Journal of Geodetic
Science
• 3(1) • 2013 • 22-31 DOI: 10.2478/jogs-2013-0001 •
Millimeter-accuracy GPS landslide monitoring using Precise Point Positioning with Single Receiver Phase Ambiguity (PPP-SRPA) resolution: a case study in Puerto Rico Research Article G. Q. Wang∗
Department of Earth and Atmospheric Sciences, National Center for Airborne Laser Mapping, University of Houston, Houston, TX 77004
Abstract: Continuous Global Positioning System (GPS) monitoring is essential for establishing the rate and pattern of super cial movements of landslides. This study demonstrates a technique which uses a stand-alone GPS station to conduct millimeter-accuracy landslide monitoring. The Precise Point Positioning with Single Receiver Phase Ambiguity (PPP-SRPA) resolution employed by the GIPSY/OASIS software package (V6.1.2) was applied in this study. Two-years of continuous GPS data collected at a creeping landslide were used to evaluate the accuracy of the PPP-SRPA solutions. The criterion for accuracy was the root-mean-square (RMS) of residuals of the PPP-SRPA solutions with respect to “true” landslide displacements over the two-year period. RMS is often regarded as repeatability or precision in GPS literature. However, when contrasted with a known ”true” position or displacement it could be termed RMS accuracy or simply accuracy. This study indicated that the PPP-SRPA resolution can provide an accuracy of 2 to 3 mm horizontally and 8 mm vertically for 24-hour sessions with few outliers (< 1%) in the Puerto Rico region. Horizontal accuracy below 5 mm can be stably achieved with 4-hour or longer sessions if avoiding the collection of data during extreme weather conditions. Vertical accuracy below 10 mm can be achieved with 8-hour or longer sessions. This study indicates that the PPP-SRPA resolution is competitive with the conventional carrier-phase double-difference network resolution for static (longer than 4 hours) landslide monitoring while maintaining many advantages. It is evident that the PPP-SRPA method would become an attractive alternative to the conventional carrier-phase double-difference method for landslide monitoring, notably in remote areas or developing countries. Keywords: accuracy • GPS • landslide monitoring • precise point positioning • single receiver phase ambiguity © Versita sp. z o.o. Received 24-09-2012; accepted 12-12-2012
landslide kinematics is a basic requirement for studying landslide mechanisms and minimizing landslide hazards. Tracking super -
1. Introduction
Landslides occur in signi cant numbers throughout the world. In the U.S., landslides account for over $ 3 billion of property loss, as
cial displacements is one of the most direct and efficient ways to study kinematics of landslides and predict a potential hazard. In the past two decades, Global Positioning System (GPS) technolo-
well as an estimated 25 to 50 deaths annually (Schuster and Highland, 2001; Spiker and Gori, 2003). The costs of landslides are in-
gies have been frequently applied to landslide studies, both as a complement, and an alternative to conventional surveying meth-
creasing rapidly as lands susceptible to failure are growing due to highway, housing, industry, and recreational use. Knowledge of
ods (e.g., Bruckl et al., 2006; Psimoulis et al. 2007; Tagliavini et al. 2007; Peyret et al. 2008; Hastaoglu and Sali, 2011; Wang et al., 2011;
∗
E-mail:
[email protected]
Wang 2012). These studies have demonstrated that high-accuracy GPS techniques are an efficient tool in landslide study. Compared
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with conventional surveying techniques, GPS techniques generally increase survey accuracy, productivity, and monitoring capability,
ential method. Displacement measurements accurate to the submillimeter level can be achieved using the differential method with
in addition to reducing cost.
