Global Positioning System Reference
In-Depth Information
( x p
= x p
x k =
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p
k (t p )
ρ
x k )
·
( x p
x k )
(5.8)
(x p
x k ) 2
y k ) 2
z k ) 2
=
+
(y p
+
(z p
p
k, 1 ,P (t k )
d k, 1 ,P (t k )
d p
δ
=
d k, 1 ,P (t k )
+
+
1 ,P (t k )
(5.9)
k
t p This is again the geometric vacuum distance that is often computed from
the ECEF receiver coordinates x k and satellite coordinates x p , taking the
earth's rotation during signal travel time into account. Given the nominal
time t p , we add the satellite clock correction given in the broadcast
message to compute and estimate the true time t p . Because the satellites
carry atomic clocks that are carefully monitored and are fairly stable, one
can safely assume that the residual error in t p is less than 1 microsecond.
p
ρ
[17
For a topocentric range rate of ρ
k (t) < 800 m/s, the computation error
p
< 1 mm because of dt p . This error is negligible.
in distance is d
ρ
Lin
0.9
——
Lon
PgE
I k, 1 ,P
Ionospheric P(Y)-code delay at L1. This delay is always positive.
It depends on the ionospheric condition along the path and on the
frequency. Details are provided in Chapter 6.
T k
Tropospheric delay. This delay is always positive. It depends upon the
tropospheric condition along the path but is independent of the carrier
frequency. Therefore, there is no need to identify the frequency.
d k, 1 ,P
Receiver hardware delay. This delay does not depend on the satellite
being observed.
[17
d k, 1 ,P
Multipath delay. This delay depends on the direction of the satellite.
d 1 ,P
Satellite hardware delay.
ε 1 ,P
Pseudorange measurement noise (approximately 30 cm for P(Y) code
pseudoranges and worse for C/A-code pseudoranges, depending on the
technology used).
The pseudorange (5.7) would equal the geometric distance from the satellite at epoch
of transmission to reception at the receiver if the propagation medium were a vacuum
and if there were no clock errors and no other biases.
The phase observable is the sum of the fractional carrier phase at nominal fre-
quency f 1 , which arrives at the antenna at the nominal time t k , and an unknown integer
constant representing full waves. In units of cycles the equation for the carrier phase
L1 is
f 1
c ρ
f 1
ϕ k, 1 (t k )
p
k (t p )
N k ( 1 )
I k, 1 (t k )
c T k (t k )
f 1 d t p
=
+
f 1 d t k +
+
+
(5.10)
p
k, 1 (t k )
+ δ
+
ε 1
p
k, 1 (t k )
d k, 1 (t k )
d 1 (t k )
δ
=
d k, 1 (t k )
+
+
(5.11)
 
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