Geoscience Reference
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2
4
3
5
sin L
cos L
00
00
cos B ˁ
cos B ˁ
0
ð
N
þ
H
Þ
ð
N
þ
H
Þ
2
4
3
5
2
4
3
5
dL
dB
dH
Δ
X 0
Δ
Y 0
cos B
M
sin B cos L
M
sin B sin L
M
00
00
00
ˁ
ˁ
H ˁ
Δ
Z 0
þ
H
þ
H
þ
cos B cos L
cos B sin L
sin B
2
3
tan B cos L
tan B sin L
1
4
5
2
3
ʵ X 00
ʵ Y 00
ʵ Z 00
sin L
cos L
0
4
5
þ
Ne 2 sin B cos B sin L
ˁ }
Ne 2 sin B cos B cos L
ˁ }
0
2
3
0
4
5
N
M e 2 sin B cos B
00
ˁ
þ
Δ
m
e 2 sin 2 B
N 1
ð
Þ
2
4
3
5
0
0
N
e 2 sin 2 B
M 2
ð
Þ
,
00
a e 2 sin B cos B
00
ˁ
sin B cos B
ˁ
da
df
ð
M
þ
H
Þ
ð
M
þ
H
Þ
ð
1
f
Þ
þ
sin 2 B
N
a
M
1
e 2 sin 2 B
e 2 sin 2 B
1
1
f
ð
7
:
23
Þ
where dL and dB are measured in arcseconds. Equation ( 7.23 ) is the generalized
differential formula for geodetic coordinates concerning the seven parameters and
changes in the size of the ellipsoid. It should be noted from the formula that da,df,
Δ
Z 0 , and
Δ
m have no effect on the geodetic longitude (i.e., dL
0 here). The
geodetic latitude and ellipsoidal height are independent of
ʵ Z . Disregarding the
effect of the rotation and scale parameters, equation ( 7.23 ) is the general differential
formula for geodetic coordinates.
7.2.3 Grid Model of Coordinate Transformation
Analogous to a grid model of deflections of the vertical and height anomalies, we
can also establish the grid model of coordinate transformation. By making use of
the coordinate values of the two geodetic coordinate systems on the common points
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