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Journal ArticleDOI

Performance of Precise Point Positioning with Ambiguity Resolution for 1- to 4-Hour Observation Periods

01 Apr 2010-Survey Review (Taylor & Francis)-Vol. 42, Iss: 316, pp 155-165
TL;DR: In this paper, the authors used 12 stations across Europe to conduct short-period (i.e., one, two, three and four hours) static PPP with ambiguity resolution from Day 245 to 251 in 2007.
Abstract: Recent progress in integer ambiguity resolution at a single station has made it possible to achieve high positioning accuracy in static precise point positioning (PPP) using a short period of observations. In this paper, 12 stations across Europe are used to conduct short-period (i.e. one, two, three and four hours) static PPP with ambiguity resolution from Day 245 to 251 in 2007. It is demonstrated that, when over three hours of observations are used, PPP can achieve a success rate of 100% for ambiguity resolution, a 3D positioning accuracy of about 1.0 cm and an occurrence of less than 1.0% for degraded solutions. Moreover, for the fixed solutions, increasing the observation period hardly improves the horizontal positioning accuracy while still improving the vertical one. Therefore, it is proposed that at least three hours of observations should be used in the ambiguity-fixed static PPP if a reliable millimetre positioning accuracy is required in the engineering applications.

Summary (3 min read)

INTRODUCTION

  • During the past three decades, the development in the processing strategy for Global Positioning System (GPS) measurements has led to the products of highly accurate satellite orbits, satellite clocks, and Earth rotation parameters (ERP).
  • During the PPP data processing, these products are employed to implement absolute and accurate positioning at only one single station without any synchronous GPS observations from the base stations.
  • The static positioning accuracy within such a short observation period can hardly achieve millimetre level if PPP has to be applied to this field survey.
  • Fortunately, recent studies have revealed that integer ambiguity resolution at a single station is possible if these UPD can be precisely determined in advance with a network of base stations ([3], [9], [16]). [9] suggested that the fractional parts of the UPD between satellites could be computed by averaging the fractional parts of all involved real-valued ambiguity estimates.
  • This paper aims at comparing the performance of ambiguity-fixed static PPP with different short observation periods (i.e. one, two, three and four hours), including the efficiency and reliability of ambiguity resolution, the improvement of positioning accuracy and the occurrence of degraded solutions.

DETERMINATION OF UNCALIBRATED PHASE DELAYS

  • For briefness, multipath effects and measurement errors are not written explicitly in Equation 1.
  • To remove the receiver-dependent UPD, between-satellite differences (BSD) are applied to the one-way ambiguity estimates at receiver k .
  • In the following, ‘NL UPD’ denotes ‘BSD NL UPD’ and ‘WL UPD’ denotes ‘BSD WL UPD’ for briefness.
  • It has been confirmed that daily mean WL UPD are quite stable over a rather long period (e.g. at least several days to even several months) ([8], [9], [16]).
  • This strategy is also adopted in this study.

AMBIGUITY RESOLUTION IN PPP

  • For the ambiguity validation, two statistical tests are used, and the integer candidates are accepted only when both tests are passed in this study.
  • Implying that the right side of Equation 10 might be too conservative.
  • To solve this problem, [25] suggested using more observations, but this is not feasible for short-period static PPP.
  • On the other hand, the authors also used the well-known ratio test which is generally defined as the ratio of the second minimum quadratic form of the residuals to the minimum quadratic form of the residuals for the fixed solution.
  • It is used to discriminate between the second optimum set of integer candidates and the optimum one.

DATA AND MODELS

  • The PANDA (Positioning And Navigation Data Analyst) software [10], originally developed at Wuhan University in China, is utilized to test short-period static PPP with ambiguity resolution.
  • The elevation cut-off angle for usable data was seven degrees.
  • The estimated parameters included the positions, the receiver clocks, the zenith tropospheric delays, the horizontal troposphere gradients and the ambiguities.
  • The 12 stations were distributed evenly within the coverage of the EPN.

