Spacecraft Collision Avoidance Technology

__Spacecraft Collision Avoidance Technology__ presents the theory and practice of space collision avoidance. The title gives models of time and space environment, their impact on high-precision orbit prediction, considers optimal orbit determination methods and models in different warning stages, and establishes basic models for warning and avoidance. Chapters present an outline of spacecraft collision warning strategy, elaborate on the basics of orbital calculation for collision avoidance, consider space object detection technology, detail space environment and object orbit, give a method for spacecraft collision warning orbit calculation, and finally, demonstrate a strategy for spacecraft collision warning and avoidance. Cover 1 Spacecraft Collision Avoidance Technology 3 Copyright 4 Contents 5 1 Outline of spacecraft collision warning 7 1.1 Distribution and characteristics of space objects 7 1.2 Characteristics and hazards of space debris 9 1.3 Collision warning of spacecraft 12 2 Basics of orbital calculation for spacecraft collision avoidance 16 2.1 Basic definitions and transformation in astronomy 16 2.1.1 Basic concepts in astronomy 16 2.1.2 Time systems and major transformation formula 19 2.1.2.1 Sidereal time 19 2.1.2.2 Solar time 20 2.1.2.3 Universal time 20 2.1.2.4 Ephemeris time 20 2.1.2.5 Atomic time 21 2.1.2.6 Coordinated universal time 21 2.1.2.7 GPS time 21 2.1.2.8 BeiDou time 22 2.1.2.9 Time system conversion 22 2.1.3 Coordinate systems and major transformation formula 23 2.1.3.1 2000.0 inertial coordinate system 23 2.1.3.2 Instantaneous mean equatorial coordinate system 23 2.1.3.3 Instantaneous true equatorial coordinates system 23 2.1.3.4 Quasi Earth-fixed coordinate system 23 2.1.3.5 International Terrestrial Reference System 24 2.1.3.6 Earth-fixed coordinate system 24 2.1.3.7 Geodetic system 25 2.1.3.8 Topocentric coordinate system 25 2.1.3.9 Satellite coordinate system 25 2.1.3.10 UNW and RTN coordinate system 25 2.1.3.10.1 UNW coordinate system 25 2.1.3.10.2 RTN coordinate system 26 2.1.3.11 Coordinate transformation 26 2.2 Space object orbit: basic definitions and transformation 26 2.2.1 Space object’s two-body motion in space 27 2.2.2 Integration of two-body problem 27 2.2.3 Basic conversion of orbital elements for space objects 30 2.2.3.1 Interchange between orbital elements and position/velocity in Cartesian system 30 2.2.3.2 Partial derivative of elements with respect to coordinates and velocity 30 2.2.3.3 Partial derivative of coordinates and velocity with respect to elements 32 2.2.3.4 Partial derivative of acceleration with respect to position/velocity in two-body motion of space object 33 2.2.4 Orbital perturbations of space object 34 3 Space object detection technology 39 3.1 Overview 39 3.1.1 Ground-based detection 39 3.1.1.1 Radio detection technology 39 3.1.1.2 Electro-optical detection technology 40 3.1.2 Space-based detection 41 3.2 Radar measurement technology 41 3.2.1 Radar measurement elements 42 3.2.1.1 Radar object angle measurement and tracking methods 42 3.2.1.2 Radar object range measurement and tracking methods 42 3.2.1.3 Object velocity measurement and tracking 43 3.2.2 Radar measurement data modeling 43 3.2.2.1 Ranging error 44 3.2.2.2 Angle measurement error 45 3.2.2.3 Velocity measurement error 48 3.2.2.4 Mathematical model of systematic errors 48 3.2.3 Typical space surveillance radar 49 3.2.3.1 Mechanical scanning tracking radar 50 3.2.3.2 Phased array radar 50 3.2.3.3 Space fence 51 3.3 Electro-optical detection technology 52 3.3.1 Principles of electro-optical detection 52 3.3.1.1 The optical structure of electro-optical telescopes 52 3.3.1.2 Optical telescope’s mount structure 53 3.3.2 Electric-optical telescopes measurement data types and positioning 54 3.3.2.1 Measurement data 54 3.3.2.2 Working mechanism and features of positioning 56 3.3.3 Measurement models of electro-optical telescope 56 3.3.3.1 Measurement model of shafting positioning 57 3.3.3.2 Measurement model of celestial positioning 57 3.3.4 Measurement errors and compensation techniques of telescopes 60 3.3.4.1 Static errors 60 3.3.4.2 Dynamic errors 61 3.3.4.3 Angle measurement error model 63 3.3.4.4 Error compensation technology 65 3.4 Public correction models for measurement data 68 3.4.1 The partial derivatives of each measurement element with respect to the space object position 68 3.4.2 Tropospheric refraction error correction 69 3.4.3 Ionospheric error correction 70 3.4.4 General relativistic effect error correction 73 3.4.5 Vertical deflection correction 74 3.5 Relationship between detection network and orbit accuracy 74 4 Space environment and object orbit 77 4.1 Atmospheric effect on space object orbit 77 4.2 Atmospheric density model 79 4.2.1 Atmospheric density modeling principle 80 4.2.1.1 Hydrostatic principle 80 4.2.1.2 Data acquisition technology 81 4.2.1.3 Introduction of parameters and fitting technique 81 