Introduction

Spatial information processing requires a robust capability to describe geometric properties such as position, direction and distance. Information may be spatially referenced to local structures and regions, to the Earth as a whole, to other celestial bodies, or to objects defined within contexts such as virtual realities. In each of these cases, a spatial reference frame is defined, with respect to which the values of geometric properties may be determined.

It is often necessary to represent position and orientation in several different spatial reference frames, simultaneously, according to the context in which the data is to be used. Each spatial reference frame corresponds to a particular way of expressing position. Spatial reference frames may be relative to moving objects (e.g. planets and spacecraft), and therefore have values that are a function of time. It is necessary to specify the time to which the spatial position refers, and the time for which the spatial reference frame is defined.

Interoperability of spatial data is facilitated through the adoption of a common and widely-known Spatial Reference Model (SRM) that allows the context in which coordinates, directions, and distances are defined to be known succinctly, and converted accurately into multiple definitions and representations of geo- and non-georeferenced space.  Georeferenced data constitute a major aspect of environmental data, although data referenced to other planetary (and solar) bodies, as well as fictitious environments, are commonly used and equally important.  These data include astronomical, orbital, geomagnetic, and local observations whose reference frame may be fixed with respect to observer, solar, celestial, or other positional standards rather than, for example, the equator plus a prime meridian on an Earth Reference Model (ERM) surface.  Other Object Reference Models (ORM; e.g., the moon or the NASA Space Shuttle) may also be employed.

Interoperability of spatial information requires that:

• spatial reference frames and ORM/ERMs be defined such that coordinates and angular measures describe position and orientation data uniquely, and
• mechanisms exist for such data to be converted/transformed between alternative spatial reference frames, should this be required.

In order to support the unambiguous description of environmental data, SEDRIS specifies both a Data Representation Model (DRM) and an Environmental Data Coding Specification (EDCS).  These address how to describe "environmental things", but explicitly avoid defining how "environmental things" are located with respect to one another and with respect to non-environmental "things".  The SEDRIS SRM addresses this need and provides an integrated framework and precise terminology for describing spatial concepts and operations on spatial information.

The SEDRIS SRM is comprised of a set of Spatial Reference Frames (SRF), their inter-relationships, and unambiguous definitions of methods for specifying and inter-converting location (including directional and orientation) information among SRFs.  Additionally, those methods are documented in terms of detailed algorithms and subsequently reduced to efficient, accurate, and portable implementations.

Achieving full interoperability of spatial data is both complex and fraught with pitfalls.  Users of environmental data may not want to become experts in geodesy, geometric transforms, or dynamics modeling.  However, we strongly believe that an adequate education is a necessary prerequisite to success in that endeavor, given that our experience has been that there is a fair amount of misunderstanding when practitioners from different disciplines talk to each other about location information.  It is believed that users of the SRM need to develop a basic familiarity with the language of geodesy and sufficient fundamental expertise to determine:

• what approximations or restrictions have been designed into a SRF,
• how different SRFs relate to each other, and
• how to choose an SRF appropriate to the application.

There are also unspoken, and all but forgotten, assumptions made within specific disciplines that are opaque to non-specialists, and either result in miscommunication or are simply no longer appropriate assumptions to make.  These problems are not unique to specialists -- they are rife within the general M&S community as well.  For example, our "common sense" notions about the apparently flat Earth we experience every day and represent on flat paper maps, are increasingly at odds with our ability to collect, process, and act on global location data and our need to correctly represent it for a variety of purposes.

Given these considerations, the treatment of these concepts necessarily includes significant didactic material, and generally covers four major areas, as follows.

• Concept Development: This includes the education prerequisites for the SRM, the scope of the SRM, as well as the design criteria.  It also includes the development of the concept of  "pure" coordinate systems and their associated transformations from basic concepts in solid and analytic geometry. Subsequently, isometric ("real world") geometry and coordinate systems are developed and extended to define the basic isometric spatial reference frames.  After exploring the role of forces and motion, the non-isometric (projected) coordinate systems are introduced.  Both non-ellipsoidal and augmented projections are subsequently developed, ending with the definition of the basic non-isometric spatial reference frames.  Concepts associated with directions (vectors), and the corresponding orientation representations, are defined. The complexities of real-world terrain surfaces (as opposed to mathematical "smooth" approximations) are addressed.
  