Efficiency of ambiguity resolution

  • Table 2 shows the number of all solutions, the number of the solutions with successful ambiguity resolution, the number of the solutions without any ambiguities fixed, the number of the solutions with incorrect ambiguity resolution and the number of the outlier solutions in PPP for different short observation periods at all test stations.
  • This 10-centimetre threshold is chosen in terms of the normal 3D position accuracy derived in hourly PPP ([13], [23]).
  • The number of the failed solutions, shown in the last three columns of Table 2, decreases to zero when the observation period is over three hours.
  • Hence, it can be concluded that longer observation periods are conducive to higher success rates of ambiguity resolution in short-period static PPP, and a 100.0% success rate is achievable when over three hours of observations are used.

Reliability of ambiguity resolution

  • Figure 2 shows the mean values of the test statistics for ambiguity validation in all fixed solutions at all test stations when different short observation periods are used.
  • The black bars denote the 2 2 fixed float σ σ test statistic whilst the grey bars denote the 2 1 opt opt R R test statistic.
  • Apparently, it appears that ambiguity resolution with longer observation period is even less reliable than that with only two hours of observations, which is not reasonable.
  • Actually, this issue can be explained in terms of the different degrees of freedom for the 2 1 opt opt R R test statistics when different periods of observations are used.

Positioning accuracy

  • Table 3 shows the mean positioning accuracy of all PPP solutions at all test stations for the different short observation periods.
  • As was demonstrated by [12], the positioning accuracy can be significantly improved through ambiguity resolution in hourly PPP.
  • Table 3 further shows that, even in 4-hourly PPP, the accuracy of the East component is still improved significantly by approximately 66.7% and the 3D improvement achieves 35.7%.
  • When the observation period increases from one hour to two, three and four hours, the 3D positioning accuracy is improved markedly from 5.0 cm to 2.9 cm, 1.9 cm and 1.4 cm, respectively.
  • This pattern is not evident in the fixed solutions.

Degraded solutions

  • [12] showed that correct ambiguity resolution may lead to degraded, rather than improved, positioning accuracy in the fixed solutions compared with the float ones.
  • These solutions are defined as degraded solutions and are identified when the 3D positioning accuracy degradation exceeds 1.0 cm.
  • When the observation period is increased to three hours, however, the percentage is decreased to 0.7% and the maximum accuracy degradation is reduced to 1.7 cm.
  • As was discussed in [12], degraded solutions are closely related to the estimation of zenith tropospheric delays.
  • Moreover, Table 5 shows the percentages of the solutions with accuracy degradation in the East, North or Up directions and the corresponding mean degradation in each direction.

CONCLUSIONS

  • PPP using short periods of observations, such as one to four hours, can hardly achieve such high accuracy when the real-valued ambiguity estimates are kept in the final solutions.
  • If the non-integer uncalibrated phase delays are separated from the real-valued ambiguity estimates, integer ambiguity resolution becomes possible, thus leading to improved positioning accuracy.
  • When the observation period is over three hours, the success rate of PPP ambiguity resolution can even reach 100.0%.
  • In the fixed solutions of short-period static PPP, over one hour of data are sufficient for the horizontal position components to achieve an accuracy of better than 1.0 cm while over three hours of data are still required for the vertical component to achieve such accuracy.
  • In addition, for degraded solutions, the accuracy degradation mainly and markedly occurred in the Up component.

