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

Chapter 7 Orbit Determination Using Carrier Phase Observation
the state transition matrix Φ can be written as follows
dΦ
= FΦ
(7-9)
dt
where,
� ∂f1
∂f1
∂f1
∂f1
∂f1
∂f1
∂f1
∂f1
�
�
...
∂x
∂y
∂z
∂x&
∂y&
∂z&
∂N
∂N
�
�
1
n �
�∂f
2 ∂f2
∂f2
∂f2
∂f2
∂f2
∂f2
∂f2
... �
� ∂x
∂y
∂z
∂x&
∂y&
∂z&
∂N
∂N
�
1
n
�∂f
∂f
∂f
∂f
∂f
∂f
∂f
∂f
�
� 3 3 3 3 3 3 3
3
... �
� ∂x
∂y
∂z
∂x&
∂y&
∂z&
∂N1
∂Nn
�
�∂f
4 ∂f4
∂f4
∂f4
∂f4
∂f4
∂f4
∂f
�
4
F =
�
... �
� ∂x
∂y
∂z
∂x&
∂y&
∂z&
∂N1
∂Nn
�
�
... �
�
...
�
�
�
�∂f
k ∂fk
∂fk
∂fk
∂fk
∂fk
∂fk
∂fk
... �
� ∂x
∂y
∂z
∂x&
∂y&
∂z&
∂N1
∂N
�
n
� ... ... ... �
�
∂fn
∂fn
∂fn
∂fn
∂fn
∂fn
∂fn
∂f
�
�
n
... �
��
∂x
∂y
∂z
∂x&
∂y&
∂z&
∂N1
∂Nn
��
87
(7-10)
The transition matrix Φ with initial ambiguities as parameters is more complex than without initial ambiguities.
The Kalman filter algorithms discussed in Chapter 6 can be used with carrier phase observation for satellite orbit
determination.
According to Eq.(7-1), the carrier phase range equations can be written as
2 2 2
i i i i i
ρ = ( x − x) + ( y − y) + ( z − z) + λN
linearizing Eq.(7-10),
(7-11)
1
∆ρi = [( xi − x) ∆x+ ( yi − y) ∆y+ ( zi − z) ∆z] + λ∆Ni
(7-12)
ρ′
Then,
ϖ ϖ ϖ
y = H∆x + ε (7-13)
where,
� ∂ρ1
∂ρ1
∂ρ1
∂ρ1
∂ρ1
∂ρ1
∂ρ1
∂ρ1
�
�
...
∂x
∂y
∂z
∂x&
∂y&
∂z&∂N
∂N
�
� ∆ρ1
� �
1
n �
�
∆ρ
� � ∂ρ 2 ∂ρ 2 ∂ρ 2 ∂ρ 2 ∂ρ 2 ∂ρ 2 ∂ρ 2 ∂ρ 2
... �
ϖ � 2 � � ∂x
∂y
∂z
∂x&
∂y&
∂z&∂N
∂N
�
1
n
y = � ∆ρ
3 � , H = � ∂ρ ∂ρ ∂ρ ∂ρ ∂ρ ∂ρ ∂ρ ∂ρ �
� � � 3 3 3 3 3 3 3
3
... �
�
...
� � ∂x
∂y
∂z
∂x&
∂y&
∂z&∂N1∂Nn�
�
�∆ρ
m �
� � ... ... ... �
�∂ρ
m ∂ρ m ∂ρ m ∂ρ m ∂ρ m ∂ρ m ∂ρ m ∂ρ �
m
�
... �
��
∂x
∂y
∂z
∂x&
∂y&
∂z&∂N1∂Nn��
ϖ
∆x = { ∆x, ∆y, ∆z, ∆x&, ∆y&, ∆z&, ∆N1,..., ∆Nn}
In developing the equations above it is assumed that all observations are continuous. If the cycle slips occur,
there are two methods to solve it: first using cycle slip fixing strategies to repair the cycle slips at the observation
preprocessing session, therefore the above equations will never be changed; secondly the new initial ambiguities