Global Positioning System Reference
In-Depth Information
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generated by the satellite with those generated internally by the receiver. The code-
tracking loop within the receiver shifts the internal replica of the PRN code in time
until maximum correlation occurs. The codes generated by the receiver are based on
the receiver's own clock, and the codes of the satellite transmissions are generated
by the satellite clock. Unavoidable timing errors at the satellite and the receiver will
cause the measured pseudorange to differ from the geometric distance corresponding
to the instants of emission and reception. Pseudoranging is applicable to P(Y)-codes
and C/A-codes.
The equation for the pseudorange observable can easily be built by considering
fir
st the spatial distance in vacuum,
=
t
p
c
=
t
k
t
p
c
p
k
(t
p
)
t
k
t
p
¯
ρ
−
+
d
t
k
−
−
d
(5.5)
[17
p
k
(t
p
)
ρ
Geometric distance (vacuum distance) traveled by the code from
transmission at satellite
p
to reception at the receiver antenna
k
. This
distance will eventually have to be computed as part of the receiver
position computations. See details below.
Lin
—
*
1
——
Lon
*PgE
t
k
True time at the receiver at the epoch the code entered the antenna. The
nominal time, i.e., the receiver clock reading, is denoted by
t
k
. This
nominal receiver time is in error by
d
t
k
.
t
p
True time at the epoch of code transmission. The nominal satellite time,
i.e., the satellite clock reading, is denoted by
t
p
. This nominal satellite
clock time is in error by
d
¯
t
p
.
[17
c
Velocity of light.
There is a direct linear relationship between codes and nominal clock time. The
code generation sequence is specified by time as a parameter. Therefore, the nominal
sa
tellite time determines which code leaves the satellite and when. The same is
tru
e regarding the nominal receiver time and the generation of the receiver's code
se
quence. The measure pseudorange is, therefore, a function of the nominal times.
Fo
r the vacuum we have
≡
t
k
−
t
p
c
P
k
(t
k
)
p
k
(t
p
)
cd t
p
= ρ
−
cd
t
k
+
(5.6)
w
here
P
k
(t
k
)
denotes the pseudorange.
The mathematical expression for the pseudorange observable must take into ac-
co
unt the effects of the ionosphere and the troposphere, as well as hardware delays
at
the satellite and at the receiver. Adding the subscript to identify the frequency, the
ac
tual expression for the pseudorange observable becomes
P
k,
1
(t
k
)
p
I
k,
1
,P
(t
k
)
T
k
(t
k
)
p
k,
1
,P
(t
k
)
k
(t
p
)
t
p
¯
= ρ
−
cd
t
k
+
cd
+
+
+ δ
+
ε
1
,P
(5.7)
with