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PERFORMANCE OF PRECISE POINT POSITIONING WITH
AMBIGUITY RESOLUTION FOR 1- TO 4-HOUR OBSERVATION
PERIODS
J. Geng, X. Meng, F. N. Teferle, A. H. Dodson
Institute of Engineering Surveying and Space Geodesy, University of Nottingham, UK
ABSTRACT
Recent progress in integer ambiguity resolution at a single station has made it possible to achieve high
positioning accuracy in static precise point positioning (PPP) using a short period of observations. In
this paper, 12 stations across Europe are used to conduct short-period (i.e. one, two, three and four
hours) static PPP with ambiguity resolution from Day 245 to 251 in 2007. It is demonstrated that, when
over three hours of observations are used, PPP can achieve a success rate of 100% for ambiguity
resolution, a 3D positioning accuracy of about 1.0 cm and an occurrence of less than 1.0% for
degraded solutions. Moreover, for the fixed solutions, increasing the observation period hardly
improves the horizontal positioning accuracy while still improving the vertical one. Therefore, it is
proposed that at least three hours of observations should be used in the ambiguity-fixed static PPP if a
reliable millimetre positioning accuracy is required in the engineering applications.
KEYWORDS. Precise point positioning. Ambiguity resolution. Short observation
period. GPS.
INTRODUCTION
During the past three decades, the development in the processing strategy for Global
Positioning System (GPS) measurements has led to the products of highly accurate
satellite orbits, satellite clocks, and Earth rotation parameters (ERP). The International
GNSS Service (IGS) and its Analysis Centres routinely generate these products which
are the basis for the development of precise point positioning (PPP) [28]. During the
PPP data processing, these products are employed to implement absolute and accurate
positioning at only one single station without any synchronous GPS observations from
the base stations. Thus PPP has become the foremost choice in some areas, such as off-
shore and desert areas, where a nearby base station is unavailable and its establishment
is difficult or not cost-effective.
It is well-known that PPP is capable of providing millimetre positioning accuracy in
the static mode using 24 hours of observations [15]. Nevertheless, such daily
observations are normally unavailable or impractical in most engineering applications
where rapid static positioning is usually required [17]. In practice, at most a few hours
of observing work are likely to be carried out in a field survey ([5], [7], [21]).
Consequently, the static positioning accuracy within such a short observation period
can hardly achieve millimetre level if PPP has to be applied to this field survey. For
instance, [13] and [23] reported that hourly position estimates in PPP could only
achieve sub-decimetre accuracy, and 4-hourly position estimates were at the level of
centimetre accuracy. On the contrary, static relative positioning can provide centimetre
accuracy using only 15 minutes of observations when double-difference ambiguity
resolution is applied to a baseline of a few tens of kilometres [17]. Hence, it can be
considered reasonable that integer ambiguity resolution in PPP is also able to
significantly improve the positioning accuracy within a short observation period.
However, to date, integer ambiguity resolution in PPP is largely ignored due to the
fact that the non-integer receiver- and satellite-dependent uncalibrated phase delays
(UPD) [1], which are related to hardware [8], are absorbed by the real-valued

