relationship between vectors in geocentric, local and project frames of reference

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Lecture 7

• relationship between vectors in geocentric, local
  and project frames of reference

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2 problems

• transform between local and project frames of
  reference

• transform between geocentric and local frames of
  reference

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h
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Coordinate Systems

• local Coordinates
• z axis vertical throughout
• right handed system
• bearings relative to y axis
• ignores shape of earth
• x,y,z

• The geodetic latitude of a point is the angle
  from the equatorial plane to the vertical
  direction of a line normal to the reference
  ellipsoid.
• The geodetic longitude of a point is the angle
  between a reference plane and a plane passing
  through the point, both planes being
  perpendicular to the equatorial plane.

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Transform between local and project frames of
reference
Y
y
P
x
p Rq R-1p R-1Rq R-1p q q R-1p
X
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Orthogonal Matrices

• the vectors have to be unit vectors
• axes must be orthogonal

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Transform between local and project frames of
reference
N
l Rp p RTl
E
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given a vector in a local reference frame rotate
by q to get the vector in the project reference
frame
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Relationship between vectors in geocentric and
local frames of reference
Z
h
n
e
X
N
Y
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Z
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e
X
N
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h
Z
f
x
X
l
l
y
l
Y
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Example
The details of a GPS baseline are given as
follows

• Compute the components of the baseline in the
  local East, North,
• Height System.
• Compute the bearing and distance in the local
  system of the baseline.

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l R-1g RTg
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Given DX, DY, DZ WGS84 Geocentric vector
Compute local vector Del, Dnl, Dhl
use vectors to solve q, s, z
Compute project vector Dep, Dnp, Dhp
Compute bearing, distance, zenith distance