# ISO/TR 16158:2021

(Amendment)## Space systems — Avoiding collisions among orbiting objects

## Space systems — Avoiding collisions among orbiting objects

This document is a guide for establishing essential collaborative enterprises to sustain the space environment and employ it effectively. This document describes some widely used techniques for perceiving close approaches, estimating collision probability, estimating the cumulative probability of survival, and manoeuvring to avoid collisions. NOTE Satellite operators accept that all conjunction and collision assessment techniques are statistical. All suffer false positives and/or missed detections. The degree of uncertainty in the estimated outcomes is not uniform across all satellite orbits or all assessment intervals. No comparison within a feasible number of test cases can reveal the set of techniques that is uniformly most appropriate for all.

## Systèmes spatiaux — Évitement des collisions entre objets en orbite

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TECHNICAL ISO/TR

REPORT 16158

Second edition

2021-10

Space systems — Avoiding collisions

among orbiting objects

Systèmes spatiaux — Évitement des collisions entre objets en orbite

Reference number

ISO/TR 16158:2021(E)

© ISO 2021

---------------------- Page: 1 ----------------------

ISO/TR 16158:2021(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.ISO copyright office

CP 401 • Ch. de Blandonnet 8

CH-1214 Vernier, Geneva

Phone: +41 22 749 01 11

Email: copyright@iso.org

Website: www.iso.org

Published in Switzerland

© ISO 2021 – All rights reserved

---------------------- Page: 2 ----------------------

ISO/TR 16158:2021(E)

Contents Page

Foreword ..........................................................................................................................................................................................................................................v

Introduction .............................................................................................................................................................................................................................. vi

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Collision avoidance workflow ................................................................................................................................................................2

5 Perceiving close approaches ................................................................................................................................................................... 2

5.1 Orbit data ..................................................................................................................................................................................................... 2

5.1.1 Inputs ............................................................................................................................................................................................ 2

5.1.2 Propagating all orbits over the interval of interest ............................................................................ 3

5.2 Initial filtering ......................................................................................................................................................................................... 3

5.2.1 All against all ......................................................................................................................................................................... 3

5.3 Eliminating infeasible conjunctions .................................................................................................................................... 3

5.3.1 General ........................................................................................................................................................................................ 3

5.3.2 Sieve ............................................................................................................................................................................................... 3

5.3.3 Toroidal elimination ........................................................................................................................................................ 4

5.3.4 Apogee-perigee filters ................................................................................................................................................... 4

5.3.5 Statistical errors ................................................................................................................................................................. 4

6 Determining potential collisions for warning and further action (close approach

screening) ................................................................................................................................................................................................................... 4

6.1 General ........................................................................................................................................................................................................... 4

6.2 Symmetric keepout............................................................................................................................................................................. 4

6.3 Bounding volume keepout ............................................................................................................................................................ 5

6.4 Probability techniques .................................................................................................................................................................... 5

6.5 Maximum probability ....................................................................................................................................................................... 7

6.6 Bounding volume based on probability ........................................................................................................................... 8

6.7 Comparison of techniques ......................................................................................................................................................... 10

7 Probability of survival ................................................................................................................................................................................10

7.1 General ........................................................................................................................................................................................................ 10

7.2 Trending .................................................................................................................................................................................................... 11

7.3 Cumulative probability ................................................................................................................................................................ 11

7.4 Bayesian assessment ...................................................................................................................................................................... 12

8 Additional information for judging courses of action ...............................................................................................13

8.1 General ........................................................................................................................................................................................................13

8.2 Manoeuvre capability .................................................................................................................................................................... 13

8.3 Spacecraft characteristics .........................................................................................................................................................13

8.4 Quality of underlying orbit data .......................................................................................................................................... 13

9 Consequence assessment .........................................................................................................................................................................13

9.1 General ........................................................................................................................................................................................................13

9.2 Guidance for population risk ......... .......................................................................................................................................... 13

9.3 Traffic impacts ..................................................................................................................................................................................... 14

10 Requirements for warning and information for avoidance ................................................................................14

10.1 General ........................................................................................................................................................................................................ 14

10.2 Orbit data .................................................................................................................................................................................................. 14

10.3 Minimum data required for warning of and avoiding collisions ............................................................ 15

