Presentation Index

Presentation Index

1 SEDRIS Spatial Reference Model	2 SRM Tutorial	3 Outline	4 Section I
5 In the Beginning ...	6 Simulation Interfaces	7 A Spectrum of Constructive, Live and Virtual Capabilities Support Training, Planning & Analysis	8 A Spectrum of Constructive, Live and Virtual Capabilities Support Training, Planning & Analysis
9 The Interface Canyons	10 Real Operational Systems	11 Why is a Spatial Reference Model (SRM) Needed?	12 SRM Requirements
13 Location is Not Enough	14 A Shared Solution is Required!	15 Structure of the SRM ISO Standard	16 Structure of the SRM ISO Standard
17 Section II	18 It’s a Loooong Way Up	19 Here’s an Interesting Perspective	20 Not All Projections are Geodetic!
21 More Familiar?	22 Spatial, the Final Frontier	23 So How Will We Get There?	24 Coordinates
25 Coordinate System Types	26 Depictions of 2D Rectilinear Coordinate Systems	27 Curvilinear Coordinate Systems	28 Time – the fourth dimension
29 Systems of Time	30 Locating a Coordinate System	31 Defining an ORM	32 Defining an ORS
33 Ellipsoid of Revolution	34 Standard Spheres	35 Standard Ellipsoids of Revolution	36 Equipotential Surfaces
37 Gravity Equipotential Reference Surfaces	38 Pressure Equipotential Reference Surfaces	39 Earth Reference Surfaces	40 Standard Horizontal Datums
41 Local Horizontal Datums	42 Relating Multiple Earth-related Surfaces	43 ORM Types (1 of 3)	44 ORM Types (2 of 3)
45 ORM Types (3 of 3)	46 Defining a SRF	47 SRF Example	48 Et Voilá: A Celestiocentric SRF
49 SRFs by Category	50 Many SRF Realizations	51 Spatial Operations	52 Operations on Coordinates
53 Types of Operation Errors	54 Spatial Reference Model	55 Section IIB	56 Ellipsoid of Revolution Geometry & Notation
57 Latitude, Longitude and Height	58 Earth Surface Relationships	59 Earth’s Gravitational Field	60 SRM Refresher
61 Section III	62 Development of Surfaces to Generate Maps	63 Map Projections	64 Projecting from 2D to 1D
65 Cylindrical Projections	66 Planar Projections	67 A Stereographic Projection	68 Conic Projections
69 Mercator Projection	70 Oblique Mercator Projection*	71 The Grid For Transverse Mercator*	72 Universal Transverse Mercator (60)
73 Lines of Constant Heading*	74 Great Circle Arc between Moscow and Washington D.C.*	75 Many Map Projections are Conformal	76 Section IV
77 Augmented Projection-Based SRFs	78 “3D” Projection-based SRFs	79 Coordinate Operations affect Geometrical Relationships	80 SRF Operation Relationships
81 Geometric Distortions	82 Distance and Elevation Angle	83 Distance Distortion Can Be Mitigated, Somewhat	84 Azimuth
85 How Much Azimuth Distortion?	86 Augmented UTM (AUTM) example:	87 Section V	88 Modelers Often Prefer Orthonormal Coordinate Systems
89 Geometry Distorting 3-D SRFs are often Used – Why ?	90 Relationships Between SRFs and Simulations	91 MCG&I and Dynamics Modeling	92 MCG&I
93 Dynamics Modeling	94 Section VI	95 Euclidean Distance for an Orthonormal System	96 Defining Geometrical Concepts
97 The Traditional Surveying Process	98 Surveying is a Complex Process	99 Traditional Distance Determination in Surveys	100 Surveying on a Plane ERS
101 Surveying on a Plane ERS with a Topographic Surface Added	102 Surveying on a Spherical ERS	103 Chaining on a Spherical ERS with a Topographic Surface Added	104 Surveying on an Ellipsoid of Revolution ERS
105 Normal Section of an Ellipsoid of Revolution ORS	106 Distance on an Ellipsoid of Revolution ORS	107 Bearing Angles (Ellipsoid of Revolution ORS)	108 Bearing when a Point P is above the Ellipsoid of Revolution ORS
109 Once the Environment is Included, There are Many Feasible Paths	110 Placing a Solid Cube on an ORS	111 Doing the Math ...	112 Placing a Cube on a Topographic Surface
113 Long Linear Structures	114 Vectors in Augmented Projection-based SRFs	115 Vectors in a Curvilinear System	116 Defining a Canonical Local Tangent Plane SRF
117 A LTP Coordinate System Embedded in a Celestiodetic SRF	118 Defining a CLTP Embedded in a Celestiodetic SRF	119 Reference Vectors	120 Reference Vector Transformations
121 SRF “North” may not be True North	122 Convergence of the Meridian	123 Representing a Projection-based SRF Vector in Terms of a CLTP	124 Computing COM For TM
125 Computing the Sine and Cosine of the COM for the Rotation Matrix	126 Observations	127 Section VII	128 Why is Accuracy Needed for Coordinate Operations?
