Global Positioning System Reference
In-Depth Information
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v
T
Pv
i
=
v
T
Pv
i
−
1
+ ∆
v
T
Pv
i
(4.142)
v
T
Pv
i
=
A
i
x
i
−
1
+
w
i
T
M
i
+
A
i
Q
i
−
1
A
i
−
1
A
i
x
i
−
1
+
w
i
(4.143)
∆
Q
i
−
1
A
i
M
i
+
A
i
Q
i
−
1
A
i
−
1
A
i
Q
i
−
1
Q
i
=
Q
i
−
1
−
(4.144)
Every sequential solution is equivalent to a one-step adjustment that contains the
sa
me observations. The sequential solution requires the inverse of the normal matrix.
Be
cause computing the inverse of the normal matrix requires many more compu-
ta
tions than merely solving the system of normal equations, one might sometimes
pr
efer to use the one-step solution instead of the sequential approach.
[11
4.7 WEIGHTED PARAMETERS AND CONDITIONS
The algorithms developed in the previous section can be used to incorporate exte-
rior information about parameters. This includes weighted functions of parameters,
weighted individual parameters, and conditions on parameters. The objective is to
incorporate new types of observations that directly refer to the parameters, to specify
parameters in order to avoid singularity of the normal equations, or to incorporate
the results of prior adjustments. Evaluating conditions between the parameters is the
basis for hypothesis testing. These cases are obtained by specifying the coefficient
matrices
A
and
B
of the mixed model. For example, the mixed model (4.86) and
(4.87) can be specified as
Lin
—
-2.
——
Nor
*PgE
[11
f
1
(
1
a
,
x
a
)
=
o
(4.145)
2
a
=
f
2
(
x
a
)
(4.146)
Th
e linearized form is
B
1
v
1
+
A
1
x
+
w
1
=
o
(4.147)
v
2
=
A
2
x
+
2
(4.148)
The specifications are
B
2
=−
2
=
I
and
w
2
. For the observation equation model we
obtain
1
a
=
f
1
(
x
a
)
(4.149)
2
a
=
f
2
(
x
a
)
(4.150)
with the linearized form being
v
1
=
A
1
x
+
1
(4.151)