4.2.2 Introduction of current atmospheric density models 82 4.2.2.1 Index model 84 4.2.2.2 Jacchia77 atmospheric model 89 4.2.2.3 MSIS00 model 98 4.3 Systematic error and random error of atmospheric density models 110 4.4 Prediction confidence level of space environment parameters influenced atmospheric density 113 4.4.1 Analysis of F10.7 prediction confidence level 113 4.4.2 Analysis of Ap prediction confidence level 114 4.4.3 Impact of environmental parameters on orbit prediction error 115 4.5 Calculation strategy of atmospheric perturbation for spacecraft collision avoidance warning calculation 119 4.5.1 Resolving atmospheric damping coefficient and absorbing systematic error 119 4.5.2 Application of atmospheric damping coefficient and analysis of orbit determination and prediction under normal geomag... 120 4.5.3 Application of atmospheric damping coefficient and analysis of orbit determination and prediction under abnormal geom... 123 5 Spacecraft collision warning orbit calculation method 127 5.1 Precise orbital calculation method 128 5.1.1 Orbital parameters optimal estimation method 128 5.1.2 Numerical integration 130 5.1.3 Numerical calculation of precise orbit 132 5.1.3.1 The elements system 132 5.1.3.2 Method matrix 132 5.1.3.3 Dynamical modeling strategy 134 5.2 Cataloged orbit calculation method 135 5.2.1 Simple numerical method (simplified dynamic model) 135 5.2.2 Cataloging orbit calculation with two-line element 135 5.2.2.1 The US cataloging system 135 5.2.2.2 The US two-line elements 136 5.2.2.3 Orbital principle of SGP4 model 138 5.2.2.4 Orbit determination based on SGP4 model 143 5.2.3 The mean elements cataloging orbit calculation method 146 5.2.3.1 Orbit extrapolation 146 5.2.3.1.1 The mean element method 146 5.2.3.1.2 The quasimean element method 148 5.2.3.2 State transition matrix 150 5.2.4 Precision analysis 150 5.2.4.1 Simple numerical method accuracy analysis 150 5.2.4.2 The US cataloging precision analysis 152 5.2.4.3 Precision analysis with the mean element method 154 5.2.4.4 Space object catalog error characteristic orbital analysis 155 6 Spacecraft collision warning and avoidance strategy 159 6.1 Collision warning calculation 160 6.1.1 Risky object screening 160 6.1.1.1 Screening by perigee and apogee 161 6.1.1.1.1 Short-term change of perigee 161 6.1.1.1.2 Long-term change of perigee 161 6.1.1.1.3 Calculation and analysis of space object orbit change 162 6.1.1.2 Screening by the geocentric distance of intersection 162 6.1.1.3 Screening by the minimum distance between orbital planes 164 6.1.2 The minimum distance calculation 165 6.1.2.1 The minimum distance 165 6.1.2.1.1 Space object orbit propagation 165 6.1.2.1.2 The minimum distance calculation 166 6.1.2.1.3 The relationship between relative velocity and relative distance at minimum distance 166 6.1.2.2 The distance calculation in three directions 167 6.1.2.3 The precision evaluation of three distance components 167 6.1.2.4 Approaching angle and velocity calculation 169 6.1.3 The probability of collision method 170 6.1.3.1 Probability of collision 170 6.1.3.2 The maximum probability of collision 170 6.1.3.3 Influence of related parameters on probability of collision 172 6.1.3.3.1 The Influence of distance and position error in N direction on probability of collision 173 6.1.3.3.2 The Influence of distance and position error in U and W direction on probability of collision 174 6.1.3.3.3 The influence of approaching angle on probability of collision 175 6.2 The method of spacecraft avoidance 176 6.2.1 Altitude avoidance method 178 6.2.2 Time avoidance method 180 6.3 Collision warning strategy for spacecraft safety operation and case studies 181 6.3.1 Risky objects screening 182 6.3.2 Daily warning analysis 187 6.3.3 Precision collision warning 188 6.3.4 Avoidance control 189 References 190 Index 196 Back Cover 205 Spacecraft Collision Avoidance Technology presents the theory and practice of space collision avoidance. The title gives models of time and space environment, their impact on high-precision orbit prediction, considers optimal orbit determination methods and models in different warning stages, and establishes basic models for warning and avoidance. Chapters present an outline of spacecraft collision warning strategy, elaborate on the basics of orbital calculation for collision avoidance, consider space object detection technology, detail space environment and object orbit, give a method for spacecraft collision warning orbit calculation, and finally, demonstrate a strategy for spacecraft collision warning and avoidance. Presents strategies, methods and real-world examples relating to space collision avoidance Considers time and space environment models in orbit prediction Gives optimal orbit determination methods and models for various warning stages Establishes and elaborates basic models for warning and avoidance Takes note of the current space environment for object detection and collision avoidance