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culable) from the information broadcast by the satellite. Therefore, there re-
main the three unknown station coordinates
X
A
,Y
A
,Z
A
and the unknown
receiver clock error
δ
A
(
t
). In other terms, at least four satellites are required
to set up four equations of type (5-6). Denoting the satellites by
j, k, l, m
,
the corresponding system of equations
R
j
A
(
t
)=
j
A
(
t
)+
cδ
A
(
t
)
,
R
A
(
t
)=
A
(
t
)+
cδ
A
(
t
)
,
R
l
A
(
t
)=
l
A
(
t
)+
cδ
A
(
t
)
,
R
A
(
t
)=
A
(
t
)+
cδ
A
(
t
)
(5-8)
is obtained or, by substituting (5-7) accordingly,
R
j
A
(
t
)=
(
X
j
(
t
)
− X
A
)
2
+(
Y
j
(
t
)
− Y
A
)
2
+(
Z
j
(
t
)
− Z
A
)
2
+
cδ
A
(
t
)
,
R
A
(
t
)=
(
X
k
(
t
)
−
X
A
)
2
+(
Y
k
(
t
)
−
Y
A
)
2
+(
Z
k
(
t
)
−
Z
A
)
2
+
cδ
A
(
t
)
,
R
l
A
(
t
)=
(
X
l
(
t
)
Z
A
)
2
+
cδ
A
(
t
)
,
R
A
(
t
)=
(
X
m
(
t
)
− X
A
)
2
+(
Y
m
(
t
)
− Y
A
)
2
+(
Z
m
(
t
)
− Z
A
)
2
+
cδ
A
(
t
)
(5-9)
results. This system of equations comprises only the previously mentioned
four unknowns
X
A
,Y
A
,Z
A
and the unknown receiver clock error
δ
A
(
t
)and
may, thus, be solved. We do not consider linearization, possible redundant
measurements, etc. We just intended to demonstrate the principle. The clock
error is a by-product, but the desired result obtained from (5-9) are the GPS
coordinates
X
A
,Y
A
,Z
A
; this means, the resulting coordinates are obatined
in the WGS 84.
As described in Sect. 5.3.4, the accuracy of the point positioning method
based on code ranges may be expected to amount some 10 m (nominally). A
much higher accuracy is achieved by relative positioning treated in the next
section.
−
X
A
)
2
+(
Y
l
(
t
)
−
Y
A
)
2
+(
Z
l
(
t
)
−
5.4.2
Relative positioning with phase pseudoranges
The objective of relative positioning is to determine the coordinates of an
unknown point with respect to a known point. In other words, relative po-
sitioning aims at the determination of the vector between the two points
which is often called the baseline vector or simply baseline (Fig. 5.3). Let
now
A
denote the known reference point,
B
the unknown point, and
b
AB
the baseline vector. Introducing the corresponding position vectors
X
A
,
X
B
,
