I. Executive Summary
The OGC Testbed 18 Engineering Report (ER) begins with an overview of important Standards Development Organizations and authorities whose Standards are discussed in this ER. Current Standards from ISO, such as ISO 19111: Geographic Information – Spatial referencing by coordinates, and the OGC GeoPOSE Standard, are not adequate for dealing with non-Earth geospatial data.
Alternative approaches by geodetic and astronautic organizations, such as the Consultative Committee for Space Data Systems (CCSDS) Navigation Data — Definitions and Conventions, the International Earth Rotation and Reference Systems Service (IERS) IERS conventions, or the NASA NAIF SPICE Toolkit are also being presented.
The resulting practices are often similar to each other but cannot be understood as defining a Standard framework or approach. In describing the coordinate reference systems and frames used in geodesy, the inadequacies and weaknesses of the existing Standards become apparent. In general, from a geodetic point of view, the main classes of coordinate reference systems (CRS) are as follows:
The exact distinction of these CRS is important for understanding transformations between them. Therefore, this ER describes these transformations. The detailed discussion includes the effect of precession, nutation, and polar motion. In addition, this ER emphasizes the need for taking time systems into account in the definition of coordinate systems and their consideration in the development of Standards. This ER specifically describes the following time systems.
Sidereal time, which refers to the stars
Solar or universal time, which refers to the Sun
Atomic time, which refers to atomic phenomena
Theoretical time, which refers to a theoretical model
Furthermore, the above theoretical discussion is supported by a demonstration in which two objects are represented in different coordinate systems. The demonstration illustrates the difference between space-fixed and Earth-fixed reference systems. Finally, this ER provides an evaluation of the existing Standards from a geodetic perspective and makes recommendations for the identified deficiencies. These should be considered when expanding current Standards. The range of objects that can be represented in the extension of Standards can be expanded enormously. This extension approaches the goal of forming a general framework for 3D+ coordinate systems to allow a complete, unambiguous, and universally understood state of any object in space.
The following are keywords to be used by search engines and document catalogues.
testbed-18, Inertial Reference System, Terrestrial Reference System, Coordinate Reference System, Time system
III. Security considerations
No security considerations have been made for this document.
IV. Submitting Organizations
The following organizations submitted this Document to the Open Geospatial Consortium (OGC):
- Institute of Geodesy, University of Stuttgart
Currently, most OGC Standards focus on data that is observed on the ground or near the Earth’s surface. Extra-terrestrial space and the exact location of remote sensors has been less in focus. Current OGC Standardizations cannot be applied to this type of spatial data processing. This OGC Testbed 18 Engineering Report (ER) first provides a detailed description of existing Standards, conventions, and tools which are particularly relevant for further evaluation. Subsequently, various coordinate and time systems are presented and improvements or extensions to existing Standards are proposed to describe objects in orbit around any celestial body or interplanetary flight through our solar system.
Testbed-18: 3D+ Standards Framework Engineering Report
This Testbed 18 Engineering Report provides information about various coordinate systems used in geodesy and aerospace. This ER is applicable to existing Standards and can be used by OGC Standard Working Groups (SWGs) as a source of ideas and recommendations for future evolution of relevant Standards.
2. Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
Open API Initiative: OpenAPI Specification 3.0.2, 2018 https://github.com/OAI/OpenAPI-Specification/blob/master/versions/3.0.2.md
], ISO 19107:2003 Geographic information — Spatial schema, 2003 https://www.iso.org/standard/26012.html
ISO 19108:2002 Geographic information — Temporal schema, 2002 https://www.iso.org/standard/26013.html
ISO 19109:2015 Geographic information — Rules for application schema, 2015 https://www.iso.org/standard/59193.html
ISO 19111:2019 Geographic information — Referencing by coordinates, 2019, https://www.iso.org/standard/74039.html
ISO 19141:2008 Geographic information — Schema for moving features, 2008 https://www.iso.org/standard/41445.html
Heazel, C., Kolbe, T., Kutzner, T., Nagel, C., Roensdorf, C., Smyth, C. S.: OGC 20-010, OGC City Geography Markup Language (CityGML) Part 1: Conceptual Model Standard, 2021 https://docs.ogc.org/is/20-010/20-010.html
Kim, K., Ishimaru, N.: OGC 19-045r3, OGC Moving Features Encoding Extension — JSON, 2020 http://docs.opengeospatial.org/is/19-045r3/19-045r3.html
R. Fielding, J. Gettys, J. Mogul, H. Frystyk, L. Masinter, P. Leach, T. Berners-Lee: IETF RFC 2616, Hypertext Transfer Protocol — HTTP/1.1. RFC Publisher (1999). https://www.rfc-editor.org/info/rfc2616.
