 Case A: Spacecraft State and Physical Parameter
Estimation 92
5.3.4 Case B: Spacecraft State and Tracking Station
Position Estimation 93
5.3.5 Evaluation Metrics 93
5.4 Numerical Simulations 95
5.4.1 Spacecraft Physical Parameter Estimation 95
5.4.2 Tracking Station Position Estimation 103
References 105
6 Autonomous Orbit Determination and Fault-tolerant Designs
Using Jet Transport 107
6.1 Executive Summary 107
6.2 Standard High Order Extended Kalman Filter 109
6.3 Fault-tolerant Variants of the JT-HEKF-n Filter 112
6.3.1 Fault Measurement Detection 112
6.3.2 False Measurement-discarding Based JT-HEKF-n Filter 113
Contents
6.3.3 Single and Multiple Scale Factor Based JT-HEKF-n Filter 114
6.4 Model Description 116
6.4.1 Equations of Motion 116
6.4.2 Measurement Model 116
6.5 Numerical Simulations 117
6.5.1 Autonomous Nonlinear Orbit Determination 118
6.5.2 Autonomous Fault-tolerant Orbit Determination References 125
7 Jet Transport-based Adaptive Order-switching Filter 135
7.1 Executive Summary 135
7.2 Order- switching Based JT-HEKF-n Filter 136
7.2.1 Design of the Adaptive Order- switching Strategy 137
7.2.2 Detailed Implementation of A JT-OSHEKF-n Filter 138
7.3 Model Description 139
7.3.1 Equations of Motion 140
7.3.2 Measurement Model 140
7.4 Numerical Simulations 141
7.4.1 Case Study A: Adverse Simulation Scenario 141
7.4.2 Case Study B: Mild Simulation Scenario 144
References 148
8 Low-thrust Station Keeping at Libration Point Orbits Using Jet Transport 151
8.1 Executive Summary 151
8.2 Equations of Motion 153
8.3 Geometric Structure Around Halo Orbits 154
8.4 Station-keeping Strategies 156
8.4.1 Limit Impulsive Control Laws 156
8.4.2 Dynamical Reshaping Control Laws 160
8.4.3 Geometric Analysis of the Limit Impulsive Control Laws 162
8.5 Numerical Simulations 165
8.5.1 Stability of the Control Laws 165
8.5.2 Long-term and Geometric Behavior of the Controlled System 168
8.5.3 Robustness of the Control Laws to Navigation Errors 174
8.5.4 Control Cost Estimations 176
8.5.5 A Note on A HSP Control Law 176
References 180