ambiguity estimates, thus destroying the integer properties of the ambiguities ([8], [9]).
Fortunately, recent studies have revealed that integer ambiguity resolution at a single
station is possible if these UPD can be precisely determined in advance with a network
of base stations ([3], [9], [16]). [9] suggested that the fractional parts of the UPD
between satellites could be computed by averaging the fractional parts of all involved
real-valued ambiguity estimates. As a comparison, [3] and [16] used the satellite clock
estimates to assimilate the UPD by constraining the ambiguities at the base stations to
integer values. [4] showed that 90% of hourly horizontal position estimates were at the
level of 2-cm accuracy after integer ambiguity resolution. [11] and [12] showed that
through ambiguity resolution the hourly positioning accuracy could be improved from
3.8 cm, 1.5 cm and 2.8 cm in the float solutions to 0.5 cm, 0.5 cm and 1.4 cm in the
fixed solutions for the East, North and Up components, respectively.
This paper aims at comparing the performance of ambiguity-fixed static PPP with
different short observation periods (i.e. one, two, three and four hours), including the
efficiency and reliability of ambiguity resolution, the improvement of positioning
accuracy and the occurrence of degraded solutions. In the following sections, the
method adopted in this study for PPP ambiguity resolution is firstly introduced. Then
the efficiency and reliability of ambiguity resolution, the positioning accuracy and the
degraded solutions in short-period static PPP are presented and discussed.
DETERMINATION OF UNCALIBRATED PHASE DELAYS
In general, the one-way GPS observation equation for carrier phase data in the unit
of length from receiver
k
to satellite
i
is written as [9]
2
ii i
mk k m mk
m
Lb
f
κ
ρλ
= +
. (1)
where
m
denotes the frequency band with corresponding wavelength
m
λ
and
frequency
m
f
;
i
k
ρ
represents the non-dispersive delay, mainly including the geometric
distance, the receiver and satellite clocks and the tropospheric delay;
2
m
f
κ
denotes the
first order ionospheric delay, and the higher order delays are ignored;
ii i
mk mk mk m
bn
φφ
=+
in which
is the integer ambiguity,
mk
φ
is the receiver-
dependent UPD and
i
m
φ
is the satellite-dependent UPD, and thus
i
mk
b
is usually
recognized as a real-valued carrier phase bias term that is constant during its
corresponding observing session. For briefness, multipath effects and measurement
errors are not written explicitly in Equation 1.
For dual frequency data, the ionosphere-free combination observable is usually used
to eliminate the first order ionospheric delay. Its carrier phase bias term in the unit of
cycles reads
2
112
12
22 22
12 12
iii
ck k k
fff
bbb
ff ff
=
−−
(2)
which can be reformulated as
112
22
12 1 2
ii i
ck nk wk
fff
bb b
ff f f
=+
+
(3)
where
i
nk
b
is the narrow-lane (NL) carrier phase bias and
i
wk
b
is the wide-lane (WL)
one. To remove the receiver-dependent UPD, between-satellite differences (BSD) are
applied to the one-way ambiguity estimates at receiver
k
. Thus Equation 3 becomes

( ) ( )
,,, ,,
112
22
12 1 2
ij ij ij ij ij
ck nk n wk w
fff
bn n
ff f f
φφ
=+
+
(4)
where
,ij
n
φ
denotes the BSD NL UPD and
,ij
w
φ
denotes the BSD WL UPD. In the
following, ‘NL UPD’ denotes ‘BSD NL UPD’ and ‘WL UPD’ denotes ‘BSD WL UPD’
for briefness.
In this paper, the Melbourne-Wübbena combination observable ([19], [27]) is used to
determine the WL UPD. That is
,,,ij ij ij
wwkwk
bb
φ
⎡⎤
=
⎣⎦
(5)
where
denotes averaging over all involved stations;
[ ]
denotes the rounding
operation. It has been confirmed that daily mean WL UPD are quite stable over a
rather long period (e.g. at least several days to even several months) ([8], [9], [16]).
Once
,ij
w
φ
is determined,
,ij
wk
n
can then be fixed to an integer. Thus Equation 4
becomes
,, , , ,
2122
12 1 12
ij ij ij ij ij
nk n w ck wk
ffff
nbn
ff f ff
φφ
+
−− =
−−
(6)
The left side of this equation can be redefined as the difference between an integer part
,
()
ij
nw k
n
and a fractional part
,
()
ij
nw
φ
. In this paper
( )
,ij
nw
φ
is still called NL UPD which is
estimated using
( )
,,,,,
12 2 12 2
112 112
ij ij ij ij ij
ck wk ck wk
nw
ff f ff f
bn bn
fff fff
φ
⎡⎤
++
=+
⎢⎥
−−
⎣⎦
(7)
Unlike WL UPD, NL UPD are normally estimated within a short observation period,
such as 15 minutes, to obtain high estimation precisions [9]. However, [12] found that
the NL UPD are rather stable during each full pass of a satellite pair over a regional
network, and thus one NL UPD is estimated within one such pass. This strategy is also
adopted in this study.
AMBIGUITY RESOLUTION IN PPP
After the WL and NL UPD are determined precisely, WL and NL ambiguity
resolution at a single station can be implemented sequentially. The integer property of
a WL ambiguity is recovered using
,,,ij ij ij
wk wk w
nb
φ
=+
(8)
The WL ambiguity resolution follows the sequential bias fixing strategy [6]. If
,ij
wk
n
is
fixed to an integer successfully, then the integer property of its corresponding NL
ambiguity is recovered by
,,,,
12 2
() ()
112
ij ij ij ij
nw k ck wk nw
ff f
nbn
fff
φ
+
=+
(9)
Due to the high correlation between the ambiguities in the short-period PPP data
processing, a search strategy based on the LAMBDA (Least-squares AMBiguity De-
correlation Adjustment) method [24] is applied to conduct the NL ambiguity resolution.
For the ambiguity validation, two statistical tests are used, and the integer candidates
are accepted only when both tests are passed in this study. One test is based on the
compatibility between the unit variances of the fixed and float solutions ([14], [25]),
which is

