Spacecraft Collision Avoidance Technology

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Spacecraft Collision Avoidance Technology
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Contents
1 Outline of spacecraft collision warning
	1.1 Distribution and characteristics of space objects
	1.2 Characteristics and hazards of space debris
	1.3 Collision warning of spacecraft
2 Basics of orbital calculation for spacecraft collision avoidance
	2.1 Basic definitions and transformation in astronomy
		2.1.1 Basic concepts in astronomy
		2.1.2 Time systems and major transformation formula
			2.1.2.1 Sidereal time
			2.1.2.2 Solar time
			2.1.2.3 Universal time
			2.1.2.4 Ephemeris time
			2.1.2.5 Atomic time
			2.1.2.6 Coordinated universal time
			2.1.2.7 GPS time
			2.1.2.8 BeiDou time
			2.1.2.9 Time system conversion
		2.1.3 Coordinate systems and major transformation formula
			2.1.3.1 2000.0 inertial coordinate system
			2.1.3.2 Instantaneous mean equatorial coordinate system
			2.1.3.3 Instantaneous true equatorial coordinates system
			2.1.3.4 Quasi Earth-fixed coordinate system
			2.1.3.5 International Terrestrial Reference System
			2.1.3.6 Earth-fixed coordinate system
			2.1.3.7 Geodetic system
			2.1.3.8 Topocentric coordinate system
			2.1.3.9 Satellite coordinate system
			2.1.3.10 UNW and RTN coordinate system
				2.1.3.10.1 UNW coordinate system
				2.1.3.10.2 RTN coordinate system
			2.1.3.11 Coordinate transformation
	2.2 Space object orbit: basic definitions and transformation
		2.2.1 Space object’s two-body motion in space
		2.2.2 Integration of two-body problem
		2.2.3 Basic conversion of orbital elements for space objects
			2.2.3.1 Interchange between orbital elements and position/velocity in Cartesian system
			2.2.3.2 Partial derivative of elements with respect to coordinates and velocity
			2.2.3.3 Partial derivative of coordinates and velocity with respect to elements
			2.2.3.4 Partial derivative of acceleration with respect to position/velocity in two-body motion of space object
		2.2.4 Orbital perturbations of space object
3 Space object detection technology
	3.1 Overview
		3.1.1 Ground-based detection
			3.1.1.1 Radio detection technology
			3.1.1.2 Electro-optical detection technology
		3.1.2 Space-based detection
	3.2 Radar measurement technology
		3.2.1 Radar measurement elements
			3.2.1.1 Radar object angle measurement and tracking methods
			3.2.1.2 Radar object range measurement and tracking methods
			3.2.1.3 Object velocity measurement and tracking
		3.2.2 Radar measurement data modeling
			3.2.2.1 Ranging error
			3.2.2.2 Angle measurement error
			3.2.2.3 Velocity measurement error
			3.2.2.4 Mathematical model of systematic errors
		3.2.3 Typical space surveillance radar
			3.2.3.1 Mechanical scanning tracking radar
			3.2.3.2 Phased array radar
			3.2.3.3 Space fence
	3.3 Electro-optical detection technology
		3.3.1 Principles of electro-optical detection
			3.3.1.1 The optical structure of electro-optical telescopes
			3.3.1.2 Optical telescope’s mount structure
		3.3.2 Electric-optical telescopes measurement data types and positioning
			3.3.2.1 Measurement data
			3.3.2.2 Working mechanism and features of positioning
		3.3.3 Measurement models of electro-optical telescope
			3.3.3.1 Measurement model of shafting positioning
			3.3.3.2 Measurement model of celestial positioning
		3.3.4 Measurement errors and compensation techniques of telescopes
			3.3.4.1 Static errors
			3.3.4.2 Dynamic errors
			3.3.4.3 Angle measurement error model
			3.3.4.4 Error compensation technology
	3.4 Public correction models for measurement data
		3.4.1 The partial derivatives of each measurement element with respect to the space object position
		3.4.2 Tropospheric refraction error correction
		3.4.3 Ionospheric error correction
		3.4.4 General relativistic effect error correction
		3.4.5 Vertical deflection correction
	3.5 Relationship between detection network and orbit accuracy
4 Space environment and object orbit
	4.1 Atmospheric effect on space object orbit
	4.2 Atmospheric density model
		4.2.1 Atmospheric density modeling principle
			4.2.1.1 Hydrostatic principle
			4.2.1.2 Data acquisition technology
			4.2.1.3 Introduction of parameters and fitting technique
		4.2.2 Introduction of current atmospheric density models
			4.2.2.1 Index model
			4.2.2.2 Jacchia77 atmospheric model
			4.2.2.3 MSIS00 model
	4.3 Systematic error and random error of atmospheric density models
	4.4 Prediction confidence level of space environment parameters influenced atmospheric density
		4.4.1 Analysis of F10.7 prediction confidence level
		4.4.2 Analysis of Ap prediction confidence level
		4.4.3 Impact of environmental parameters on orbit prediction error
	4.5 Calculation strategy of atmospheric perturbation for spacecraft collision avoidance warning calculation
		4.5.1 Resolving atmospheric damping coefficient and absorbing systematic error
		4.5.2 Application of atmospheric damping coefficient and analysis of orbit determination and prediction under normal geomag...
