ISO/TR 16158:2021
(Main)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
ii
© 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
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ISO/TR 16158:2021(E)
Annex B (informative) Probability contour visualization .21
Bibliography .31
iv
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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.
v
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---------------------- 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.
vi
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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 references
There 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
1
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ISO/TR 16158:2021(E)
3.6
false alarm
statistical Type I error, when a statistical test fails to reject a false null hypothesis
3.7
interface control document
ICD
specification that describes the characteristics that can be controlled at the boundaries between
systems, subsystems, and other elements
3.8
operational concept
roles, relationships, and information flows among tasks and stakeholders and the way systems and
processes will be used
3.9
orbital elements
parameters that describe the evolution of the trajectory and which can be used to estimate the
trajectory in the future
4 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
2
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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
3
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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 filters
This 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.
4
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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
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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 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 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 references
There 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
velocity at intermediate times
© ISO 2021 – All rights reserved PROOF/ÉPREUVE 1
---------------------- 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
3.7
interface control document
ICD
specification that describes the characteristics that can be controlled at the boundaries between
systems, subsystems, and other elements
3.8
operational concept
roles, relationships, and information flows among tasks and stakeholders and the way systems and
processes will be used
3.9
orbital elements
parameters that describe the evolution of the trajectory and which can be used to estimate the
trajectory in the future
4 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 filters
This 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.
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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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