10.4 Optional elements of information ...................................................................................................................................... 15

11 Conjunction and collision assessment workflow and operational concept .......................................16

Annex A (informative) Relationship between combined object size, combined positional

error, and maximum probability ....................................................................................................................................................19

iii© ISO 2021 – All rights reserved

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ISO/TR 16158:2021(E)

Annex B (informative) Probability contour visualization .........................................................................................................21

Bibliography .............................................................................................................................................................................................................................31

© ISO 2021 – All rights reserved---------------------- Page: 4 ----------------------

ISO/TR 16158:2021(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.This document was prepared by Technical Committee ISO/TC 20, Aircraft and space vehicles,

Subcommittee SC 14, Space systems and operations.This second edition cancels and replaces the first edition (ISO/TR 16158:2013), which has been

technically revised.The main changes compared to the previous edition are as follows:

— improved figures for clarity;

— added plot of maximum probability;

— switched to “decimal comma” per ISO editorial rules;

— simplified operational concepts figures;

— added informative annexes containing collision probability relational nomograms;

— added collision probability topology in both graphical and tabular look-up formats;

— reordered the bibliography.Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.© ISO 2021 – All rights reserved

---------------------- Page: 5 ----------------------

ISO/TR 16158:2021(E)

Introduction

This document describes the workflow for perceiving and avoiding collisions among orbiting objects,

data requirements for these tasks, techniques that can be used to estimate the probability of collision

and guidance for executing avoidance manoeuvres. Diligent collaboration is strongly encouraged

among all who operate satellites.The process begins with the best possible trajectory data, provided by satellite operators or sensor

systems developed for this purpose. The orbits of satellites can be compared with each other to discern

physically feasible approaches that can result in collisions. The trajectories so revealed can then be

examined more closely to estimate the probability of collision. Where the possibility of a collision

has been identified within the criteria established by each satellite operator, the spectrum of feasible

manoeuvres is examined.There are several different approaches to conjunction assessment. All have merits and deficiencies.

Most focus on how closely satellites approach each other. This is often very uncertain since satellite

orbits generally change more rapidly under the influence of non-conservative forces than observations

of satellites in orbit can be acquired and employed to improve orbit estimates. Spacecraft operators

require the fullness of orbit data to judge the credibility and quality of conjunction perception. This

information includes the moment of time of the last elaboration of orbit (the epoch) and the standard

time scale employed, state vector value or elements of orbit at this moment of time, the coordinate

system description that presents the orbital data, the forces model description that was used for orbital

plotting, and information about the estimation errors of the orbital parameters. Essential elements of

information for this purpose are specified in ISO 26900.There are also diverse approaches to estimating the probability that a close approach can really result

in a collision. This is a statistical process very similar to weather forecasting. Meteorologists no longer

make definitive predictions. They provide the probability of precipitation, not whether it will rain. All

conjunction assessment approaches are in some way founded in probabilities. Probability of collision

is also a highly desirable element of data. It can be accompanied by metadata that allows operators to

interpret the information within their own operational procedures.How near satellites can be to each other and the probability they can collide if they were that close

are only two discriminants of potentially catastrophic events. Since the objective is that the satellite

survives despite many potential close approaches, cumulative probability of survival is also important

information. Responding precipitously to the close approach nearest at hand can only delay the demise

of the satellite or even contribute to a subsequent more serious event. The evolution of close approaches

and the cumulative probability that a satellite can survive are also important.Finally, the state of each of the conjunction partners, their ability to manoeuvre or otherwise avoid

contact, and the outcomes of past events that are similar guide courses of action.

© ISO 2021 – All rights reserved---------------------- Page: 6 ----------------------

TECHNICAL REPORT ISO/TR 16158:2021(E)

Space systems — Avoiding collisions among orbiting

objects

1 Scope

This document is a guide for establishing essential collaborative enterprises to sustain the space

environment and employ it effectively.This document describes some widely used techniques for perceiving close approaches, estimating

collision probability, estimating the cumulative probability of survival, and manoeuvring to avoid

collisions.NOTE Satellite operators accept that all conjunction and collision assessment techniques are statistical.

All suffer false positives and/or missed detections. The degree of uncertainty in the estimated outcomes is not

uniform across all satellite orbits or all assessment intervals. No comparison within a feasible number of test

cases can reveal the set of techniques that is uniformly most appropriate for all.