short baselines (e.g., Clark Hughes et al., 2006; Wang 2012). The pri-
Surveying-level GPS units record satellite signals and do not di-
mary disadvantage of the differential method is the requirement to have at least two receivers, even for a single user who only requires
rectly provide high-precision positions. Complex calculations are required to achieve high-precision positioning in order to obtain centimeter- or millimeter-accuracy displacement measurements. GPS data processing algorithms generally implement two approaches to achieve high-precision GPS positioning measurements, relative positioning and absolute positioning. The relative positioning approach uses simultaneous observations from two or more GPS receivers; at least one of these receivers is in a known location within a speci c reference frame. The position of a new station can be determined relative to a single or multiple reference stations by applying a so-called carrier- phase double-difference method, which xes between-station and between-satellite differenced phase bias ambiguities to integer values. The relative method is also called differential method. Since common errors decrease with the shorting of the distance between the rover and reference station, the success of the differential method is highly dependent on the length of their baseline (e.g., HofmannWellenhof et al., 2001; Leick, 2003; Soler et al., 2006; Wang 2011). The absolute positioning approach solves for the position of a single GPS station using precise satellite ephemeris and clock information, without using any synchronous observations from other ground GPS stations. Precise Point Positioning (PPP) is a typical absolute positioning method using un-differenced dual-frequency pseudo-range and carrier-phase observations along with precise satellite orbit and clock information to determine the position of a stand-alone GPS station (e.g., Goad, 1985; Zumberge et al., 1997; Kouba and Springer, 2001; Ray et al., 2004; Kouba, 2005). The theoretical foundation of PPP is documented in Zumberge et al. (1997). PPP has attracted broad interest because of its operational simplicity. The PPP method has been integrated into several scienti c GPS software packages, such as the GIPSY/OASIS software developed by Jet Propulsion Laboratory (JPL) (Blewitt, 1989; Webb and Zumberge 1997) and the Bernese GPS software (V5.0 or higher) developed by Astronomical Institute of the University of Berne (Hugentobler et al. 2006; Dach et al., 2007; Teferle et al., 2007). PPP has become the foremost choice for positioning in many remote areas, in which nearby base stations are unavailable, or the establishment
his or her own location. Unlike the differential method where most GPS errors and biases are essentially cancelled, all errors and biases must be rigorously modeled in PPP processing. The PPP technique takes advantage of accurate satellite orbit and clock products obtained from the global infrastructure of permanent stations. In general, PPP resolution provides slightly less accurate results than a carefully designed differential network resolution, particularly in the east-west (EW) component (e.g., Ebner and Featherstone, 2008; Grinter and Roberts, 2011; Grinter and Janssen, 2012). As a result, the carrier-phase double-difference based GPS techniques have been dominantly used in high- accuracy surveying applications, while PPP is often considered a useful “ ll-in” method for GPS data processing in areas where a local continuous GPS network is not available and it is too costly to install temporary reference stations. In GPS positioning, resolving the integer cycle ambiguity in the carrier-phase data can signi cantly improve positioning accuracy, particularly in the EW component for equatorial to middle-latitude stations (Blewitt, 1989). During the past few years, several studies have revealed that xing integer ambiguity at a single GPS station is possible if the hardware related phase biases can be precisely determined in advance in a network of ground stations (e.g., Ge et al., 2007; Laurichesse and Mercier, 2007; Ge et al., 2008; Collins, 2008; Laurichesse et al., 2009; Geng et al., 2009; Geng et al., 2010a; Geng et al., 2010b). Bertiger et al. (2010) introduced an approach to perform ambiguity-resolved PPP resolution using the wide lane and phase bias (WLPB) estimates obtained from a global network of ground GPS stations. This method had been implemented into the GIPSY/OASIS software package (Version 5.2 or higher). GIPSY/OASIS users can produce an ambiguity-resolved point-positioning solution for a single receiver by using the wide lane and phase bias information provided by JPL. Bertiger et al. (2010) showed that daily accuracy (repeatability) improved by 1030% compared to the conventional PPP resolution, particularly in the EW component. Daily repeatability of 2.1 mm, 1.9 mm, and 6.0 mm in the north-south (NS), east-west (EW), and up-down (UD)
of base stations is difficult or not cost-effective.
components, respectively, were achieved in their study (Bertiger et al., 2010). Thus the PPP with Single Receiver Phase Ambiguity (PPP-
GPS landslide surveys, as well as other engineering surveys that requires centimeter or higher accuracy, have traditionally been
SRPA) method would offer a great opportunity to conduct highly accurate landslide monitoring with a stand-alone GPS unit by a sin-
carried out using the differential positioning method. This is mainly due to the higher accuracy obtained with the carrier-phase
gle eld crew. To test this idea, we processed two-year continuous GPS data recorded at a creeping landslide in Puerto Rico using the
double-difference resolution compared to the PPP resolution. The
PPP-SRPA method employed in the GIPSY/OASSIS (V6.1.2) software package. Final satellite orbits and clocks provided by International
differential techniques inherit high accuracy from the fact that closely-spaced GPS receivers share the same errors and biases. The
GNSS Service (IGS) (Dow et al., 2009) and wide lane and phase bias
shorter the receiver separation (baseline), the more similar the errors and biases will be. As such, for those receivers, a major part
estimates provided by the Jet Propulsion Laboratory (JPL) (Bertiger et al., 2010) were used in this study. Major parameters estimated
of the GPS error budget can be removed by applying the differ-
and key models applied in static positioning for this study include
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Journal of Geodetic
Science
VMF1 troposphere mapping model (Boehm et al., 2006), second order ionospheric delay (Kedar et al., 2003), ocean tidal loading FES2004 (http://www.oso.chalmers.se/~loading), tro-
20˚ Dominican
pospheric gradients (Bar-Sever et al., 1998), zenith troposphere delay as a random walk with variance of 5.0x10−8 m/sqrt(h), gra-
Republic
Puerto Rico
dient troposphere wet delay as a random walk with variance of 5.0x10−9 m/sqrt(h), receiver clock as white noise with updates every measurement epoch, and minimum elevation cutoff of 7 degrees.