( )
2
,;
2
11
fixed
mr t m
float
m
F
rt
α
σ
σ
−−
<+
(10)
where
r
is the number of observations,
m
is the number of ambiguity parameters and
t
is the number of the remaining parameters;
,;mr t m
F
α
−−
denotes the F-distribution of a
confidence level
α
with
m
and
rtm−−
degrees of freedom. Furthermore,
2
2
fixed float
float float
R
rtm
rt
σ
σ
Ω+
−−
=
−Ω
(11)
where
float
Ω
is the quadratic form of the residuals in the float solution;
( ) ( )
ˆ
ˆˆ
T
R =
-1
n
nn Q nn
((
in which
ˆ
n
denotes the real-valued ambiguity vector;
n
(
denotes the integer candidate vector and
ˆ
n
Q
denotes the variance-covariance matrix of
ˆ
n
[14]. Actually,
R
denotes the distance between
ˆ
n
and
n
(
under the metric of
ˆ
n
Q
,
and thus a smaller
R
indicates that the real-valued ambiguity estimates are more close
to the optimum integer candidates. In other words, a smaller
2
2
fixed
float
σ
σ
indicates a more
reliable ambiguity resolution.
However, in this study this test often failed even when correct integer ambiguities
were found, implying that the right side of Equation 10 might be too conservative. To
solve this problem, [25] suggested using more observations, but this is not feasible for
short-period static PPP. As a trade-off between maximizing the pass rate in the
ambiguity validation and minimizing the number of the incorrectly fixed solutions, a
critical value of 1.8, which was empirically determined in terms of all
2
2
fixed
float
σ
σ
estimates
derived from all solutions in this study, was set instead of the right side of Equation 10.
On the other hand, we also used the well-known ratio test which is generally defined
as the ratio of the second minimum quadratic form of the residuals to the minimum
quadratic form of the residuals for the fixed solution. It is used to discriminate between
the second optimum set of integer candidates and the optimum one. In this study, we
used
2
1
opt
opt
R
c
R
>
instead, where
1opt
R
and
2opt
R
correspond to the optimum and the
second optimum integer candidates, respectively [14]. Due to the unknown statistical
distribution of
2
1
opt
opt
R
R
([25], [26]), in this paper the critical criterion
c
is set to 3 which
is generally deemed as conservative in ambiguity validation [14]. The ratio value is
usually considered as an index of denoting the reliability of ambiguity resolution, and a
larger ratio value indicates a more reliable ambiguity resolution.
DATA AND MODELS
In this study, the PANDA (Positioning And Navigation Data Analyst) software [10],
originally developed at Wuhan University in China, is utilized to test short-period
static PPP with ambiguity resolution. It is a versatile tool for the scientific analysis of
GPS positioning and navigation data, and currently serves as a fundamental platform
for scientific studies in China and several international research centres.
Figure 1 shows a network of about 80 stations from the EUREF (European
Reference Frame) Permanent Network (EPN) [2] of which daily observations covering

