Presentation Index

 
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1

PPT Slide

2

SRM Tutorial

3

Prerequisite

4

PPT Slide

5

PPT Slide

6

Section I

7

In the Beginning ...

8

PPT Slide

9

Simulation Interfaces

10

Other Interoperability Examples

11

SRM Requirements

12

The Meaning Of Accuracy Is Context Dependent

13

Why is Accuracy Needed for Coordinate Transformations?

14

PPT Slide

15

It’s a Loooong Way Up

16

The SRM Encompasses More Than The Earth

17

The Scope Of The SRM

18

The SRM Requires a Shared Solution

19

Structure of the SRM ISO Standard

20

Structure of the SRM ISO Standard

21

Section II

22

So How Will We Get There?

23

Coordinates

24

2-D Rectilinear Coordinate Systems

25

Curvilinear Coordinate Systems(1 of 2)

26

Curvilinear Coordinate Systems (2 of 2)

27

Projection-based Coordinate Systems

28

Spatial Referencing

29

Indirect Embeddings

30

Example: Vancouver_2002

31

Example: Vancouver_2002 Cont’d

32

Example: Vancouver_2002 Cont’d

33

Spatial Reference Frame

34

Reference Datums (1 of 4)

35

Reference Datums (2 of 4)

36

Reference Datums (3 of 4)

37

Reference Datums (4 of 4)

38

Reference Datum Set

39

Orthonormal RDS Class

40

Oblate Spheroid RDS Class

41

Infrastructure Review

42

Section III

43

Development of Surfaces to Generate Maps

44

Projecting from 2D to 1D

45

Distance Distortion Can Be Mitigated, Somewhat

46

Cylindrical Map Projections

47

Planar Map Projections

48

A Stereographic Map Projection

49

Conic Map Projections

50

Mercator Map Projection

51

Oblique Mercator Map Projection*

52

The Grid for Transverse Mercator*

53

Universal Transverse Mercator (60)

54

Lines of Constant Heading*

55

Great Circle Arc between Moscow and Washington D.C.*

56

Augmented Projection-Based SRFs

57

Projection-based “3D” SRFs

58

The Use of Augmented Systems Changes Geometrical Relationships

59

SRF Operation Relationships

60

Geometric Distortions

61

Augmented map projection vertical distortion

62

Flattening the ORM: Distance and Geometry

63

Placing a Solid Cube on an OBS

64

Doing the Math ...

65

Placing a Cube on the Topographic Surface Model

66

Long Linear Structures

67

Vectors in Augmented Projection-based SRFs

68

Vectors in a Curvilinear System

69

Defining a Canonical Local Tangent Plane SRF

70

A LTP Coordinate System Embedded in a Celestiodetic SRF

71

Defining a CLTP Embedded in a Celestiodetic SRF

72

Reference Vectors

73

Reference Vector Transformations

74

Convergence of the Meridian

75

SRF “North” may not be True North

76

Convergence of the Meridian

77

Section IV

78

ORMs vs. Object Models

79

Celestial Object Models

80

Example: Earth

81

Earth Surface Model Terminology

82

Section V

83

Spatial Operations

84

Spatial Operations

85

Coordinate Conversion

86

Coordinate Transformation

87

Spatial Reference Model

88

Quality Assurance for Spatial Operations

89

Conformance Verification for the SEDRIS Implementation

90

Acceptance Testing Methodology

91

SRM Concept Management

92

SRF Relationships

93

Section VI

94

Why is Accuracy Needed for Coordinate Operations?

95

Shooting at a Visible Target in the Real World

96

Simulation of Shooting at a Visible Target

97

Servicing a Non-visible Target in the Real World

98

Error Sources in Coordinate Operations Software

99

Definition of Computational Error

100

Numerical Methods

101

Analytic (closed form) Solutions

102

Taylor/Maclaurin Series Methods

103

Iterative Methods

104

Direct Approximation of a Function or Its Inverse

105

Direct Approximation of a Function or Its Inverse (cont)

106

Error in Power Series Expansions

107

Error Analysis and Resolution of Disagreements

108

Effect of Small Errors

109

Fuzzy Creep/Coordinate Drift

110

Bounds Checking

111

Distortion in Map Projection-based SRFs

112

Treatment of Point Scale

113

Distortion and Computation Error Tradeoff

114

Distortion-Accuracy Tradeoff Experiment for TM

115

Authoritative Sources Sometimes Appear to Disagree

116

Difference between SR-7 & Extended Formulas for Transverse Mercator

117

Transverse Mercator Map Projection Point Scale Equations

118

Linear Distortion Error For TM

119

Conclusions of Experiment

120

What to Do?

121

The Chaining Problem

122

Section VII

123

Modelers Often Prefer Orthonormal Coordinate Systems

124

Euclidean Distance for an Orthonormal System

125

Once the Environment is Included, there are Many Feasible Paths

126

Geometry Distorting 3-D SRFs are often Used – Why ?

127

Section VIII

128

SRFs in the DRM

129

DRM <Location> (Sheet 15)

130

SRFs Supported

131

Section IX

132

PPT Slide

133

ERM Datum Transformations

134

WGS84 Geoidal Separation

135

PPT Slide

136

Types of Operation Errors

137

“Valid” Coordinates

138

Coordinate Validity

139

Implementation Details (1 of 2)

140

Implementation Details (2 of 2)

141

Range Extension (1 of 2)

142

Range Extension (2 of 2)

143

PPT Slide

144

Operation Implementation Status

145

Coordinate Operation Chains

146

Interface Specification(s)

147

Status Codes (1 of 3)

148

Status Codes (2 of 3)

149

Status Codes (3 of 3)

150

Operation Setup

151

Change SRF Operation

152

Multi-change SRF Operation

153

Boundary Checking

154

Operation Teardown

155

Vector Operation

156

Matrix Operation

157

Convergence of the Meridian

158

Further Reading

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