ISO: Geographic information — Reference model — Part 1: Fundamentals, 2014. https://www.iso.org/standard/59164.html
OGC: GeoPose Specification draft, 2021. https://github.com/opengeospatial/GeoPose/
3. Terms, definitions and abbreviated terms
This document uses the terms defined in OGC Policy Directive 49, which is based on the ISO/IEC Directives, Part 2, Rules for the structure and drafting of International Standards. In particular, the word “shall” (not “must”) is the verb form used to indicate a requirement to be strictly followed to conform to this document and OGC documents do not use the equivalent phrases in the ISO/IEC Directives, Part 2.
This document also uses terms defined in the OGC Standard for Modular specifications (OGC 08-131r3), also known as the ‘ModSpec’. The definitions of terms such as standard, specification, requirement, and conformance test are provided in the ModSpec.
For the purposes of this document, the following additional terms and definitions apply.
One of a sequence of numbers designating the position of a point.
Note 1 to entry: In a spatial coordinate reference system, the coordinate numbers are qualified by units.
[SOURCE: ISO 19111]
3.2. coordinate system
A set of mathematical rules for specifying how coordinates are to be assigned to points.
[SOURCE: ISO 19111]
3.3. coordinate reference system
A coordinate system that is related to an object by a datum.
Note 1 to entry: Geodetic and vertical datums are referred to as reference frames.
Note 2 to entry: For geodetic and vertical reference frames, the object will be the Earth. In planetary applications, geodetic and vertical reference frames may be applied to other celestial bodies.
[SOURCE: ISO 19111]
3.4. Abbreviated terms
Consultative Committee for Space Data Systems
Celestial Ephermis Pole
Global Navigation Satellite Service
Global Positioning Service
International Earth Rotation and Reference Systems Service
International Organization for Standardization
Navigation and Ancillary Information Facility
North Celestial Pole
North Ecliptical Pole
Rotation around axis with angle
Universal Time Coordinated
The exact positioning of sensors in 3D space and corresponding 3D data streaming, analytics, and portrayal plays an important role in many geospatial scenarios and applications. Remote sensing of the Earth’s ground, atmosphere, or stratosphere has become routine in many domains.
In classical geodesy, a Coordinate Reference System (CRS) is a framework used to precisely measure locations on the surface of the Earth as coordinates. Defining a CRS is the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space. The definition of a specific CRS comprises a choice of Earth ellipsoid, horizontal datum, map projection (except in the geographic coordinate system), origin point, and unit of measure. Thousands of CRSs have been specified for use around the world or in specific regions and for various purposes, necessitating transformations between different CRSs. CRSs are a crucial basis for the sciences and technologies of Geoinformatics, including cartography, geographic information systems, surveying, remote sensing, and civil engineering. This has led to international Standards such as the OGC-ISO 19111:2019 Geographic information—Spatial Referencing by coordinates.
The TestBed-18 activity documented in this ER aims to go beyond the surface of the Earth and enable full location determination, orientation, and trajectory description of objects in orbit around celestial bodies or in free flight in our solar system. This ER evaluates current Standards with respect to the exact positioning of sensors at any location within the solar system. This ER proposes extensions to current Standards to cover broader needs such as an inertial coordinate reference system.
5. Standards, Conventions and Tools
5.1. Authorities responsible for providing Standards and definitions for coordinate reference systems
A complete listing of all organizations contributing to this topic would exceed the scope of this report. Therefore only the most relevant are presented in this ER.
5.1.1. International Organization for Standardization
The International Organisation for Standardization (ISO) is a global network of 167 national Standards bodies with one member per country. It is an independent, non-governmental organization that provides a platform for developing practical tools through common understanding and cooperation with all stakeholders. ISO develops, approves and publishes Standards for everything except electrical and electronic engineering and telecommunication.