Day 245 to 251 in 2007 were used to determine the WL and NL UPD. We also used
the final products of the satellite orbits and clocks, the ERP and the differential code
biases produced by CODE (Centre for Orbit Determination in Europe). Meanwhile, we
applied the absolute antenna phase centres, the phase wind-up corrections and the
station displacement conventions from the International Earth Rotation and Reference
System Service [18]. The elevation cut-off angle for usable data was seven degrees.
The estimated parameters included the positions, the receiver clocks, the zenith
tropospheric delays, the horizontal troposphere gradients and the ambiguities. All
stations that use cross-correlation receivers were excluded due to their relatively poor
pseudo-range quality [9].
Fig. 1. Station distribution. The solid circles denote the EPN stations used for the determination of uncalibrated
phase delays (UPD) whilst the solid triangles with names aside denote the IGS stations for testing the short-period
static PPP with ambiguity resolution
In order to assess the performance of ambiguity resolution when utilizing these
regional UPD estimates, we selected 12 stations from the IGS network (Figure 1)
which were not used for the UPD determination to conduct short-period static PPP
from Day 245 to 251 in 2007. Hence, there were 168 hourly, 84 2-hourly, 56 3-hourly
and 42 4-hourly solutions for each station if there were no large data gaps. We
removed the solutions when the data gaps are longer than half of the required
observation period, or when less than five satellites were available during more than
half of the required observation period. The 12 stations were distributed evenly within
the coverage of the EPN. The models adopted at these stations were the same as those
for the EPN stations except for the horizontal troposphere gradients, which cannot be

Citations
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Journal ArticleDOI
TL;DR: In this article, the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent and only they are assimilated into the clocks and ambiguities is established.
Abstract: Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a network solution. One method to achieve these products is to estimate the FCBs by averaging the fractional parts of the float ambiguity estimates, and the other is to estimate the integer-recovery clocks by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent and only they are assimilated into the clocks and ambiguities. To verify this equivalence, we implement both methods in the Position and Navigation Data Analyst software to process 1 year of GPS data from a global network of about 350 stations. The mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively. Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of the position estimates minus those from the International GNSS Service weekly solutions for the former method differs by below 0.1 mm on average for each component from that for the latter method. Therefore, considering the recognized millimeter-level precision of current GPS-derived daily positions, these statistics empirically demonstrate the theoretical equivalence of the ambiguity-fixed position estimates derived from these two methods. In practice, we note that the former method is compatible with current official clock-generation methods, whereas the latter method is not, but can potentially lead to slightly better positioning quality.

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Abstract: The Integration of TLS and Continuous GPS to Study Landslide Deformation: A Case Study in Puerto Rico Terrestrial Laser Scanning (TLS) and Global Positioning System (GPS) technologies provide comprehensive information on ground surface deformation in both spatial and temporal domains. These two data sets are critical inputs for geometric and kinematic modeling of landslides. This paper demonstrates an integrated approach in the application of TLS and continuous GPS (CGPS) data sets to the study of an active landslide on a steep mountain slope in the El Yunque National Forest in Puerto Rico. Major displacements of this landslide in 2004 and 2005 caused the closing of one of three remaining access roads to the national forest. A retaining wall was constructed in 2009 to restrain the landslide and allow the road reopen. However, renewed displacements of the landslide in the first half of 2010 resulted in deformation and the eventual rupture of the retaining wall. Continuous GPS monitoring and two TLS campaigns were performed on the lower portion of the landslide over a three-month period from May to August 2010. The TLS data sets identified the limits and total volume of themoving mass, while the GPS data quantified the magnitude and direction of the displacements. A continuous heavy rainfall in late July 2010 triggered a rapid 2-3 meter displacement of the landslide that finally ruptured the retaining wall. The displacement time series of the rapid displacement is modeled using a fling-step pulse from which precise velocity and acceleration time series of the displacement are derived. The data acquired in this study have demonstrated the effectiveness and power of the integrating TLS and continuous GPS techniques for landslide studies.

41 citations


Additional excerpts

  • ...…GPS landslide monitoring in Puerto Rico (Wang 2010) and other empirical studies about the precision of GPS (Eckl et al., 2001; Soler et al., 2006; Geng et al., 2010; Firuzabadi and King, 2010), both 8-hour session static and 1-hour session rapid static GPS can provide sub-centimeter precision…...