129 Shooting at a Target in the Real World	130 Simulation of Shooting at a Target	131 Error Sources in Coordinate Operations Software	132 Definition of Error
133 Numerical methods	134 Analytic (closed form) Solutions	135 Taylor/Maclaurin Series Methods	136 Iterative Methods
137 Error in Power Series Expansions	138 Authoritative Sources Sometimes Appear to Disagree	139 Direct Approximation of a Function or Its Inverse	140 Direct Approximation of a Function or Its Inverse (cont)
141 Error Analysis and Resolution of Disagreements	142 Effect of Small Errors	143 Fuzzy Creep/Coordinate Drift	144 Bounds Checking
145 What to Do?	146 Distortion and Computation Error Tradeoff	147 Distortion in Projection-based SRFs	148 Distortion-Accuracy Trades for UTM
149 Point Scale Equations	150 UTM Point Scale Equations	151 Linear Distortion Error For UTM	152 Difference between SR-7 & Extended Formulas for Transverse Mercator
153 Conclusions of Experiment	154 The Chaining Problem	155 Section VIII	156 SRFs
157 DRM <Location> (Page 15)	158 SRFs Supported	159 SRFs with CS Origin Offsets*	160 Local Space Rectangular
161 Local Space Rectangular (2D)	162 Geocentric	163 Geodetic	164 Geodetic (2D)
165 Local Tangent Plane	166 Local Tangent Plane (2D)	167 GCS	168 Mercator
169 Augmented Mercator	170 Oblique Mercator	171 Augm. Oblique Mercator	172 Transverse Mercator
173 Augm. Transverse Mercator	174 Universal Transverse Mercator	175 Augm. Univ. Transverse Mercator	176 Lambert Conformal Conic
177 Augm. Lambert Conformal Conic	178 Polar Stereographic	179 Augm. Polar Stereographic	180 Universal Polar Stereographic
181 Augm. Univ. Polar Stereographic	182 Equidistant Cylindrical	183 Augm. Equidistant Cylindrical	184 Geocentric Equatorial Inertial
185 Geomagnetic	186 Geocentric Solar Ecliptic	187 Geocentric Solar Magnetic	188 Solar Magnetic
189 Section IX	190 PPT Slide	191 ERS “Datum” Transformations	192 Init WGS84 Geoidal Separation
193 Get WGS84 Geoidal Separation	194 PPT Slide	195 Types of Operation Errors	196 “Valid” Coordinates
197 Coordinate Validity	198 Implementation Details (1 of 2)	199 Implementation Details (2 of 2)	200 Range Extension (1 of 2)
201 Range Extension (2 of 2)	202 PPT Slide	203 Op Support	204 Coordinate Operation Chains
205 Status Codes (1 of 3)	206 Status Codes (2 of 3)	207 Interface Specification(s)	208 Status Codes (3 of 3)
209 Operation Setup	210 Conversion Operation	211 Multi-conversion Operation	212 Boundary Checking
213 Operation Teardown	214 Vector Operation	215 Matrix Operation*	216 Transformation Operation
217 Convergence of Meridian Operation	218 "SRM Check Utility"*	219 Further Reading	.