NOTE Electrical and electronic engineering Standards are developed by the International Electrotechnical Commission (IEC), and the telecommunication by the International Telecommunication Union (ITU).
5.1.2. Open Geospatial Consortium
The Open Geospatial Consortium (OGC) is an open-membership, worldwide voluntary consensus Standards organization that defines, documents, approves, and maintains geoprocessing Standards. OGC geospatial Standards can be used in geographic information systems (GIS) and systems for Earth imaging, Web mapping, location-based services, surveying and mapping, CAD-based facility management, webs of geolocated sensors, navigation, cartography, automated mapping, etc. The OGC Standards define open interfaces, protocols, schemas, and other components. Implementation of these Standards enable different systems and applications to exchange geospatial data and instructions and enable the complete integration of these capabilities into a range of information systems. The OGC collaborates with other Standards organizations such as the W3C and ISO. Since several Standards were jointly developed by ISO and the OGC they will be discussed together.
5.1.3. Consultative Committee for Space Data Systems
Another organization that often cooperates with ISO is the Consultative Committee for Space Data Systems (CCSDS). CCSDS was formed by the major space agencies of the world to provide a forum for discussion of common problems in the development and operation of space data systems. CCSDS is currently composed of 11 member agencies, 32 observer agencies, and over 119 industrial associates. CCSDS Standards are widely used in aerospace. The publications of the CCSDS can be divided into different categories, color coded. The most important are Recommended Standards (Blue), Recommended Practices (Magenta), and Informational Reports (Green). Therefore, the CCSDS does not necessarily provide Standards but rather conventions and practices.
5.1.4. International Earth Rotation and Reference Systems Service
The main objective of the International Earth Rotation and Reference Systems Service (IERS) is the suggested conventions regarding various transformations and reference system definitions that are widely used in geodesy and of great importance for the work defined in this ER.
The IERS provides definitions of various coordinate reference systems and their realizations as well as the Earth orientation parameters required to study Earth orientation variations to transform between the defined CRSs. For all systems and frames, the associated Standards, constants and models are given.
A detailed discussion of the IERS observations, conventions, and more is made in Clause 6 — Clause 8.
5.1.5. NASA’s Navigation and Ancillary Information Facility
NASA’s Navigation and Ancillary Information Facility is responsible for developing a tool that will be discussed later in this ER. NASA’s Navigation and Ancillary Information Facility (NAIF) was established at the Jet Propulsion Laboratory to lead the design and implementation of the “SPICE” ancillary information system. The NAIF is dedicated to the issues of producing high precision, clearly documented and readily used “ancillary information” required by space scientists and engineers.
5.1.6. International Astronomical Union
The International Astronomical Union (IAU) was founded in 1919 to promote and safeguard the science of astronomy in all its aspects, including research, communication, education, and development, through international cooperation. Its members — structured into Divisions, Commissions, and Working Groups — are 12113 astronomers active in professional research and education in astronomy from 93 countries worldwide. Among other activities, it acts as the recognized authority for assigning designations and names to celestial bodies (stars, planets, asteroids, etc.) and any surface features on them.
The Working Group on Cartographic Coordinates and Rotational Elements was established with the purpose to avoid a proliferation of inconsistent cartographic and rotational systems, and therefore to define the cartographic and rotational elements of the planets and satellites on a systematic basis and to relate the new cartographic coordinates rigorously to the rotational elements.
5.2. ISO Standardizations
The first and most important set of standards referenced in this ER are standards developed by ISO Technical Committee 211 (TC211) and the Open Geospatial Consortium (OGC). These Standards define foundational concepts which will serve as the basis for later discussions, evaluations, and requirements.
5.2.1. Referencing by coordinates
ISO 19111:2019 Geographic information — Referencing by coordinates is arguably the most important standard addressed by this initiative. TC211 and OGC strive to maintain a separation between coordinate values and the coordinate reference system where those values apply. This allows new coordinate reference systems (projections, geoids, etc.) to be defined without impacting existing standards and implementations. However, this requires that there be a standard way to describe a coordinate reference system. ISO 19111 fills this need by defining “the conceptual schema for the description of referencing by coordinates” and the data required to define a coordinate reference system. ISO 19111 compliant registries allow applications to retrieve, interpret, and apply these coordinate reference system definitions at run time. This is a key capability enabling geospatial technologies to be applied to non-Earth locations.
