单双频GPS接收机的自动循环滑码检测与修复新方法
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本文探讨了一种针对单个双频GPS接收机的新型自动循环滑码检测和修复方法。该研究发表在《JGeod》期刊上，doi为10.1007/s00190-010-0426-y，是一篇原创文章。作者是Zhizhao Liu，论文于2010年6月8日接收，11月8日接受。这项工作的重要性在于它提供了一种仅依赖单个双频GPS接收器就能进行精确的滑码事件识别和处理策略。
在传统的GPS定位中，循环滑码（cycle slip）是一种常见问题，可能导致定位精度下降或数据失真。循环滑码通常发生在接收机无法正确跟踪卫星信号的相位变化时，这可能由于接收机内部错误、多路径效应或其他干扰引起。双频GPS接收机利用L1和L2频率的数据，可以提高定位精度和抗干扰能力。
新提出的算法利用了两个关键指标：离子osphere total electron content rate (TECR)率和Melbourne-Wübbena wide lane (MWWL)组合。TECR通过分析双频载波相位测量，能够提供关于离子层电子密度变化的精细信息，这对于定位误差的校正至关重要。MWWL则是基于接收机接收到的不同频率信号之间的差异，用于估计信号传播路径上的延迟。
循环滑码的检测机制基于这样一个原理：当发生滑码时，MWWL的模糊度会发生变化，同时由于滑码引起的虚假TECR会显著增加，远超过正常物理TECR的贡献。通过比较当前和前一时刻的这两个参数，算法能够区分出真实的离子层变化与滑码产生的异常现象。一旦检测到滑码，修复过程会通过反演和校准来消除其影响，从而恢复接收机的定位性能。
值得注意的是，这种方法依赖于双频数据的高精度，因此，对于单个接收机而言，利用这种技术可以提升其在复杂环境下的鲁棒性和定位稳定性。此外，通过自动化的方式处理滑码，降低了人工干预的需求，节省了时间和资源，提高了整个系统的实时性。
总结来说，这篇文章介绍了一种创新的GPS接收机滑码检测和修复策略，它利用双频信息和特定的信号处理技术来有效地识别和纠正循环滑码，这对于提升全球定位系统的可靠性具有实际应用价值。
A new automated cycle slip detection and repair method
approach may provide unexpected results (Dai et al. 2009).
As a matter of fact, at present there is only one modernized
GPS satellite in space broadcasting signals at L1, L2, and L5
three frequencies. The use of dual-frequency GPS receivers
and satellites is still prevailing in the applications.
In this paper, a new cycle slip detection and repair method
that employs the ionospherictotal electron content (TEC) rate
(TECR) is proposed. Unlike other methods where the iono-
spheric variation is regarded as a nuisance or simply ignored,
in this method, the ionospheric variation, characterized by
the TEC rate, is precisely estimated and used to detect and
repair cycle slip. Without cycle slips, the ionospheric phys-
ical TECR is normally bounded by a certain value. In this
study, we choose the threshold value as 0.15 TECU/s. When
there are cycle slips, the ionospheric TECR will become
significantly larger, with most contribution from the artifi-
cial ionospheric TECR that is resulted from cycle slips. The
Melbourne–Wübbena wide lane (MWWL) ambiguity will
also change when there are cycle slips. With the data of both
ionospheric TECR change and MWWL ambiguity change,
the cycle slips can be precisely and uniquely determined.
This paper is organized as below. The methodology of
detecting and repairing cycle slip is developed in detail in
Sect. 2. The accuracies of the estimated cycle slip terms are
analyzed too. The analyses of the method performance are
performed in Sect. 3. In Sect. 4, the application of this method
is discussed. The conclusion is given in Sect. 5.
