by Dr. Paul A. Birkel, MITRE Corporation & Dr. Ralph Toms, SRI International

1. SEDRIS Spatial Reference Model (SRM) It’s not just coordinate systems any more! Presented at the SEDRIS Technology Conference September 28-30, 1999 Arlington, VA by Dr. Paul A. Birkel, MITRE Corporation & Dr. Ralph Toms, SRI International

2. Tutorial Organization I. Simulation Interoperability from a Physical Environment Interface Perspective II. Introduction to the SEDRIS Spatial Reference Model (SRM) III. Earth Reference Models (ERMs) and Coordinate Frameworks IV. Map Projections V. Augmented Map Projections VI. Selection of a Coordinate Framework for Models and Simulations VII. ERM Geometry VIII. Computational Considerations IX. Interface Specification

3. Section I Simulation Interoperability from a Physical Environment Interface Perspective

4. The traditional hierarchy of models does not work very well. Complex, labor intensive interface processing is required. Although there are software based linkages for connecting dissimilar models this does not guarantee that it is meaningful to do so. A major problem is the lack of commonality of interfaces due to the use of different earth reference models and coordinate systems. This leads to inconsistent positions and environmental representations. The lack of commonality is intensified by traditional aggregation policies. It is much easier, but certainly not pro forma, to interface between entity level simulation classes. The interface between aggregated constructive simulations and entity level simulations has been referred to as the “Grand Canyon”.* The Interfaces Between Each Class of Simulations Makes Interoperability Difficult *Blumenthal, Bridging the Grand Canyon, 1997

5. Lots of detail does not necessarily imply accuracy, fidelity or functional completeness. A Spectrum of Constructive, Live and Virtual Capabilities Support Training, Planning & Analysis Aggregated Constructive Entity Level Tactical Simulators Ranges and Live Exercises War Constructive • Closed for Analysis • Interactive for Training • Units normally are Bns or higher • Environmental effects aggregated • Usually deterministic not stochastic • Attrition often based on Lanchester differential equations • Entity states not maintained Large • Closed for analysis • Interactive for training & planning • Player inputs tactics or uses SAF • Generally “stochastic” • More detailed environment • Acquisition is modeled • 2-D Graphics with 3-D Disp. • Virtual, always interactive • Principally for training • 3-D graphics with 2-D display • Acquisition by humans • Principally for distributed play • OPFOR is primarily constructive • Protocol stds. enforced • Real Platforms • Emulated wpns. delivery • Simulated BDA • Acquisition by HITL in real environment • Training and procurement support • Simulations used for fire control solutions, sensor pointing, guidance and control S c o p e Low Low High Level of Detail

6. JCM CASTFOREM ELAN CMTC/ JRTC Lots of detail does not necessarily imply accuracy, fidelity or functional completeness. A Spectrum of Constructive, Live and Virtual Capabilities Support Training, Planning & Analysis Aggregated Closed & Interactive Constructive Entity Level War Constructive Simulators Live Exercises and Ranges CEM,THUNDER, RSAS, METRIC ENWGS, JTLS TACWAR, ITEM Seminar War Games JTF/Theater Corps/ CVBG/ARV CBS TACSIM S c o p e NTC VIC EAGLE Div JTCTS SPECTRUM (MOOTW) Bde/ CVW JTS JCATS BBS MTWAS EADSIM Janus Operational Planners Bn/Wng MODSAF/ CCTT SAF Co/Sqdn DFIRST CCTT SIMNET Embedded Fire Control, Guidance, etc. Plt SOFNET Sqd Low High Engineering Simulations Level of Detail R. Toms 2/18/97

7. The Interface Canyons • This is a notional view of the scope of the problem. Aggregated Constructive Entity Level Constructive War Ranges & Live Exercises Simulators Low Level of Detail High A consistent SRM is critical to addressing the interface problem.

8. Section II Introduction to the SEDRIS Spatial Reference Model (SRM)

9. Defining and using a consistent spatial reference framework is critical for M&S interoperability Military models (men, material, …) Environmental data, models, phenomena Systems Systems, where? Systems, and what else? The void ... The SNE starts with locating your forces; sometimes that’s about all you could afford in legacy simulations. The SNE continues with defining the context within which forces engage; and that context can advantage, or disadvantage, forces ... The Synthetic Natural Environment(SNE) begins with a location ...