A detailed description of this ISO 19111 can be found in the OGC Testbed 18 D025 — Reference Frame Transformation Engineering Report (OGC 22-038) and is therefore not discussed here.
5.2.2. Temporal Schema
ISO 19108:2002 Geographic information — Temporal schema defines concepts for describing temporal characteristics of geographic information. The majority of this Standard addresses the representation of Earth-centric systems (calendars) for dates. However, it also provides a framework for representing time. This framework allows for the association of spatial and temporal reference systems. These associations make it possible to define a spatial-temporal reference system; a coordinate reference system for 4D space-time. This concept is explored in greater detail within this Engineering Report and in D025 — Reference Frame Transformation Engineering Report.
5.2.3. A Feature Model for Space Objects
Before we can describe non-terrestrial objects, we must first have a conceptual model of the universe. The OGC and ISO TC211 provide that model in ISO 19109:2015 Geographic information — Rules for application schema. 19109 defines the General Feature Model (GFM). The GFM defines the concept of a Feature, its components, and behaviors.
The OGC and ISO define a Feature as an “Abstraction of real-world phenomena” (ISO 19101-1:2014).
A Feature, then, is a high-level abstraction for anything that does or could exist in the universe.
The General Feature Model further refines the concept of a Feature. The following principles are most relevant for this ER.
A Feature can be a FeatureType or an Instance of a FeatureType (AnyFeature).
FeatureTypes can form a taxonomy (inheritance).
Features possess characteristics (Properties).
A Property of a Feature can be an Operation, Attribute, or Association.
Figure 1 — General Feature Model
The resulting model is sufficient to describe a Feature’s identity (IdentifiedType), what it is (FeatureType), what it can do (Operations), the Feature’s observable characteristics (Attributes), and any associations with other Feature instances.
5.2.4. Geometry in 3 Dimensions
The applicable OGC/ISO standard for geometries is ISO 19107:2003 Geographic information — Spatial schema. While a new version was approved in 2019, it hasn’t propagated through the rest of the ISO standards baseline. As a result, 19107:2003 is the most recent implemented version.
18.104.22.168. Features and Geometry
The General Feature Model treats geometry as an attribute of the Feature. In addition, it defines the following three types of attributes which are useful for associating geometry with a Feature in a standard manner.
SpatialAttributeType: Geometries (GM_Object) and Topologies (TP_Object)
LocationalAttributeType: Named locations, extents, and points
TemporalAttributeType: Temporal objects (TM_Object)
Figure 2 — General Feature Model Attribute Types
Figure 3 — General Feature Model Spatial Attribute Types
Figure 4 — General Feature Model Locational Attribute Types
Figure 5 — General Feature Model Temporal Attribute Types
22.214.171.124. The Geometry Model
An important feature of the ISO Geometry Model is that it does not specify or assume a coordinate reference system. The SC_CRS class, defined in ISO 19111, is used to define a coordinate reference system. The “Coordinate Reference System” association is used to associate a GM_Object instance with the appropriate SC_CRS instance. Since all geometry classes are descended from GM_Object, any geometry object can have its own unique coordinate reference system.
Figure 6 — GM_Object UML Model
While the ISO Geometry Model is very complex, at its core is the DirectPosition class. This is the fundamental specification of a position within a coordinate reference system. Its purpose is simply to hold the coordinates for a position within the specified coordinate reference system.
Figure 7 — Direct Position UML Model
The DirectPosition class contains two attributes, “dimension” and “coordinate”. The “coordinate” attribute is a sequence of numbers. Each number represents the location of the DirectPosition on a coordinate axis. There are no constraints on the number of numbers in the sequence. Therefore, a DirectPosition can represent an unlimited number of dimensions. The “dimension” attribute specifies the number of axis in the applicable coordinate reference system. This corresponds to the number of values in the “coordinate” sequence.
Like GM_Object, DirectPositions are associated with an SC_CRS through the “coordinateReferenceSystem” association. This association is typically not used since DirectPositions, as data types, will usually be included in larger objects (such as GM_Objects) that have their own references to SC_CRS. When this association is left NULL, the coordinate reference system of the DirectPosition instance will take on the value of the containing object’s SC_CRS.