2 Methodology
In this cycle slip detection and repair method, two sets of
measurements are jointly employed to precisely determine
the size of the cycle slips. One is the Melbourne–Wübbena
linear combination that has been widely used for cycle slip
detection and ambiguity resolution because of its 86-cm long
wavelength (Melbourne 1985; Wübbena 1985; Blewitt 1990;
Kass et al. 2009; Bock et al. 2009). This combination removes
the effects from the atmosphere (including both ionosphere
and troposphere), the geometry, and the satellite and receiver
clocks. Therefore, this combination is useful to check GPS
observations for cycle slips (Dach et al. 2006). The other set
of measurements is the ionospheric TECR that is inferred
from L1 and L2 carrier phase measurements.
2.1 Carrier phase and pseudorange observations
We assume that the dual-frequency GPS receiver observes
the satellite p. The observation equations for dual-frequency
GPS carrier phase and pseudorange measurements can be
written as:
λ
1
p
1
= ρ
p
+ c(dt − dT
p
) − I + T + λ
1
N
p
1
, (1)
λ
2
p
2
= ρ
p
+ c(dt − dT
p
) − γ I + T + λ
2
N
p
2
, (2)
P
p
1
= ρ
p
+ c(dt − dT
p
) + I + T, (3)
P
p
2
= ρ
p
+ c(dt − dT
p
) + γ I + T, (4)
where λ
1
and λ
2
are the wavelengths of the GPS L1 and
L2 signals, respectively;
p
1
and
p
2
are carrier phase mea-
surements on L1 and L2 frequencies, respectively; P
p
1
and
P
p
2
are the pseudorange measurements; ρ
p
is the geometrical
distance between the receiver and the satellite p; dt and dT
p
are the GPS receiver and satellite clock errors, respectively;
c is the speed of light in vacuum; I is the ionospheric range
delay on GPS L1 signal; T is the tropospheric range delay;
N
p
1
and N
p
2
are the integer number of cycles for GPS L1 and
L2 signals, respectively, which are often called ambiguities;
γ = f
2
1
/ f
2
2
is the ratio of the squared frequencies of GPS
L1 and L2 signals. The carrier phase measurements
p
1
and
p
2
and the ambiguities N
p
1
and N
p
2
are in the unit of cycle.
The dt and dT
p
are in the unit of second. The rest variables
are all in the unit of meter.
2.2 Cycle slip determined from the Melbourne–Wübbena
wide-lane combination
The well-known MWWL linear combination at a given epoch
can be formed as below (Melbourne 1985; Wübbena 1985).
The tag for epoch is omitted for brevity.
L
MWWL
=
f
1
· λ
1
p
1
− f
2
· λ
2
p
2
f
1
− f
2
−
f
1
· P
p
1
+ f
2
· P
p
2
(
f
1
+ f
2
)
= λ
WL
N
p
WL
, (5)
where λ
WL
= c/
(
f
1
− f
2
)
≈ 86 cm and N
p
WL
= N
p
1
− N
p
2
.
The λ
WL
and N
p
WL
are called wide-lanewavelength and wide-
lane ambiguity, respectively. Thus, the wide-lane ambiguity
at a given epoch can be estimated as:
N
p
WL
=
L
MWWL
λ
WL
=
p
1
−
p
2
−
f
1
· P
p
1
+ f
2
· P
p
2
λ
WL
(
f
1
+ f
2
)
. (6)
We assume that at epoch (k−1) there are no cycle slips, or the
cycleslips havebeen repaired if any.But at epoch (k) there are
cycle slips on both L1 and L2 carrier phase measurements
p
1
(k) and
p
2
(k). The cycle slips are denoted as N
p
1
(k)
and N
p
2
(k), respectively. After cycle slips are detected and
repaired, the correct carrier phase measurements at epoch (k)
should be calculated as:
p
1
(k) =
p
1
(k) + N
p
1
(k), (7)
p
2
(k) =
p
2
(k) + N
p
2
(k), (8)
where
p
1
and
p
2
denote the correct L1 and L2 phase mea-
surements, respectively, after cycle slips are repaired.
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