Global Positioning System Reference
In-Depth Information
all the satellites belonging to the same system (i.e. GPS, GLONASS, Galileo) are
synchronized each others but they are not with respect to different GNSSs;
the receiver clock is not synchronized with the GNSS time-scale (as the school clock in
the example of section 2 was not synchronized to Alice and John's watches). The actual
time at the receiver can be written as
− , where GNS t is the actual time on
the GNSS time-scale and Δ is the bias with respect to the clock on board of the
satellite. For sake of simplicity, we assume that Δ remains constant over time. In the
notation, the superscripts refer to the time-scale, while we use subscripts to identify
definite time instants;
R
S
t
t
all the examples and equations are given for the GPS satellites only but the explanation
can be considered valid and easily extended for other GNSS systems too.
With these hypothesis in mind, once the preamble has been correctly detected, every
navigation data for each satellite in view can be tagged with additional information such as the
corresponding subframe, the number of bits read from the beginning of that subframe as well
as the number of samples processed up to that time instant by acquisition and tracking stages.
In this way, it will be easy to make comparisons among channels and calculate the time delay
of the satellites. In fact, “ during the collection of the digitized data there is no absolute time reference
and the only time reference is the sampling frequency. Moreover, the pseudorange can be measured only
in a relative way because the clock bias of the receiver is an unknown quantity ” (Tsui, 2000). Therefore
the pseudorange can be computed as the distance (or time) between two reference points. The
way the reference points are chosen makes the main difference in the two methods that are
commonly used in commercial receivers for the pseudorange computation and that we can
call “ common transmission time ” and “ common reception time ”, respectively.
4.1.1 Common transmission time
According to this approach, since all the satellites are synchronized, they broadcast the same
preamble at the same moment, which is received by the user at different instants, due to
different propagation delays. This approach follows what pragmatically happens in a real
scenario where the satellites have different distances with respect to the user.
The left side of Fig. 7 represents the same subframe transmitted by the satellites at GPS
tx t . On
the right, Fig. 7 shows the local codes displacement at the receiver, assuming four tracked
satellites. The blue rectangular is the TLM word of the subframe, which is received at
different instants
GPS
rx i
t
, because of the different traveling times
τ . These can be written as :
,
GPS
GPS
τ
=
t
t
(9)
i
rx i
,
tx
GPS
rx i
R
GPS
where
t
corresponds to the time instants
t
=
t
Δ
on the receiver time-scale.
,
rx i
,
rx i
,
The receiver recovers GPS
tx t decoding the HOW of the previous subframe, which includes a
truncated version of the absolute GPS time. The receiver reads
R
rx i
t
, but it is not able to
,
GPS
rx i
compute
t
, since
Δ is unknown. If the receiver was able to compute
τ , the distances
,
between the receiver and satellites would be simply obtained as:
ρτ
=
(10)
i
i
where c stands for the speed of light.
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