10. Traditionally the M&S community has not been consistent in the treatment of models of the earth and related coordinate systems. Consistency is required for joint distributed simulation in order to: achieve a reasonably level playing field, to support meaningful VV&A. A number of different earth reference models (ERMs) are currently employed and this affects: representation of the environment in simulations & authoritative data bases. dynamics formulations, both kinematics and kinetics (movement). acquisition modeling and processing (inter-visibility). Approximations in coordinate transformation algorithms made to reduce processing time may introduce additional inconsistencies. An SRM is needed to promote lossless and accurate transformations. A nomenclature inconsistency evolves when there is no SRM For example, how do these variables relate? Altitude, elevation, height, geodetic height, ellipsoidal height, orthometric height, height above sea level, height above mean sea level, terrain height, pressure altitude, temperature altitude, nap of the earth, ... Why is a Spatial Reference Model(SRM) Needed?

11. SRM Requirements • Completeness • Must include coordinate frameworks in common usage. • Must tie those systems together into a common framework. • Must educate the system developer. • E.g., What’s a horizontal datum? A vertical datum? • Accuracy • Generally higher than required for C4ISR systems. • Typically better than 1 cm. up past geosynchronous orbit. • Performance • Never fast enough! • Many environmental data sets dominated by location data • Therefore efficient interconversion key to meeting 72 hour “ready-to-run” mandate. • Federate costs for distributed simulation using heterogeneous coordinate systems can be substantial (e.g., 20% or more).

12. Suggested References 1. “Handbook for Transformation of Datums, Projections, Grids and Common Coordinate Systems”, U.S. Army Corps of Engineers, Topographic Engineering Center, TEC-SR-7, 1998. 2. “Department of Defense World Geodetic System 1984”, National Imagery and Mapping Agency, Third Edition, TR8350.2, 1997. 3. “Geodesy for the Layman”, National Imagery and Mapping Agency, on-line at http://164.214.59/geospatial/products/GandG/geolay/toc.htm. 4. Richard H. Rapp, “Geometric Geodesy Part I & II”, The Ohio State University, Dept. of Geodetic Science & Surveying, 1993. 5. John P. Snyder, “Map Projections -- A Working Manual”, U.S. Geological Survey Professional Paper 1395, 1987. 6. Paul D. Thomas, “Conformal Projections in Geodesy and Cartography”, U.S. Department of Commerce, Coast and Geodetic Survey, Special Publication 251.

13. Section III Earth Reference Models (ERMs)and Coordinate Frameworks

14. Earth Reference Models (ERMs) • Earth’s shape • Sphere: Used by meteorology community (see JMCDM). • Ellipsoid: 21 (as per NIMA TR 8350.2). • Mathematical approximations are not the earth. • ERMs do not include the natural environment (smooth surfaces). • Horizontal Datum • 200+ (as per NIMA TR 8350.2) • Common interoperability problem in C4ISR community • Vertical Datum • Many ... • Earth Reference Model (i.e., sphere/ellipsoid) • WGS-84 Geoid • MSL (local) • Others (e.g., NAVD-88, EGM-96) • Interoperability problem in littoral regions.

15. SEDRIS Reference Ellipsoids

16. SEDRIS Reference Spheres Reference Sphere Radius (meters) Code Name NOG NOGAPS 6371000.00 COA COAMPS 6371229.00 MMR MMR (AFWA) 6370000.00 ACM ACMES 6371221.30 MFE 6366707.02 MultiGen Flat Earth MOD_T Tropical 6378390.00 MOD_M Midlatitude 6371230.00 MOD_S Subartic 6356910.00

17. Horizontal Datums

18. A coordinate framework is a combination of an ERM and a coordinate system. Not much hope in getting everyone to use one coordinate framework. Some coordinate systems, combinations of systems and ERMs are natural to a specific application. Trend is towards standard ERMs, but not there yet. Some hope of reducing the number of coordinate systems required to a manageable set. Standardizing Coordinate Frameworks