2 Normative referencesThere are no normative references in this document.

3 Terms and definitions

For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminology databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp— IEC Electropedia: available at https:// www .electropedia .org/

3.1

collision

act of colliding; instance of one object striking another

3.2

conjunction

apparent meeting or passing of two or more objects in space

3.3

covariance

measure of how much variables change together

Note 1 to entry: For multiple dependent variables, a square, symmetric, positive definite matrix of dimensionality

N × N, where N is the number of variables.3.4

encounter plane

plane normal to the relative velocity at the time of closest approach

3.5

ephemeris

time-ordered set of position and velocity within which one interpolates to estimate the position and

velocity at intermediate times© ISO 2021 – All rights reserved

---------------------- Page: 7 ----------------------

ISO/TR 16158:2021(E)

3.6

false alarm

statistical Type I error, when a statistical test fails to reject a false null hypothesis

3.7interface control document

ICD

specification that describes the characteristics that can be controlled at the boundaries between

systems, subsystems, and other elements3.8

operational concept

roles, relationships, and information flows among tasks and stakeholders and the way systems and

processes will be used3.9

orbital elements

parameters that describe the evolution of the trajectory and which can be used to estimate the

trajectory in the future4 Collision avoidance workflow

The avoidance process begins with orbit data, the content of which is specified in ISO 26900. The data

can be provided by collaborating satellite operators and from observers who are capable of viewing

satellites. It is also important to know the nature of each object if possible. This information includes

size, mass, geometry, and the operational state (e.g. active or inactive). Finally, collision probability

estimates consider the inevitable imprecision associated with orbit determination and other hypotheses

and measurements. Figure 1 depicts this top-level workflow.Figure 1 — Top-level collision avoidance workflow

5 Perceiving close approaches

5.1 Orbit data

5.1.1 Inputs

Inputs to conjunction assessment are principally data that specify the trajectories of the objects of

interest. These are one of three types of information: orbital elements, ephemerides, or observations

of satellites. Orbital elements in this context include parameters that describe the evolution of the

© ISO 2021 – All rights reserved---------------------- Page: 8 ----------------------

ISO/TR 16158:2021(E)

trajectory and which can be used to estimate the trajectory in the future. They are derived from past

observations of satellites. Ephemerides are time-ordered sets of position and velocity within which one

interpolates to estimate the position and velocity at intermediate times. Ephemerides need to span the

future time interval of interest, where the equations of motion having been propagated by the provider.

Observations are measurements of satellite position and velocity from one or more well-characterized

and registered instruments. The recipient can use those observations to estimate the evolution of the

trajectory either through direct numerical integration of governing equations or by developing orbital

elements for subsequent propagation. ISO/TR 11233 describes the way a provider's orbit determination

scheme is codified. There are normative formats for orbital elements and ephemerides (see ISO 26900).

See CCSDS 503.0-B-2 for normative formats for transmitting observations.It is extremely important to realize that trajectory estimates are derived from measurements that

cannot be precise such as spheres. Therefore, they are called “estimates.” The input information can

include characterized uncertainties. Uncertainty in any of the independent variables or parameters

introduces imprecision in all the dependent variables that describe the evolution. The appropriate

expression of uncertainty is, therefore, a square matrix whose dimension is the number of elements of

the state, called a state vector. If uncertainties are not provided or are wrong, one cannot determine

properly the probability that two objects can collide.5.1.2 Propagating all orbits over the interval of interest

All orbits being under consideration are best forecasted by the model in which they were created.

Since orbit determination and propagation are uncertain, the propagation scheme can be well suited

for this interval. ANSI/AIAA S-131-2010 is a normative reference for orbit propagation. Osculating

orbit estimates grow imprecise over time intervals long compared to the time span of underlying

observations. This imprecision is sufficient to make collision probabilities misleading. Therefore,

conjunction assessment in low Earth orbit is unreliable at the present state of the art for periods longer

than approximately one week beyond the latest orbit determination, depending on the orbit of interest.