• Spatial Reference Frame Specifications and Formulations: This covers the complete specification of the SRM and each of the included SRFs.
  
  
• Error Specification and Algorithmic Development: This addresses how to define error specifications in 2D and 3D, and the development of efficient and accurate coordinate operations algorithms among the SRFs included in the SRM.  Also included is a discussion of transitivity and chaining when converting between SRFs, which may use a sequence of operation steps rather than a single optimized direct conversion.
  
  
• Implementation, Testing and Application: This involves the reduction of the developed algorithms to efficient, accurate, portable implementations that maintain the stated operation accuracies and performance.  The methods used to test and verify the implementations are developed, and the results of extensive testing, are presented and reviewed.  The software interface specification is defined, and guidelines for its use are documented.
  

The detailed information covering the various topic areas of the SRM are captured, at appropriate levels of detail, in a number of documents, or sections of documents, which include the ISO/IEC 18026:2006 (the SRM standard), the SRM concept documents and user guides, overview papers, technical tutorials, and software development guides. Several of these documents are further referenced in the subsequent sections.

Standards

The ISO/IEC 18026:2006 (SRM) International Standard may be viewed on-line or downloaded for local use.

In particular, the Concepts clause of the SRM standard provides a rich overview of the key issues that the standard addresses.

Implementations and User Guides

NOTE:  The implementation of the Orientation capabilities is not contained               in the 4.1.x SDKs currently offered for download from the website,               but is available in Release 4.3 and later of the SRM SDK.                 SRM SDKs with a version number greater than 4.1.3 contain more               advanced orientation capabilities and interface changes that are not               compatible with SEDRIS SDK 4.1.x releases, but they can be used               apart from the main SEDRIS SDK baseline. The new SRM SDK 4.4               capabilities will be incorporated into the main SEDRIS SDK baseline               in a future release.

Transformations

The ISO/IEC 18026:2006 (SRM) International Standard may be viewed on-line or downloaded for local use.

In particular, the Concepts clause of the SRM standard provides a rich overview of the key issues that the standard addresses.

Accuracy and Timing Test Results

A series of tests have been conducted on the implementations of the ISO/IEC 18026:2006 - Spatial Reference Model (SRM) to measure both the accuracy of the implementation and the speed of execution. These tests apply to the latest SRM SDK releases, which include SRM SDK 4.1.3 (part of the latest release of SEDRIS SDK 4.1.3) and the advanced SRM SDKs (version 4.3 and 4.4) that contain the Orientation capabilities.

This first phase of testing concentrated on a subset of the SRM capabilities. The timing tests were conducted in response to specific customer requests and focused on the most widely used coordinate conversion operations, specifically conversions between 3D geodetic, geocentric, and augmented UTM spatial reference frames. The accuracy tests were conducted using a new and independently developed comprehensive test data package, which covers a relatively large subset of the SRM capabilities. Both tests were conducted on the C++ implementation of the SRM (tests of the C and Java implementations will be posted here, when conducted and completed). The tests have also been independently conducted and verfied.

The accuracy tests for the coordinate conversion and transformation operations were conducted using a comprehensive test vector data set that was independently developed and verified by Craig Rollins of the US National Geospatial-Intelligence Agency (NGA). The reference accuracy test data set can be obtained directly from NGA, as it is a universal test data package that may be used to test any coordinate transformation or conversion library.

The test results, test harness software, along with the corresponding procedure and input configuration files, for both the timing and the accuracy assessments, can be downloaded from the following links. The accuracy and timing results documents contain not only the results of the respective tests, but also an overview of the tests, as well as the procedures for conducting the tests.

Papers

Tutorials

Tutorials on the SRM, presented at SEDRIS Technology Conference (STC) 2004, are also available for download or can be viewed on-line.