Global Positioning System Reference
In-Depth Information
The CS data editing limit checks the pseudoranges and performs third-difference
tests on the raw L1 and L2 observables. The third-difference test compares consecu-
tive sequences of L1 and L2 observables against thresholds. If the third-difference
test exceeds these thresholds, then those observables are discarded for subsequent
use in that interval. Such data editing protects the CS Kalman filter from question-
able measurements. Ionosphere-corrected, L1 pseudorange, and phase measure-
ments,
φ
c
, respectively, are computed using the standard ionosphere
correction (see Section 7.2.4.1):
ρ
c
and
1
(
)
ρρ
=−
−
⋅
ρρ
−
c
1
(
)
1
2
1
α
(3.1)
1
(
)
φφ
=+
−
⋅
φφ
−
(
)
c
1
1
2
1
α
(154/120)
2
, and
where
1, 2 are the validated L1 and L2
pseudorange and phase measurements, respectively.
Ionosphere-corrected pseudorange and carrier-phase measurements are related
by
a constant offset. By exploiting this fact, a smoothed pseudorange measurement,
ρ
c
, is formed from a carrier phase as follows:
α =
ρ
i
and
φ
i
for
i
=
ρφ
c
=+
B
(3.2)
c
where
B
is an unknown constant computed by averaging the L1 ionosphere-cor-
rected pseudorange and carrier-phase measurement,
ρ
c
and
φ
c
, differences
(
(
)
(
)
)
∑
B
=
ρ
z
−
φ
z
(3.3)
c
j
c
j
over all validated measurements in the smoothing interval. The CS pioneered such
carrier-aided smoothing of pseudoranges in the early 1980s.
The CS Kalman filter performs measurement updates every 15 minutes based on
its uniform GPS time scale (i.e., GPS system time). The smoothing process generates
second-order pseudorange and carrier-phase measurement polynomials in the
neighborhood of these Kalman update times. A phase measurement polynomial,
consisting of bias, drift, and drift rate,
$
X
c
, is formed using a least-squares fit of the
last five phase measurements in the smoothing interval,
r
c
:
r
(
)
$
XA AAW
c
−1
T
T
=
⋅
(3.4)
c
where
()
()
()
()
()
φ
z
z
z
z
z
1
1
1
−2τ 4τ
ττ
0
τ
2
c
−
2
φ
φ
φ
φ
−
2
r
c
−
1
A
=
,
=
(3.5)
0
c
c
0
1
12
τ
2
c
1
τ
4
τ
2
c
2
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