Some particularly stable orbits can be estimated reliably for longer periods. Probability of collision

can be estimated over long periods using consistent statistical descriptions of satellite orbits and the

evolution of the debris environment. These techniques estimate whether a conjunction will occur or not

but cannot expose which specific objects can be involved.5.2 Initial filtering

5.2.1 All against all

The most complete process would examine each object in orbit against all others over the designated

time span. Most techniques eliminate A-B duplication, defined as screening B against A in addition to A

against B. Therefore, the number of screenings necessary is not the factorial of the number of satellites.

It is impossible to know how many objects orbit the Earth. Many escape perception. The best a satellite

operator can do is to consider those that have been detected. One cannot screen against unknown

objects that one estimates can be present.5.3 Eliminating infeasible conjunctions

5.3.1 General

Much of the population in orbit physically cannot encounter many other satellites during the period of

interest. For example, even if uncontrolled, geostationary satellites 180 degrees apart in longitude are

not threats to each other.5.3.2 Sieve

Sieve techniques employ straightforward geometric and kinematic processes to narrow the spectrum

of feasible conjunctions based on the minimum separation between orbits. They are based variously

on orbit geometry, numerical relative distance functions, and actual orbit propagation. The concept is

© ISO 2021 – All rights reserved---------------------- Page: 9 ----------------------

ISO/TR 16158:2021(E)

to examine proximity of one satellite to another sequentially in parameter space beginning with the

parameter that most effectively discriminates separation distance. To account for approximations

in orbit analysis, a distance buffer (pad) can be added to the filter screening distance threshold. For

example, if in-track separation is likely to be the best indicator of separation, satellites that are far apart

in-track do not need to be screened further cross-track. They differ in computational efficiency and

the degree to which close approaches are all perceived. There is no normative approach since different

techniques are satisfactory for different satellites and operator judgements.5.3.3 Toroidal elimination

Toroidal elimination eliminates objects by determining which mean orbits can touch a toroidal volume

defined by the orbit of the satellite of interest and a keepout volume cross-sectional area.

5.3.4 Apogee-perigee filtersThis approach eliminates satellites whose apogees are lower than the perigee of the satellite of

interest and perigees are sufficiently greater than the apogee of the satellite of interest. The criterion

for sufficiency is based either on operator experience or risk tolerance. Risk can be quantified with

techniques of signal detection and receiver operating characteristics discussed subsequently.

Volumetric screening is of the same nature, eliminating satellites whose orbits are outside the volume

of space described by the orbit of the satellite of interest.5.3.5 Statistical errors

Since each of these techniques relies on trajectory information that is imprecise, these filters will suffer

from Type I failure to identify real threats and Type II errors (including satellites that are not threats).

Filter parameter selection is based on the user's tolerance for both kinds of errors. Every filtering

scheme will include events that can have been discarded and discarded events that ought to have been

included.6 Determining potential collisions for warning and further action (close

approach screening)

6.1 General

Initial filtering provides little information for mitigating collisions. The next task is judging whether

the actual states of the involved satellites are sufficiently threatening. The first step is determining

whether satellites come extremely close to each other. This is the judgement of each satellite operator. It

can be based on satellite sizes, the consequences of a collision, the confidence one has in orbit estimates

and propagation, and other subjective factors. As with initial filtering, even this more refined level of

discrimination will miss some threats. The possibility of false alarms and missed detections increases

the farther in the future one extrapolates.6.2 Symmetric keepout

The most straightforward keepout volume is symmetric. These are easiest to implement but can

encompass considerably more than the vulnerable geometry of the satellite. These can be spheres,

cubes, or any other three-dimensional volumes of operator-judged size. The satellite of interest can be

enveloped symmetrically, and osculating orbits of other satellites tested for penetrating the volume.

Alternatively, the bounding volumes of both satellites can be screened for intersection. This is generally

the most conservative approach, identifying as potential collisions requiring action many events that

are extremely improbable.© ISO 2021 – All rights reserved

---------------------- Page: 10 ----------------------

ISO/TR 16158:2021(E)

6.3 Bounding volume keepout

This approach envelops the satellite of interest in a volume that is not symmetric. The volume can be

ellipsoidal, a rectangular parallelepiped, or a shape composed of surfaces nearly conformal with the

satellite. The geometry of the bounding volume can be based on operator experience. For example, one

can use consistent orbit uncertainties along track, radial from Earth Center, and normal to the plane

defined by both directions. The volume can also be determined from more exhaustive probabilistic

calculations that are too resource intensive to use frequently.6.4 Probability techniques

