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

Chapter 4 Major Error Sources of Satellite Observations
= A[
R(
τ ′ + dT / 2)
− R(
τ ′ − dT / 2)]
cos( ∆ϕ)
α A[ R(
τ ′ −δ
+ dT / 2)
− R(
τ ′ −δ
− dT / 2)]
cos( ∆ϕ
−θ
) = 0
(4-25)
I D
+ m
The problem is how the multipath signal delay time δ affects correlation time τ ′ . If multipath effects do not
exist, i.e. α = 0 , Eq.(4-24) and Eq.(4-25) hold only and only if τ′ = τ . Due to multipath effects, Eq.(4-24) and
Eq.(4-25) will hold when τ′ ≠ τ , i.e. zero-crossing point is distorted.
The envelopes of influence of multipath signal time delay δ on τ ′ from Eq.(4-25) can be developed as follows.
Suppose
� | τ ′ |
�
′ ≤ T
R ′
1−
| τ |
( τ ) = � T
(4-26)
�� 0
τ ′ > T
and d=1, cos( ∆ϕ ) = 1 , cos( ϕ −θ
) = 1 .
∆ m
T
If δ −τ ′ ≤ , Eq.(4-25) becomes
2
| τ ′ + T / 2 | | τ ′ −T
/ 2 | | τ ′ + T / 2 −δ
| | τ ′ −T
/ 2 −δ
|
− + = −α
( −
+
)
T T
T
T
i.e.
α
τ ′ = δ
1 + α
T
If δ − τ ′ > , then R ( τ ′ − T / 2 − δ ) = 0 ,
2
Eq.(4-25) becomes
37
(4-27)
| τ ′ + T / 2 | | τ ′ −T
/ 2 | | τ ′ + T / 2 −δ
|
− + = −α
( 1−
)
T T
T
3 α
τ ′ = ( T −δ
)
(4-28)
2 2 −α
Assuming cos( θ ) = −1
, cos( θ θ ) = −1,
Eq.(4-27) and Eq.(4-28) become
τ ′ =
τ ′ =
c
m − c
α
−δ
1−
α
(4-29)
3 α
−(
T −δ
)
2 2 + α
(4-30)
According to Eq.(4-27), Eq.(4-28), Eq.(4-29) and Eq.(4-30) and assuming α = 05
. , the multipath error
envelopes of code pseudoranges are drawn in Figure 4-2 and Figure 4-3 respectively.