One limitation of the DirectPosition class is that it does not support complex numbers. However, since DirectPosition does have a “coordinateReferencesystem” association with SC_CRS, it should be possible to model complex numbers in the CRS definition as two orthogonal axis.
126.96.36.199. Features in 3D
Non-point Features which are not bound to a planetary surface have special requirements. These Features are capable of movement in three dimensions. Additionally, these Features have non-trivial three-dimensional shapes which may change over time. Therefore, the movement of the Feature and the shape of the Feature are two separate properties.
A measurement of movement would capture changes in location and orientation. Movement is measured from the perspective of an external observer. Therefore, movement should be specified using a coordinate reference system which is external to the Feature.
The shape of a Feature is independent of its location. A rigid body has the same shape regardless of where it is or who is observing it. The object’s geometry should be self-contained. This requires use of an internal coordinate reference system.
This leads to the following two postulates.
Postulate 1: The Locational Attribute of a 3D Feature is a GM_Point which locates the origin of the local CRS within an external CRS.
Postulate 2: The Spatial Attribute of a 3D Feature is one or more GM_Objects which define the shape of the Feature in the local CRS.
188.8.131.52. 3D Geometries
ISO 19107 makes a distinction between a geometric object and the surface which contains that object. One advantage of this approach is that there can be multiple surfaces associated with one object. For example, an island located in a lake would be represented by an interior surface (the island) of a polygon (the lake) bounded by the exterior surface (the shoreline).
ISO 19107 uses the GM_Object class to define an object and the GM_Boundary class to define a containing surface. Both GM_Object and GM_Boundary are defined as root level geometry classes. The association between GM_Object and GM_Boundary is achieved through the “boundary()” operation on the GM_Object class. This operation is inherited by all subclasses of GM_Object.
In the case of a 3D Feature, GM_Solid is the subclass of GM_Object while GM_SolidBoundary is the subclass of GM_Boundary. GM_Solid describes the volume while GM_SolidBoundary describes the shape.
Figure 8 — 3D Geometry UML Model
GM_Object is subclassed into GM_Primitive and then into GM_Solid. The “volume()” operation on GM_Solid returns the volume (defined in ISO 19103) of space contained within that GM_Solid. Thus, ISO 19107 supports the concept of a 3D volume.
Real 3D objects are often not solid. So the 3D model must also support voids, or even entire 3D Features within their interior. GM_Primitive addresses this need through the “interior to” association. The two roles on this association are the containingPrimitive (the GM_Primitive which contains another GM_Primitive) and the containedPrimitive (the GM_Primitive which is contained). This association has proven its worth in 2D space so there is little doubt that it will be just as effective in 3D.
A 3D volume is delineated by a bounding surface. GM_Boundary is the root class for boundaries. The subclass GM_PrimitiveBoundary provides the boundary for GM_Primitives. The GM_PrimitiveBoundary subclass GM_SolidBoundary is defined as the boundary for a GM_Solid.
Figure 9 — 3D Boundaries UML Model
ISO 19107 goes even farther. A GM_SolidBoundary is composed of both interior and exterior boundaries. These boundaries are defined by the GM_Shell class. Therefore, the following can be observed.
A GM_Shell is a GM_CompositeSurface
A GM_CompositeSurface is composed of GM_OrientablePrimitives
A GM_Surface is a type of GM_OrientablePrimitive
A GM_PolyhedralSurface is a type of GM_Surface
A GM_PolyhedralSurface can be composed of GM_Polygons
A GM_PolyhedralSurface which is composed of GM_Polygons is an example of Boundary Representation (B-Rep) of a surface. This approach is fundamental to rendering 3D computer graphics. (ref Adam Powers 1981)
184.108.40.206.1. Closure Surfaces
Some structures, such as a tunnel or overpass, pose difficulties for this geometry model. The boundary surface can be constructed so that it continues into the interior of the structure. That would make the interior of a tunnel external to the tunnel object. This is not always a desireable result. CityGML 3.0 addresses this issue thought the concept of a “Closure Surface”.
A Closure Surface is a surface which is a logical part of the object but does not correspond to a physical part of the object. For example, the entrance to a tunnel can have a closure surface. This surface allows the tunnel to be treated as a three-dimension solid, even though there is a hole in the bounding surface.