The probability that two objects separated by a given distance at closest approach would actually

collide is assessed as the integral of the intersection of the objects' position probability densities as a

function of time.All satellite orbits are imprecise. Approximations to physical processes (process noise) and imprecise

observations of satellite states of motion (measurement noise) lead to imprecise estimates of the future

states of satellites. The imprecision is represented by variances and covariances of the dependent

parameters among each other. These form a covariance matrix. It represents generally mean squared

deviations of estimated (expected) values of each dependent variable from those inferred from

measurements. A covar**...**

TECHNICAL ISO/TR

REPORT 16158

Second edition

Space systems — Avoiding collisions

among orbiting objects

Systèmes spatiaux — Évitement des collisions entre objets en orbite

PROOF/ÉPREUVE

Reference number

ISO/TR 16158:2021(E)

ISO 2021

---------------------- Page: 1 ----------------------

ISO/TR 16158:2021(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.ISO copyright office

CP 401 • Ch. de Blandonnet 8

CH-1214 Vernier, Geneva

Phone: +41 22 749 01 11

Email: copyright@iso.org

Website: www.iso.org

Published in Switzerland

ii PROOF/ÉPREUVE © ISO 2021 – All rights reserved

---------------------- Page: 2 ----------------------

ISO/TR 16158:2021(E)

Contents Page

Foreword ..........................................................................................................................................................................................................................................v

Introduction ................................................................................................................................................................................................................................vi

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Collision avoidance workflow ................................................................................................................................................................. 2

5 Perceiving close approaches .................................................................................................................................................................... 2

5.1 Orbit data ..................................................................................................................................................................................................... 2

5.1.1 Inputs ......................................................................................................................................................................................... 2

5.1.2 Propagating all orbits over the interval of interest ............................................................................ 3

5.2 Initial filtering .......................................................................................................................................................................................... 3

5.2.1 All against all ....................................................................................................................................................................... 3

5.3 Eliminating infeasible conjunctions ..................................................................................................................................... 3

5.3.1 General...................................................................................................................................................................................... 3

5.3.2 Sieve ............................................................................................................................................................................................ 3

5.3.3 Toroidal elimination ..................................................................................................................................................... 4

5.3.4 Apogee-perigee filters ................................................................................................................................................. 4

5.3.5 Statistical errors ............................................................................................................................................................... 4

6 Determining potential collisions for warning and further action (close approach

screening) .................................................................................................................................................................................................................... 4

6.1 General ........................................................................................................................................................................................................... 4

6.2 Symmetric keepout ............................................................................................................................................................................. 4

6.3 Bounding volume keepout ............................................................................................................................................................ 5

6.4 Probability techniques ..................................................................................................................................................................... 5

6.5 Maximum probability ........................................................................................................................................................................ 7

6.6 Bounding volume based on probability ............................................................................................................................ 8

6.7 Comparison of techniques .........................................................................................................................................................10

7 Probability of survival .................................................................................................................................................................................10

7.1 General ........................................................................................................................................................................................................10

7.2 Trending.....................................................................................................................................................................................................11

7.3 Cumulative probability .................................................................................................................................................................11

7.4 Bayesian assessment ......................................................................................................................................................................12

8 Additional information for judging courses of action ................................................................................................13

8.1 General ........................................................................................................................................................................................................13

8.2 Maneuver capability ........................................................................................................................................................................13

8.3 Spacecraft characteristics ...........................................................................................................................................................13

8.4 Quality of underlying orbit data ............................................................................................................................................13

9 Consequence assessment .........................................................................................................................................................................13

9.1 General ........................................................................................................................................................................................................13

9.2 Guidance for population risk ...................................................................................................................................................13

9.3 Traffic impacts ......................................................................................................................................................................................14

10 Requirements for warning and information for avoidance ..................................................................................14

10.1 General ........................................................................................................................................................................................................14

10.2 Orbit data ..................................................................................................................................................................................................14

10.3 Minimum data required for warning of and avoiding collisions ...............................................................15

10.4 Optional elements of information .......................................................................................................................................15

11 Conjunction and collision assessment workflow and operational concept .........................................16

Annex A (informative) Relationship between combined object size, combined positional

error, and maximum probability ......................................................................................................................................................19

