Global Positioning System Reference
In-Depth Information
•
ρ
is the reference pseudorange, corresponds to the satellite closest to the user. Even if
the receiver does not know the distance between this satellite and the user, a realistic
value of ρ can be set as an approximation. In fact, by considering that a typical travel
time from the satellites to the Earth is on the order of 65-83 ms, an appropriated value
could be
ρτ⋅ . It is important to
note that such approximated reference pseudorange, does not affect the computation of
the user's position. Eventually, a the error due to on such approximation falls in the
terms that takes into account the clock bias.;
τ
1
=70
ms (Borre et al., 2006), thus
=
c
= 20985.47
Km
1
1
•
Δ has not been determined yet, but it will be solved computing the set of equations
(6).
4.1.2 Common reception time
The second approach performs the pseudoranges estimation, setting a common receiving
time
u
t
over all the channels. Also in this case, the reference channel is the one that receives
the subframe transmitted at
GPS
tx
t
first. For all the tracked satellites (including the reference
one), the receiver counts the elapsed time between the reception of subframe and
R
u
t
.This
means that the receiver measure the delays as:
RR
δ
=
t
−
t
∀
i
= 1,.., 4
(13)
i
urx
,1
Fig. 8 depicts the method of fixing a unique time of reception for four GPS satellites in view
Fig. 8. Pseudorange computation based on “comon reception time”, evaluating the start of
the subframe for a GPS system
Once the δ has been computed, the receiver is able to calculate the pseudorange easily. This
can be accomplished by evaluating the delta-difference ( Δ) of delays with respect to the
satellites and the reference one. The aforementioned relative difference
Δ is stated as:
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