Relationship Between Cartesian and Ellipsoidal Coordinates

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Lecture 5

• Relationship Between Cartesian and Ellipsoidal
  Coordinates

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Geodetic and Cartesian Coords
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Relationship Between Cartesian and Ellipsoidal
Coordinates
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Computation of the X Y Z coordinates of a point
located at a geometric height h above the
reference ellipsoid.
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Geocentric Cartesian Coordinates
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Conversion from Latitude, Longitude, and Height
to ECEF XYZ.
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Example
The geodetic coordinates of an observer on earth
are
Given that a 6378160m and
e2 0.006694541855 Calculate the corresponding
Cartesian coordinates
Page 65 Stolz An Introduction to Geodesy
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Example
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The Inverse Formula
More important given Cartesian coords eg ECEF
WGS84, calculate geodetic coords
1st Approach
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Conversion of Cartesian Coordinates to Geodetic
Coordinates
2nd Approach
iterative solution as h is a function of f and
vice versa
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Converting geodetic (ellipsoidal) coordinates to
Cartesian coordinates and the inverse conversion
Task Given the geodetic latitude longitude and
height above the ellipsoid, calculate the
corresponding Cartesian coordinates for a point
above the ellipsoid. Perform the inverse
conversion using the results of the first section
as input data (i.e. X, Y, and Z Cartesian
coordinates)
Input Data Semi-major axis of the WGS84
ellipsoid (in meters), height above the ellipsoid
(in meters), and the flattening , latitude and
longitude information,
a 6378137
h 313.13
f .003
f 23o 20 10.22
l 245o 10 40.22
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calculate the radius of curvature in the prime
vertical
n 6381489.59834
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Inverse Solution
The longitude requires no iteration since it only
depends on given Cartesian coordinates. But you
need to be careful about the quadrant! How?
Examine the sign of Y and X. In this case, both
X and Y have negative values therefore the angle
is in the third quadrant, therefore,
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calculate approx values for f and h
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calculate values for f and h
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