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References
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Journal ArticleDOI
TL;DR: This work determines precise GPS satellite positions and clock corrections from a globally distributed network of GPS receivers, and analysis of data from hundreds to thousands of sites every day with 40-Mflop computers yields results comparable in quality to the simultaneous analysis of all data.
Abstract: Networks of dozens to hundreds of permanently operating precision Global Positioning System (GPS) receivers are emerging at spatial scales that range from 10(exp 0) to 10(exp 3) km. To keep the computational burden associated with the analysis of such data economically feasible, one approach is to first determine precise GPS satellite positions and clock corrections from a globally distributed network of GPS receivers. Their, data from the local network are analyzed by estimating receiver- specific parameters with receiver-specific data satellite parameters are held fixed at their values determined in the global solution. This "precise point positioning" allows analysis of data from hundreds to thousands of sites every (lay with 40-Mflop computers, with results comparable in quality to the simultaneous analysis of all data. The reference frames for the global and network solutions can be free of distortion imposed by erroneous fiducial constraints on any sites.

3,013 citations


"Performance of Precise Point Positi..." refers background in this paper

  • ...The International GNSS Service (IGS) and its Analysis Centres routinely generate these products which are the basis for the development of precise point positioning (PPP) [28]....

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Journal ArticleDOI
TL;DR: In this article, the authors developed expressions for calculating the ratios (mapping functions) of the "line of sight" hydrostatic and wet atmospheric path delays to their corresponding zenith delays at radio wavelengths for elevation angles down to 3°.
Abstract: I have developed expressions for calculating the ratios (mapping functions) of the “line of sight” hydrostatic and wet atmospheric path delays to their corresponding zenith delays at radio wavelengths for elevation angles down to 3°. The coefficients of the continued fraction representation of the hydrostatic mapping function depend on the latitude and height above sea level of the observing site and on the day of the year; the dependence of the wet mapping function is only on the site latitude. By comparing with mapping functions calculated from radiosonde profiles for sites at latitudes between 43°S and 75°N, the hydrostatic mapping function is seen to be more accurate than, and of comparable precision to, mapping functions currently in use, which are parameterized in terms of local surface meteorology. When the new mapping functions are used in the analysis of geodetic very long baseline interferometry (VLBI) data, the estimated lengths of baselines up to 10,400 km long change by less than 5 mm as the minimum elevation of included data is reduced from 12° to 3°. The independence of the new mapping functions from surface meteorology, while having comparable accuracy and precision to those that require such input, makes them particularly valuable for those situations where surface meteorology data are not available.

1,499 citations


"Performance of Precise Point Positi..." refers background in this paper

  • ...Parameters Models & a priori constraints Static position 1 metre for each component Receiver clock White noise, 9000 metres Zenith tropospheric delay Constant within each hour, 20 cm, Niell mapping function [20] Ambiguity 10000 cycles...

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Journal ArticleDOI
TL;DR: This paper will describe the approach, summarize the adjustment procedure, and specify the earth- and space-based models that must be implemented to achieve cm-level positioning in static mode and station tropospheric zenth path delays with cm precision.
Abstract: The contribution details a post-processing approach that used undifferentiated dual-frequency pseudorange and carrier phase observations along with IGS procise orbit products, for stand-alone precise geodetic point positioning (static or kinematic) with cm precision. This is possible if one takes advantage of the satellite clock estimates available with the satellite coordinates in the IGS precise orbit products and models systematic effects that cause cm variations in the satelite to user range. This paper will describe the approach, summarize the adjustment procedure, and specify the earth- and space-based models that must be implementetd to achieve cm-level positioning in static mode. Furthermore, station tropospheric zenth path delays with cm precision and GPS receiver clock estimates procise to 0.1 ns are also obtained. © 2001 John Wiley & Sons, Inc.

