Global Positioning System Reference
In-Depth Information
k-th
satellite coordinates), keeping their clocks synchronized to a common time scale. The
user estimates the distances
ρ
k
with a set of satellites, measuring the travel time from the
satellite to the receiving antenna.
Measured range
(pseudorange)
Range due to the
receiver clock bias
Fig. 1. Example of trilateration in case of clock biased receiver
The user needs at least 4 equations to be able to compute (, , )
kkk
xyz
, because of the bias δ
t
between his clock and the satellite time scale. Due to the presence of a common bias that
affects all the measures of distance between the user and the satellites, we have to refer to
such a distance as a
pseudorange
ρ instead of a range. From this moment on, the reader
has to keep in mind this distinction.
⎧
2
2
2
ρ
=
(
xx
−+−+−+⋅
)
(
yy
)
(
zz
)
δ
t c
1
1
u
1
u
1
u
⎪
2
2
2
ρ
=
(
xx
−+−+−+⋅
)
(
yy
)
(
zz
)
δ
t c
⎪
2
2
u
2
u
2
u
(6)
2
2
2
ρ
=
(
xx
−+−+−+⋅
)
(
yy
)
(
zz
)
δ
tc
3
3
u
3
u
s
u
⎪
⎪
2
2
2
ρ
=
(
xx
−+−+−+⋅
)
(
yy
)
(
zz
)
δ
t c
⎩
4
4
u
4
u
4
u
The system (6) is the set of equations that every GNSS receiver has to solve. With the
problem stated above and having in mind the task of the receiver, this chapter explains the
operations performed to measure the user-satellite ranges. The focus will be mainly on
measurements taken on the received spreading codes, while for carrier-phase
measurements, interested readers can find comprehensive theory in (Misra & Enge, 2001;
Jonge & Teunissen, 1996).
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