19. SRM Reference Frames L o c a l S p a c e R e c t a n g u l a r C o o r d i n a t e S y s t e m A r b i t r a r y L S R G e o d e t i c C o o r d i n a t e S y s t e m E a r t h - S u r f a c e , G l o b a l G D C G e o c e n t r i c C o o r d i n a t e S y s t e m E a r t h - C e n t e r e d , E a r t h - F i x e d G C C M e r c a t o r Projected Coordinate System (PCS) M O b l i q u e M e r c a t o r P C S O M Polar Stereographic PCS P S Universal Polar Stereographic PCS UPS E a r t h - S u r f a c e , P r o j e c t e d L a m b e r t C o n f o r m a l C o n i c P C S L C C EC Equidistant Cylindrical PCS T r a n s v e r s e M e r c a t o r P C S T M U n i v e r s a l T r a n s v e r s e M e r c a t o r P C S U T M E a r t h - S u r f a c e , L o c a l G l o b a l C o o r d i n a t e S y s t e m G C S (Topocentric) L o c a l T a n g e n t P l a n e C o o r d i n a t e S y s t e m L T P G e o m a g n e t i c C o o r d i n a t e S y s t e m G M G E I E a r t h - C e n t e r e d , R o t a t i n g a t e S y s t e m G e o c e n t r i c E q u a t o r i a l I n e r t i a l C o o r d i n ) (I n e r t i a l & Q u a s i -I n e r t i a l G e o c e n t r i c S o l a r E c l i p t i c C o o r d i n a t e S y s t e m G S E G e o c e n t r i c S o l a r M a g n e t o s p h e r i c C o o r d i n a t e S y s t e m G S M S o l a r M a g n e t i c C o o r d i n a t e S y s t e m S M

20. Ellipsoidal Earth Reference Model (ERM)Geometry & Notation P(X, Y, Z) or P(Ø, , h) • Z • P(W,Z) Z h Pe Ze Pe ø Y  ø W We Where W2 = X2 + Y2 X Generic ERM & notation Meridian plane geometry • Ellipsoids are standard in current geodesy practice. • For SNE data modeling, spheres are often used to simplify dynamics equations. • Geocentric coordinates (GCC) are defined by the point P(X, Y, Z). • Geodetic coordinates (GDC) are defined by the point P(Ø, , h).

21. P(X, Y, Z) or P( , , h) For spheres Longitude is the same as for the ellipsoidal case, is the geocentric latitude & hos is height above the sphere. The line through P is perpendicular to the sphere. In mapping, charting and geodesy spherical ERMs are almost never used. Latitude, Longitude and Heightfor Ellipsoids & Spheres P(X, Y, Z) or P(Ø, , h) • • Z Z h hos Pe Pe ø Y Y   X X For ellipsoids Latitude, longitude and geodetic height are defined as per this diagram. The line through P is perpendicular to the ellipsoid. Longitude  is generally referenced to the Prime Meridian.

22. North/South Cross Section of theGeoid, Ellipsoid and the Earth’s Surface Earth's Physical Surface H Geoid h Geoid Ellipsoid Geoid Separation: + N Ellipsoid The geoid is a gravity equipotential surface selected to match mean sea level as well as possible. Geoid Separation: - N • h is the geodetic height • H is the orthometric height • N is the separation of the geoid For more on this see NIMA’s “Geodesy for the Layman” at http://164.214.2.59/geospatial/products/GandG/geolay/toc.htm

23. Gravitational Field and theGeoid, Ellipsoid and the Earth’s Surface Gravity vector depends on: latitude, longitude, and H (or h) Gravity potential results in a gravity field Earth's Physical Surface P • H Geoid h Geoid Geoid Separation: + N Ellipsoid • h is the geodetic height • H is the orthometric height • N is the separation of the geoid Geoid Separation: - N

24. Section IV Map Projections Map projections were invented to support paper map development ---- a long time ago.

25. Development of Surfaces to Generate Maps Developable Surfaces A cone or cylinder can be cut and laid out flat. Non-developable Surfaces The surface of an ellipsoid cannot be cut so it will lie flat without tearing or stretching.

26. Map Projections associate points on the surface of an ERM with points on an X-Y plane • A map projection is a mathematical transformation from a three dimensional ellipsoidal or spherical ERM surface onto a two dimensional plane. Y X • Since spheres and ellipsoids are not developable, distortions must occur. • Note that the transformation is from three to two dimensions and there is no vertical axis in the plane.

27. N Note that the red points do not map! s s s A Simple Projection Projection from the point N of all points on the circleonto a line. • Note the stretching of the length of the arc s after the projection. • The concept of a projection can be extended to projecting the points • on the surface of an ERM onto a plane.