1,200 citations


"Performance of Precise Point Positi..." refers methods in this paper

  • ...It is well-known that PPP is capable of providing millimetre positioning accuracy in the static mode using 24 hours of observations [15]....

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Journal ArticleDOI
Maorong Ge, Gerd Gendt, Markus Rothacher, Chuang Shi1, Jingbin Liu1 
TL;DR: It is shown that UPDs are rather stable in time and space, and can be estimated with high accuracy and reliability through a statistical analysis of the ambiguities estimated from a reference network.
Abstract: Precise Point Positioning (PPP) has been demonstrated to be a powerful tool in geodetic and geodynamic applications. Although its accuracy is almost comparable with network solutions, the east component of the PPP results is still to be improved by integer ambiguity fixing, which is, up to now, prevented by the presence of the uncalibrated phase delays (UPD) originating in the receivers and satellites. In this paper, it is shown that UPDs are rather stable in time and space, and can be estimated with high accuracy and reliability through a statistical analysis of the ambiguities estimated from a reference network. An approach is implemented to estimate the fractional parts of the single-difference (SD) UPDs between satellites in wide- and narrow-lane from a global reference network. By applying the obtained SD-UPDs as corrections to the SD-ambiguities at a single station, the corrected SD-ambiguities have a naturally integer feature and can therefore be fixed to integer values as usually done for the double-difference ones in the network mode. With data collected at 450 stations of the International GNSS Service (IGS) through days 106 to 119 in 2006, the efficiency of the presented ambiguity-fixing strategy is validated using IGS Final products. On average, more than 80% of the independent ambiguities could be fixed reliably, which leads to an improvement of about 27% in the repeatability and 30% in the agreement with the IGS weekly solutions for the east component of station coordinates, compared with the real-valued solutions.

741 citations


"Performance of Precise Point Positi..." refers background or methods in this paper

  • ...Unlike WL UPD, NL UPD are normally estimated within a short observation period, such as 15 minutes, to obtain high estimation precisions [9]....

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  • ...[9] suggested that the fractional parts of the UPD between satellites could be computed by averaging the fractional parts of all involved real-valued ambiguity estimates....

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  • ...156 ambiguity estimates, thus destroying the integer properties of the ambiguities ([8], [9])....

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  • ...All stations that use cross-correlation receivers were excluded due to their relatively poor pseudo-range quality [9]....

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  • ...at least several days to even several months) ([8], [9], [16])....

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Journal ArticleDOI
TL;DR: In this article, a technique for resolving the ambiguities in the GPS carrier phase data (which are biased by an integer number of cycles) is described which can be applied to geodetic baselines up to 2000 km in length and can be used with dual-frequency P code receivers.
Abstract: A technique for resolving the ambiguities in the GPS carrier phase data (which are biased by an integer number of cycles) is described which can be applied to geodetic baselines up to 2000 km in length and can be used with dual-frequency P code receivers. The results of such application demonstrated that a factor of 3 improvement in baseline accuracy could be obtained, giving centimeter-level agreement with coordinates inferred by very-long-baseline interferometry in the western United States. It was found that a method using pseudorange data is more reliable than one using ionospheric constraints for baselines longer than 200 km. It is recommended that future GPS networks have a wide spectrum of baseline lengths (ranging from baselines shorter than 100 km to those longer than 1000 km) and that GPS receivers be used which can acquire dual-frequency P code data.

578 citations


"Performance of Precise Point Positi..." refers background in this paper

  • ...However, to date, integer ambiguity resolution in PPP is largely ignored due to the fact that the non-integer receiver- and satellite-dependent uncalibrated phase delays (UPD) [1], which are related to hardware [8], are absorbed by the real-valued...

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Frequently Asked Questions (1)
Q1. What have the authors contributed in "Performance of precise point positioning with ambiguity resolution for 1- to 4-hour observation periods" ?

In this paper, 12 stations across Europe are used to conduct short-period ( i. e. one, two, three and four hours ) static PPP with ambiguity resolution from Day 245 to 251 in 2007.