Global Positioning System Reference
In-Depth Information
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This expression differs from the pseudorange (5.7) as follows:
N
k
(
1
)
Integer ambiguity: This integer refers to the first epoch of observations
and remains constant during the period of observation. During this
period, the receiver accumulates the phase differences between
arriving phases and internally generated receiver phases. The
receiver, therefore, effectively generates an accumulated carrier
phase observable that reflects the changes in distance to the
satellite. The observation series is continuous until a cycle slip
occurs, which introduces an integer jump. After the cycle slip
has occurred, the observation series continues with a new integer
constant
N
k
.
I
k,
1
,ϕ
Ionospheric L1 carrier phase advance. This value is negative. The
numerical value is a function of the frequency and the ionospheric
condition along the path. See Chapter 6 for details of this delay and its
relation to the corresponding ionospheric pseudorange delay.
[17
Lin
—
0.8
——
Lon
PgE
p
k,
1
,ϕ
δ
Hardware delays and multipath effects on the L1 carrier phase.
ε
1
,ϕ
L1 phase measurement noise (
<
0
.
01 cycles)
The carrier phase can be scaled to unit of length by multiplying with
λ
1
=
c/f
1
. Thus
(5.10) becomes
p
k,
1
(t
k
)
p
k
(t
p
)
+ λ
1
N
k
(
1
)
I
k,
1
,
Φ
T
k
(t
k
)
cdt
p
Φ
= ρ
−
cd
t
k
+
+
(t
k
)
+
(5.12)
p
k,
1
,
Φ
+ δ
(t
k
)
+
ε
1
,
Φ
[17
Th
e subscript
Φ
implies that the respective quantities are in units of length, e.g.,
I
k,
1
,
Φ
= λ
1
I
k,
1
,ϕ
.
Receivers observe pseudoranges and carrier phases to several satellites at the same
ti
me. Today's all-in-view receivers generate these observables for all visible satellites
at
the same nominal time
t
k
, for L1 and L2 frequencies. Therefore, the receiver clock
er
ror and the hardware delays are the same for all observations at the same epoch.
Si
nce GLONASS satellites transmit at different frequencies, special attention must
be
given to the implications of the receiver clock errors when expressing the carrier
ph
ases. For details on GLONASS phase processing, see Section 7.7.6.
The following simple functions of the L1 and L2 frequencies are useful for future
re
ferences,
(f
1
/f
2
)
2
(
77
/
60
)
2
α
f
=
=
≈
1
.
647
(5.13)
f
1
/
f
1
f
2
= α
f
/
α
f
−
1
=
77
2
/
77
2
60
2
≈
β
f
=
−
−
2
.
546
(5.14)
f
2
/
f
1
f
2
=
1
/
α
1
=
60
2
/
77
2
60
2
≈
γ
f
=
−
−
−
1
.
546
(5.15)
f
f
1
f
2
/
f
1
f
2
=
√
α
f
/(
60
/
77
2
60
2
≈
δ
f
=
−
α
f
−
1
)
=
77
∗
−
1
.
984
(5.16)