© ISO 2021 – All rights reserved PROOF/ÉPREUVE iii---------------------- Page: 3 ----------------------

ISO/TR 16158:2021(E)

Annex B (informative) Probability contour visualization ...........................................................................................................21

Bibliography .............................................................................................................................................................................................................................31

iv PROOF/ÉPREUVE © ISO 2021 – All rights reserved---------------------- Page: 4 ----------------------

ISO/TR 16158:2021(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/

iso/ foreword .html.This document was prepared by Technical Committee ISO/TC 20, Aircraft and space vehicles,

Subcommittee SC 14, Space systems and operations.This second edition cancels and replaces the first edition (ISO/TR 16158:2013), which has been

technically revised.The main changes compared to the previous edition are as follows:

— improved figures for clarity;

— added plot of maximum probability;

— switched to “decimal comma” per ISO editorial rules;

— simplified operational concepts figures;

— added informative annexes containing collision probability relational nomograms;

— added collision probability topology in both graphical and tabular look-up formats;

— reordered the bibliographyAny feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.© ISO 2021 – All rights reserved PROOF/ÉPREUVE v

---------------------- Page: 5 ----------------------

ISO/TR 16158:2021(E)

Introduction

This document describes the workflow for perceiving and avoiding collisions among orbiting objects,

data requirements for these tasks, techniques that can be used to estimate the probability of collision

and guidance for executing avoidance maneuvres. Diligent collaboration is strongly encouraged among

all who operate satellites.The process begins with the best possible trajectory data, provided by satellite operators or sensor

systems developed for this purpose. The orbits of satellites can be compared with each other to discern

physically feasible approaches that can result in collisions. The trajectories so revealed can then be

examined more closely to estimate the probability of collision. Where the possibility of a collision

has been identified within the criteria established by each satellite operator, the spectrum of feasible

maneuvers is examined.There are several different approaches to conjunction assessment. All have merits and deficiencies.

Most focus on how closely satellites approach each other. This is often very uncertain since satellite

orbits generally change more rapidly under the influence of non-conservative forces than observations

of satellites in orbit can be acquired and employed to improve orbit estimates. Spacecraft operators

require the fullness of orbit data to judge the credibility and quality of conjunction perception. This

information includes the moment of time of the last elaboration of orbit (the epoch) and the standard

time scale employed, state vector value or elements of orbit at this moment of time, the coordinate

system description that presents the orbital data, the forces model description that was used for orbital

plotting, and information about the estimation errors of the orbital parameters. Essential elements of

information for this purpose are specified in ISO 26900.There are also diverse approaches to estimating the probability that a close approach can really result

in a collision. This is a statistical process very similar to weather forecasting. Meteorologists no longer

make definitive predictions. They provide the probability of precipitation, not whether it will rain. All

conjunction assessment approaches are in some way founded in probabilities. Probability of collision

is also a highly desirable element of data. It can be accompanied by metadata that allows operators to

interpret the information within their own operational procedures.How near satellites can be to each other and the probability they can collide if they were that close

are only two discriminants of potentially catastrophic events. Since the objective is that the satellite

survives despite many potential close approaches, cumulative probability of survival is also important

information. Responding precipitously to the close approach nearest at hand can only delay the demise

of the satellite or even contribute to a subsequent more serious event. The evolution of close approaches

and the cumulative probability that a satellite can survive are also important.Finally, the state of each of the conjunction partners, their ability to maneuver or otherwise avoid

contact, and the outcomes of past events that are similar guide courses of action.

vi PROOF/ÉPREUVE © ISO 2021 – All rights reserved---------------------- Page: 6 ----------------------

TECHNICAL REPORT ISO/TR 16158:2021(E)

Space systems — Avoiding collisions among orbiting

objects

1 Scope

This document is a guide for establishing essential collaborative enterprises to sustain the space

environment and employ it effectively.This document describes some widely used techniques for perceiving close approaches, estimating

collision probability, estimating the cumulative probability of survival, and manoeuvring to avoid

collisions.NOTE Satellite operators accept that all conjunction and collision assessment techniques are statistical.

All suffer false positives and/or missed detections. The degree of uncertainty in the estimated outcomes is not

uniform across all satellite orbits or all assessment intervals. No comparison within a feasible number of test

cases can reveal the set of techniques that is uniformly most appropriate for all.

