Global Positioning System Reference
In-Depth Information
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network. Most of the time, however, the observation equation model is preferred,
because the simple rule “one observation, one equation” is suitable for setting up
general software. Table 4.1 lists the important expressions for all three models.
4.6 SEQUENTIAL SOLUTION
Assume that observations are made in two groups, with the second group consisting
of one or several observations. Both groups have a common set of parameters. The
two mixed adjustment models can be written as
1
a
,
x
a
)
=
f
1
(
o
(4.86)
[11
2
a
,
x
a
)
=
f
2
(
o
(4.87)
Bo
th sets of observations should be uncorrelated, and the a priori variance of unit
w
eight should be the same for both groups; i.e.,
Lin
—
4.4
——
Nor
*PgE
P
1
Σ
−
1
1
O
O
2
0
P
=
= σ
(4.88)
Σ
−
1
2
OP
2
O
The number of observations in
2
a
are
n
1
and
n
2
, respectively; and
r
1
and
r
2
are the number of equations in the models
f
1
and
f
2
, respectively. The linearization
of (4.86) and (4.87) yields
1
a
and
[11
B
1
v
1
+
A
1
x
+
w
1
=
o
(4.89)
B
2
v
2
+
A
2
x
+
w
2
=
o
(4.90)
where
1
b
,
x
0
1
b
,
x
0
,
-
∂
f
1
∂
∂
f
1
∂
x
B
1
=
A
1
=
w
1
=
f
1
(
1
b
,
x
0
)
1
(4.91)
2
b
,
x
0
2
b
,
x
0
.
∂
f
2
∂
∂
f
2
∂
x
B
2
=
A
2
=
w
2
=
f
2
(
2
b
,
x
0
)
2
The function to be minimized is
φ
v
1
,
v
2
,
k
1
,
k
2
,
x
=
2
k
1
B
1
v
1
+
w
1
v
1
P
1
v
1
+
v
2
P
2
v
2
−
A
1
x
+
(4.92)
2
k
2
B
2
v
2
+
w
2
−
A
2
x
+
The solution is obtained by setting the partial derivatives of (4.92) to zero,