		4.5.3 Application of atmospheric damping coefficient and analysis of orbit determination and prediction under abnormal geom...
5 Spacecraft collision warning orbit calculation method
	5.1 Precise orbital calculation method
		5.1.1 Orbital parameters optimal estimation method
		5.1.2 Numerical integration
		5.1.3 Numerical calculation of precise orbit
			5.1.3.1 The elements system
			5.1.3.2 Method matrix
			5.1.3.3 Dynamical modeling strategy
	5.2 Cataloged orbit calculation method
		5.2.1 Simple numerical method (simplified dynamic model)
		5.2.2 Cataloging orbit calculation with two-line element
			5.2.2.1 The US cataloging system
			5.2.2.2 The US two-line elements
			5.2.2.3 Orbital principle of SGP4 model
			5.2.2.4 Orbit determination based on SGP4 model
		5.2.3 The mean elements cataloging orbit calculation method
			5.2.3.1 Orbit extrapolation
				5.2.3.1.1 The mean element method
				5.2.3.1.2 The quasimean element method
			5.2.3.2 State transition matrix
		5.2.4 Precision analysis
			5.2.4.1 Simple numerical method accuracy analysis
			5.2.4.2 The US cataloging precision analysis
			5.2.4.3 Precision analysis with the mean element method
			5.2.4.4 Space object catalog error characteristic orbital analysis
6 Spacecraft collision warning and avoidance strategy
	6.1 Collision warning calculation
		6.1.1 Risky object screening
			6.1.1.1 Screening by perigee and apogee
				6.1.1.1.1 Short-term change of perigee
				6.1.1.1.2 Long-term change of perigee
				6.1.1.1.3 Calculation and analysis of space object orbit change
			6.1.1.2 Screening by the geocentric distance of intersection
			6.1.1.3 Screening by the minimum distance between orbital planes
		6.1.2 The minimum distance calculation
			6.1.2.1 The minimum distance
				6.1.2.1.1 Space object orbit propagation
				6.1.2.1.2 The minimum distance calculation
				6.1.2.1.3 The relationship between relative velocity and relative distance at minimum distance
			6.1.2.2 The distance calculation in three directions
			6.1.2.3 The precision evaluation of three distance components
			6.1.2.4 Approaching angle and velocity calculation
		6.1.3 The probability of collision method
			6.1.3.1 Probability of collision
			6.1.3.2 The maximum probability of collision
			6.1.3.3 Influence of related parameters on probability of collision
				6.1.3.3.1 The Influence of distance and position error in N direction on probability of collision
				6.1.3.3.2 The Influence of distance and position error in U and W direction on probability of collision
				6.1.3.3.3 The influence of approaching angle on probability of collision
	6.2 The method of spacecraft avoidance
		6.2.1 Altitude avoidance method
		6.2.2 Time avoidance method
	6.3 Collision warning strategy for spacecraft safety operation and case studies
		6.3.1 Risky objects screening
		6.3.2 Daily warning analysis
		6.3.3 Precision collision warning
		6.3.4 Avoidance control
References
Index
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