2 Normative referencesThere are no normative references in this document.

3 Terms and definitions

For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp— IEC Electropedia: available at http:// www .electropedia .org/

3.1

collision

act of colliding; instance of one object striking another

3.2

conjunction

apparent meeting or passing of two or more objects in space

3.3

covariance

measure of how much variables change together

Note 1 to entry: For multiple dependent variables, a square, symmetric, positive definite matrix of dimensionality

N × N, where N is the number of variables.3.4

encounter plane

plane normal to the relative velocity at the time of closest approach

3.5

ephemeris

time-ordered set of position and velocity within which one interpolates to estimate the position and

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3.6

false alarm

statistical Type I error, when a statistical test fails to reject a false null hypothesis

3.7interface control document

ICD

specification that describes the characteristics that can be controlled at the boundaries between

systems, subsystems, and other elements3.8

operational concept

roles, relationships, and information flows among tasks and stakeholders and the way systems and

processes will be used3.9

orbital elements

parameters that describe the evolution of the trajectory and which can be used to estimate the

trajectory in the future4 Collision avoidance workflow

The avoidance process begins with orbit data, the content of which is specified in ISO 26900. The data

can be provided by collaborating satellite operators and from observers who are capable of viewing

satellites. It is also important to know the nature of each object if possible. This information includes

size, mass, geometry, and the operational state (e.g. active or inactive). Finally, collision probability

estimates consider the inevitable imprecision associated with orbit determination and other hypotheses

and measurements. Figure 1 depicts this top-level workflow.Figure 1 — Top-level collision avoidance workflow

5 Perceiving close approaches

5.1 Orbit data

5.1.1 Inputs

Inputs to conjunction assessment are principally data that specify the trajectories of the objects of

interest. These are one of three types of information: orbital elements, ephemerides, or observations

of satellites. Orbital elements in this context include parameters that describe the evolution of the

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trajectory and which can be used to estimate the trajectory in the future. They are derived from past

observations of satellites. Ephemerides are time-ordered sets of position and velocity within which one

interpolates to estimate the position and velocity at intermediate times. Ephemerides need to span the

future time interval of interest, where the equations of motion having been propagated by the provider.

Observations are measurements of satellite position and velocity from one or more well-characterized

and registered instruments. The recipient can use those observations to estimate the evolution of the

trajectory either through direct numerical integration of governing equations or by developing orbital

elements for subsequent propagation. ISO 11233 describes the way a provider's orbit determination

scheme is codified. There are normative formats for orbital elements and ephemerides (see ISO 26900).

See CCSDS 503.0-B-2 for normative formats for transmitting observations.It is extremely important to realize that trajectory estimates are derived from measurements that

cannot be precise such as aspheres. Therefore, they are called “estimates.” The input information can

include characterized uncertainties. Uncertainty in any of the independent variables or parameters

introduces imprecision in all the dependent variables that describe the evolution. The appropriate

expression of uncertainty is, therefore, a square matrix whose dimension is the number of elements of

the state, called a state vector. If uncertainties are not provided or are wrong, one cannot determine

properly the probability that two objects can collide.5.1.2 Propagating all orbits over the interval of interest

All orbits being under consideration are best forecasted by the model in which they were created.

Since orbit determination and propagation are uncertain, the propagation scheme can be well suited

for this interval. ANSI/AIAA S-131-2010 is a normative reference for orbit propagation. Osculating

orbit estimates grow imprecise over time intervals long compared to the time span of underlying

observations. This imprecision is sufficient to make collision probabilities misleading. Therefore,

conjunction assessment in low Earth orbit is unreliable at the present state of the art for periods longer

than approximately one week beyond the latest orbit determination, depending on the orbit of interest.

Some particularly stable orbits can be estimated reliably for longer periods. Probability of collision

can be estimated over long periods using consistent statistical descriptions of satellite orbits and the

evolution of the debris environment. These techniques estimate whether a conjunction will occur or not

but cannot expose which specific objects can be involved.5.2 Initial filtering

5.2.1 All against all

The most complete process would examine each object in orbit against all others over the designated

time span. Most techniques eliminate A-B duplication, defined as screening B against A in addition to A

against B. Therefore, the number of screenings necessary is not the factorial of the number of satellites.

