Chapter 7
Satellite Positioning
7.1 Historical Background
7.2 Orbital Motion of Satellite Systems
7.2.1 Satellite Orbits
• Orbit plane
• Orbit shape
• Orbit altitude
r ma mv
Fcentripetal = 2 =
Earth 2
Earth Earth
gravity mg
R mGM
F = =
l centripeta 2
2 Earth
gravity F
R m v g
R m mGM F
c c c
c
=
=
⋅
=
=
2 Earth c
c v
R = GM
) 1 . 7 (
) 2 . 7 (
) 3 . 7 (
) 4 . 7 (
7.2.2 Keplerian Elements
7.3 Global Positioning System
7.3.1 GPS Segments
7.3.2 Satellite Constellation
• Block I
• Block II
• Block IIA
• Block IIR
• Block IIF and Block III
7.3.3 Pilot Signals and Spreading Codes
7.3.4 Navigation Message
7.3.5 GPS Services
7.3.6 GPS Positioning
Identification of satellites Range measurements Position calculation
t c z
Z y
Y x
X
pi = ( i − )2 +( i − )2 +( i − )2 + ∆ (7.5)
7.3.7 GPS Error Budget
=
= −
2 2
2 2
) (
t tz
ty tx
zt z
zy zx
yt yz
y yx
xt xz
xy x
σ σ
σ σ
σ σ
σ σ
σ σ
σ σ
σ σ
σ σ
1 T
ECEF A A
Q
=
2 2
2
u ue
un
eu e
en
nu ne
n
σ σ
σ
σ σ
σ
σ σ
σ Qgeo
RDoP
σ σ =
) 6 . 7 (
) 7 . 7 (
) 8 . 7 (
7.4 Differential GPS
s r i s
r i s r i
i p r c t
p = , − , = ⋅∆ ,
∆
)
( , ,
, ,
,
,mr i i mr i mr i mr i rs i rs
i p r c t c t
p −∆ = + ⋅∆ +ε − ⋅∆ +ε
Σ
∗ ≈ r +c⋅ ∆t −∆t = r +∆t
pi i,mr ( i,mr i,rs) i,mr
2 2
2
,rs ( i rs) ( i rs) ( i rs)
i X x Y y Z z
r = − + − + −
s r i s r i s
r i s
r
i r c t
p, = , + ⋅∆ , +ε ,
) 9 . 7 (
) 10 . 7 (
) 11 . 7 (
) 12 . 7 (
) 13 . 7 (
