Global Positioning System Reference
In-Depth Information
Table 2.1
Determination of Geodetic Height
and Latitude in Terms of ECEF Parameters
pxy
=
2
+
2
z
p
a
b
tan
u
=
Iteration Loop
cos
1
2
u
=
1
+
tan
2
u
sin
2
u
=−
1
cos
2
u
zeb
+
′
2
sin
cos
3
u
tan
ϕ =
pea
−
2
3
u
b
a
tan
u
=
tan
ϕ
until tan
u
converges, then
N
a
e
=
1
−
2
sin
2
φ
p
h
=
−
N
ϕ
≠ ±
90
°
cos
φ
otherwise
z
2
h
=
−
NeN
+
ϕ
≠
0
sin
φ
2.2.3.2 Conversion from Geodetic Coordinates to Cartesian Coordinates in
ECEF Frame
For completeness, equations for transforming from geodetic coordinates back to
Cartesian coordinates in the ECEF system are provided later. Given the geodetic
parameters
λ
,
ϕ
, and
h
, we can compute
u
=
(
x
u
, y
u
, z
u
) in closed form as follows:
a
cos
λ
+
h
cos
λφ
cos
(
)
2
2
11
+−
e
tan
φ
a
sin
λ
u
=
+
h
sin
λ
cos
φ
(
)
2
2
11
+−
e
tan
φ
(
)
2
ae
1
−
sin
φ
+
h
sin
φ
1
−
e
2
sin
2
φ
2.2.3.3 WGS 84 Reference Frame Relationships
There have been four realizations of WGS 84 as of this edition. The original WGS
84 was used for the broadcast GPS orbit beginning January 23, 1987. WGS 84
(G730), where the “G730” denotes GPS week, was used beginning on June 29,
1994. WGS 84 (G873) started on January 29, 1997 [5]. And, the current frame,
WGS 84 (G1150), was introduced on January 20, 2002. These reference frame real-
izations have brought the WGS 84 into extremely close coincidence with the Inter-
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