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雷达坐标与GPS和其他坐标系的转换公式

雷达坐标

GPS

笛卡尔坐标系

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雷达坐标与GPS和其他坐标系的转换公式。 1. Preface 2 2. Calculation of Geodetic Coordinates from Radar Spherical Coordinates 3 2.1. What do we know! 3 2.2. Calculation of Geocentric Coordinates 5 2.3. Transformations of Geocentric to Geodetic Coordinates 5 2.4. A new radar position 6 3. Calculation of Geodetic Coordinates from Stereographic Coordinates 8 3.1. The MADAP track server 8 3.2. From Stereographic Coordinates to Geodetic Coordinates, method 1 9 3.2.1. From system Stereographic Coordinates to system Cartesian Coordinates 9 3.2.2. System Cartesian Coordinates to Geocentric Coordinates 10 3.2.3. A new origin 10 3.3. From Stereographic Coordinates to Geodetic Coordinates, method 2 11 3.3.1. Stereographic Coordinates to coordinates on a conformal sphere 11 3.3.2. Coordinates on a conformal sphere to Geodetic Coordinates 12 3.4. From Stereographic Coordinates to Geodetic Coordinates, method 3 12 3.4.1. Stereographic Coordinates to Geodetic Coordinates 12 3.4.2. Geodetic Coordinates to Stereographic Coordinates 13 3.5. The three methods 14

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NATO UNCLASSIFIED

NATO UNCLASSIFIED 1

Transformations to

Geodetic Coordinates

alt

lat

long

lat

rotation

about z

Investigation on the differences between various methods to convert

geodetic coordinates into Cartesian coordinates and Stereographic

coordinates and vice versa.

J.M.Spitter, NC3A, The Hague, 19 April 1999 – 11 June 1999

NATO UNCLASSIFIED

NATO UNCLASSIFIED 2

Contents

1. Preface 2

2. Calculation of Geodetic Coordinates from Radar Spherical Coordinates 3

2.1. What do we know! 3

2.2. Calculation of Geocentric Coordinates 5

2.3. Transformations of Geocentric to Geodetic Coordinates 5

2.4. A new radar position 6

3. Calculation of Geodetic Coordinates from Stereographic Coordinates 8

3.1. The MADAP track server 8

3.2. From Stereographic Coordinates to Geodetic Coordinates, method 1 9

3.2.1. From system Stereographic Coordinates to system Cartesian

Coordinates 9

3.2.2. System Cartesian Coordinates to Geocentric Coordinates 10

3.2.3. A new origin 10

3.3. From Stereographic Coordinates to Geodetic Coordinates, method 2 11

3.3.1. Stereographic Coordinates to coordinates on a conformal sphere 11

3.3.2. Coordinates on a conformal sphere to Geodetic Coordinates 12

3.4. From Stereographic Coordinates to Geodetic Coordinates, method 3 12

3.4.1. Stereographic Coordinates to Geodetic Coordinates 12

3.4.2. Geodetic Coordinates to Stereographic Coordinates 13

3.5. The three methods 14

Symbols 17

Appendix A 19

Appendix B 27

Appendix C 35

Appendix D 41

Appendix E 46

Appendix F 52

Appendix G 58

References 64

NATO UNCLASSIFIED

NATO UNCLASSIFIED 3

1. Preface

For my traineeship I wrote this article about Coordinate transformations. First I describe a

method for calculating Geodetic Coordinates of a target given the Geodetic Coordinates

of the radar and the radar Spherical Coordinates. You can also find a way to calculate the

radar Spherical Coordinates after you changes the radar position.

In the next chapter there are three methods for calculating the Geodetic Coordinates of a

target knowing its Stereographic Coordinates. In the first and the last method you can

change the origin and calculated the Stereographic Coordinates with respect to the new

origin. In the last paragraph I compare the three methods.

NATO UNCLASSIFIED

NATO UNCLASSIFIED 4

2. Calculation of Geodetic Coordinates from Radar

Spherical Coordinates

In the following paragraphs you will find a way to calculate the Geodetic Coordinates of

a target knowing the Geodetic Coordinates of the radar and the Radar Spherical

Coordinates of the target. In App. A you will find a C++ source code for this method.

2.1. What do we know!

The Earth Ellipsoid is defined according to WGS-84 (WGS = World Geodetic System)

by the following values:

w Main or equatorial semi-axis in [m]: a = 6378137.0

w Secondary or polar semi-axis in [m]: b = 6356752.3142

w Flattening: f = (a-b)/a

w First eccentricity squared: e

= f(a+b)/a

w First eccentricity: e = sqrt(e

)

The WGS-84 ellipsoid [1] is generated when an ellipse is rotated about its minor axis.

The minor axis passes through the north and the true south poles, as shown in Fig 1. Most

charts and navigation tools are expressed in the (lat, long, alt) geodetic coordinates,

where lat denotes latitude, long denotes longitude, and alt denotes altitude. Latitude is the

angle between the ellipsoidal normal N and the equatorial plane. Note that the extension

of the normal toward the interior of the WGS-84 ellipsoid will not intersect the center of

the earth. Longitude is the angle in the equatorial plane between the prime meridian and

the projection of the point of interest onto the equatorial plane. Altitude is the distance

along the ellipsoidal normal, away from the interior of the ellipsoid, between the surface

of the ellipsoid and the point of interest. The earth surface does not always coincides with

the WGS-84 ellipsoid.

alt

lat

long

lat

rotation

about z

Figure 1 Geodetic coordinate system

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