Precise Orbit Determination of Global Navigation Satellite System of ...

Chapter 4 Major Error Sources of Satellite Observations
θ m multipath relative phase( θ = ωδ )
The signals received by satellite receiver are
S r = S d + S m = A cosω ( t −τ
) + αA
cos[ ω(
t −τ
) + θ m ]
= A cosω ( t −τ
) + αA
cosω
( t −τ
) cosθ
−αA
sin ω(
t −τ
) sinθ
where
A
1+
α cosθ
m
α sinθ
m
= Ar
[ cosω
( t −τ
) − sin ω(
t −τ
)
A
A
r
2
2 2 2 2
r = A 1+
cosθ
m ) + α A sin θ m = A 1+
2α
cosθ
m
m
( α + α
Finally Eq.(4-33) becomes
= A [cosφ cosω
( t −τ
) − sin φ sin ω(
t −τ
)]
S r r
Ar = cos[ ω ( t −τ
) + φ]
where
− α sinθ
m
φ = tan ( ) + nπ
1+
α cosθ
m
1
φ is the phase error caused by multipath effects
r
m
39
m
2
(4-33)
(4-34)
From Eq.(4-34), it is clear that the received signals are distorted by the multipath effects. The amplitude of the
received signal A becomes A r and the phase of the signals introduces phase shift φ .
Suppose the local receiver produces a synchronous signal
Sl = A cosω ( t −τ
′ )
where
τ ′ correlation time error between replica and incoming signal produced by the receiver
The auto-correlation function of the receiver may be written as follows:
= � S r ( τ ) S ( ′ )
� Ar cos[ ( t −τ
) + φ]
Acosω
( t −τ
′ ) dt = Ar
A
′
� cos[ ω(
t −τ
) + φ]
cosω
( t −τ
( τ ′ )
τ dt
R l
(4-35)
= ω ) dt
(4-36)
For simplicity, the time error, propagation errors and receiver errors (PLL track errors etc.) are not considered
and assuming α is a constant.
In order to make Eq.(4-36) maximum, let
ω ( t −τ ) + φ = ω(
t −τ
′ )
i.e.
τ = τ ′ + ∆τ
(4-37)
and
φ 1 −1
α sinθ
m
∆τ
= = [tan ( ) + nπ
]
ω 2π
1+
α cosθ
where
f m
1 α sinθ
m 1 α sinθ
m 3
≈ [
− ( ) + ... + nπ
]
(4-38)
2π
1+
α cosθ
3 1+
α cosθ
f m
m