28. Cylindrical Projections

29. Planar Projections

30. Stereographic Projection

31. Conic Projections

32. Simple Conic Projection* A simple conic map of the northern hemisphere. A simple conic projection. * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

33. Cylindrical Projection* * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

34. Mercator Projection A Mercator projection is a cylindrical projection.

35. Oblique Mercator Projection* A Transverse Mercator (TM) Projection is defined when the cylinder is parallel to the equator. * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

36. Transverse Mercator Map of the Western Hemisphere* • In geodetic coordinates the origin is at (0, -π/2, 0) • The longitude of the origin is shown as 90º W. * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

37. Y X Transverse Mercator Map - the Meridians are curved and the Spacing between them is stretched* • In geodetic coordinates the origin is at (0, -π/2, 0) • The longitude of the origin is shown as 90º W. * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

38. Universal Transverse Mercator • Widely used for paper maps by the U. S. Army. • Defined on six degree wide regions with 60 origins on the equator. • A grid numbering scheme is used to define the Military Grid Reference System.

39. Lines of Constant Heading on a Mercator Map* • This line is called a rhumb line or loxodrome. • Mercator projection is used for maritime navigation. * Adapted from: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

40. Rhumb Line or Loxodrome on a Globe* * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

41. Great Circle Arc between Moscow and Washington D.C.* This is a Mercator map. This is an oblique Mercator map for a sphere with the central meridian on the great circle arc between cities. * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.

42. Many Map Projections Are Conformal • • Conformal means that the mathematical transformation preserves angles. • • What does this mean? • • The curves between A & B and B & C are on the surface of an ERM. • • The projected curves (not necessarily the same shape) are on the plane. • • For a conformal transformation the angles ABC and abc are the same. A Y B a C b c X

43. The taxonomy for classifying mathematical transformations is complex and there are a lot of types: isometric, linear, bi-linear, conformal, orthogonal, affine, isomorphic, ... For SEDRIS, two classifications are sufficient for transformations associated with earth referenced coordinate frameworks. Geometry Invariant (GI): that class of transformations between coordinate reference frames that do not distort geometrical relationships. Non-Geometry Invariant (NGI): that class of transformations between coordinate reference frames that distort some geometrical relationships. Transformations may or may notchange Geometrical Relationships

44. SRM Coordinate System Relationships for an Ellipsoidal ERM Map projections (2D) Transformations between map projections and these areNGI. Transformations among earth referenced 3D systems are GI. Universal Transverse Mercator Global Coordinate System Transverse Mercator Local Tangent Plane Mercator Geodetic Coordinate System Oblique Mercator Geocentric Lambert Conformal Conic Geomagnetic Geocentric Equatorial Inertial Geocentric Solar Ecliptic Geocentric Solar Magnetospheric Solar Magnetic Polar Stereographic Universal Polar Stereographic

45. Section V Augmented Map Projections These are used, used and used but, they are distorted, distorted and distorted.

46. Augmented Map Projections • Models & simulations usually require three dimensions. • Some frameworks are three dimensional by definition. • Map projections are commonly augmented with a vertical axis to create a three dimensional system. • Various vertical measures are used, such as mean sea level height, orthometric height, geodetic height, pressure altitude and others. • This practice adds additional geometric distortions.

47. Projection from 2-D to 1-D and then Augmentation with a Vertical Axis causes distortions N Note that the red points do not map s s s s Distance is distorted by the projection Z X An augmented projection produces another 2D system. Note that there are now two distortions with respect to the original rectangular system. This process can be extended to the 3D case but even if the projection is conformal, elevation anglesare not preserved.

48. Distance Distortioncan be mitigated, somewhat N Note that the red points do not map s s s s O Scale here = 1 Scale here < 1 On the green line the average distortion is reduced

49. Augmented UTM (AUTM) was often used in legacy ground combat simulations because, under simplifying assumptions, unit dynamics equations take on a simple form that minimizes processing time. For AUTM several distortions are introduced, especially at the higher latitudes. The results of such distortions may not be so apparent when all simulations involved use UTM. However, in a federation involving real world coordinate systems the distortions may become evident. Use of AUTM increases visibility, causes the battle to prosecute too fast, leads to an uneven playing field and is not recommended for use in joint simulations. Augmented UTMeffectively “flattens the ERM” plane of the projection 90o East • • • • UTM plane inset to reduce average distortion (scale factor .9996 at the central meridian) Central meridian

50. Y X Transverse Mercator Map - Revisited* • In geodetic coordinates the origin is at (0, -π/2, 0) • The longitude of the origin is shown as 90º W. * From: N. Bowditch, American Practical Navigator, U.S. Navy Hydrographic Office, 1966 Ed.