It is impossible to know how many objects orbit the Earth. Many escape perception. The best a satellite

operator can do is to consider those that have been detected. One cannot screen against unknown

objects that one estimates can be present.5.3 Eliminating infeasible conjunctions

5.3.1 General

Much of the population in orbit physically cannot encounter many other satellites during the period of

interest. For example, even if uncontrolled, geostationary satellites 180 degrees apart in longitude are

not threats to each other.5.3.2 Sieve

Sieve techniques employ straightforward geometric and kinematic processes to narrow the spectrum

of feasible conjunctions based on the minimum separation between orbits. They are based variously

on orbit geometry, numerical relative distance functions, and actual orbit propagation. The concept is

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to examine proximity of one satellite to another sequentially in parameter space beginning with the

parameter that most effectively discriminates separation distance. To account for approximations

in orbit analysis, a distance buffer (pad) can be added to the filter screening distance threshold. For

example, if in-track separation is likely to be the best indicator of separation, satellites that are far apart

in-track do not need to be screened further cross-track. They differ in computational efficiency and

the degree to which close approaches are all perceived. There is no normative approach since different

techniques are satisfactory for different satellites and operator judgements.5.3.3 Toroidal elimination

Toroidal elimination eliminates objects by determining which mean orbits can touch a toroidal volume

defined by the orbit of the satellite of interest and a keepout volume cross-sectional area.

5.3.4 Apogee-perigee filtersThis approach eliminates satellites whose apogees are lower than the perigee of the satellite of

interest and perigees are sufficiently greater than the apogee of the satellite of interest. The criterion

for sufficiency is based either on operator experience or risk tolerance. Risk can be quantified with

techniques of signal detection and receiver operating characteristics discussed subsequently.

Volumetric screening is of the same nature, eliminating satellites whose orbits are outside the volume

of space described by the orbit of the satellite of interest.5.3.5 Statistical errors

Since each of these techniques relies on trajectory information that is imprecise, these filters will suffer

from Type I failure to identify real threats and Type II errors (including satellites that are not threats).

Filter parameter selection is based on the user's tolerance for both kinds of errors. Every filtering

scheme will include events that can have been discarded and discarded events that ought to have been

included.6 Determining potential collisions for warning and further action (close

approach screening)

6.1 General

Initial filtering provides little information for mitigating collisions. The next task is judging whether

the actual states of the involved satellites are sufficiently threatening. The first step is determining

whether satellites come extremely close to each other. This is the judgement of each satellite operator. It

can be based on satellite sizes, the consequences of a collision, the confidence one has in orbit estimates

and propagation, and other subjective factors. As with initial filtering, even this more refined level of

discrimination will miss some threats. The possibility of false alarms and missed detections increases

the farther in the future one extrapolates.6.2 Symmetric keepout

The most straightforward keepout volume is symmetric. These are easiest to implement but can

encompass considerably more than the vulnerable geometry of the satellite. These can be spheres,

cubes, or any other three-dimensional volumes of operator-judged size. The satellite of interest can be

enveloped symmetrically, and osculating orbits of other satellites tested for penetrating the volume.

Alternatively, the bounding volumes of both satellites can be screened for intersection. This is generally

the most conservative approach, identifying as potential collisions requiring action many events that

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6.3 Bounding volume keepout

This approach envelops the satellite of interest in a volume that is not symmetric. The volume can be

ellipsoidal, a rectangular parallelepiped, or a shape composed of surfaces nearly conformal with the

satellite. The geometry of the bounding volume can be based on operator experience. For example, one

can use consistent orbit uncertainties along track, radial from Earth Center, and normal to the plane

defined by both directions. The volume can also be determined from more exhaustive probabilistic

calculations that are too resource intensive to use frequently.6.4 Probability techniques

The probability that two objects separated by a given distance at closest approach would actually

collide is assessed as the integral of the intersection of the objects' position probability densities as a

function of time.All satellite orbits are imprecise. Approximations to physical processes (process noise) and imprecise

observations of satellite states of motion (measurement noise) lead to imprecise estimates of the future

states of satellites. The imprecision is represented by variances and covariances of the dependent

parameters among each other. These form a covariance matrix. It rep**...**

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