Virgin Islands
16˚
Ponce Landslide
2. The Ponce, Puerto Rico landslide Puerto Rico is located in the northeastern Caribbean Sea, east of
−72˚
−68˚
−64˚
the Dominican Republic and west of the Virgin Islands. Mountainous terrain and a tropical climate make this island one of the most landslide-prone areas in the United States (Jibson, 1986, 1989). This study used continuous GPS data recorded at an active landslide site in Ponce, Puerto Rico. The location of Puerto Rico and the landslide are shown in Fig. 1. The landslide spanned approximately 300 m from head to toe, and 30 m across the head area and extending to 150-m wide near the toe. It began to creep in the summer of 2007, and destroyed 10 houses over time. In addition, 15 houses near the margins had to be abandoned (Wang, 2012). The sliding mass cut through the sole access road to the community, as well as the utility pipes under the road. A permanent GPS station (PONC) was installed on a two- oor building within the affected landsurface in May 2009. A reference GPS station was installed on the roof of a single-story building outside the sliding mass. The baseline length was 130 m. Both the landslide GPS (PONC) and the reference GPS stations were equipped with Trimble NetRS receivers and choke ring antennas from June 1, 2009 to September 3, 2010. The rover GPS was changed to a Trimble NetR8 receiver and a Zephyr Geodetic antenna. The reference GPS was changed to a Topcon GB 1000 receiver and a PG-A1 antenna with ground plane after September 4, 2010. AC power was available at both sites. Continuous observations ranging from June 1, 2009 to May 31, 2011 were used in this study. Our GPS monitoring indicates that the landslide movement was dominated by local precipitation (Wang 2011, Wang 2012). The accumulated displacements during the two years were up to 20 cm, 27 cm, and 15 cm in NS, EW, and
Figure 1.
Map showing the location of the Ponce, Puerto Rico landslide and the locations of 6 continuous operating reference GPS stations used in carrier-phase double-difference network processing.
line (130 m) achieved sub-millimeter accuracy for all three components (NS-0.4 mm, EW-0.5 mm, UD-0.9 mm). In this study, the displacement time series derived from the short-baseline doubledifference method were regarded as “true” landslide displacements since their achieved sub-millimeter accuracy. The differences (residuals) between the PPP-SRPA results and the “true” landslide displacements were assessed statistically. Consequently, the term “accuracy” rather than “precision” is used in assessing the landslide displacements derived from the PPP solutions. In evaluating the accuracy of the PPP-SRPA solutions, a twocriterion approach for identifying and removing outliers developed from Firuzabadi and King (2011) and Wang (2011) was applied component by component in this study. The rst step is to identify and remove those PPP-SRPA results whose uncertainties are 2 times larger than the average uncertainties of all measurements of this component (about 700 samples). This criterion serves to exclude poor measurements due to loss of data, signi cant multipath effects, large wet tropospheric delay, or failure to resolve inter-cycle phase ambiguities. The second step is to overlap the displacement time series derived from the PPP-SRPA method
UD directions, respectively (Wang and Soler, 2012).
and the true displacement time series by applying a least-square adjusting approach, which leads to a minimal root-mean-square
3. True landslide displacements and criteria for removing outliers
(RMS) of the residual time series. The third step is to identify and remove those positions whose residuals are 3 times larger than the
Figure 2 illustrates the three-component landslide displacement time series derived from the landslide GPS (PONC) over a two-
RMS of all residuals. The residual cutoff services to avoid biasing the statistical results with the presence of a small number of out-
year period from June 1, 2009 to May 31, 2011. The black points represent daily positions of the GPS antenna related to the refer-
liers for which the reasons are not well known. We found that the outliers were dominated by the rst category, which constituted
ence GPS, 130 meters away. The relative positions were resolved
about 85% of the total outliers. Our previous study indicated that
by using the carrier-phase double-difference method implicit in the GAMIT software package developed at Massachusetts Insti-
the choice of the threshold (ratio) used in identifying outliers may slightly affect the numbers of outliers. However, the effect on nal
tute of Technology (Herring et al., 2009). The red points represent PPP-SRPA solutions. A previous study (Wang 2011) indicated
RMS is minor since the statistics are based on more than 700 samples (2-years data) (Wang 2011). After removing all outliers, the dis-
that the double differencing method with an extremely short base-
placement time series derived from the PPP-SRPA method and the
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PPP vs. PPP-SRPA
Landslide Displacements Measured by GPS
2
0 -5
4-h session: 8:00-12:00 a.m. (local time) Accuracy (RMS, mm)--NS,EW,UD
0
PPP: 5.0, 13.8, 18.8 PPP-SRPA: 5.0, 5.4, 16.0
-10
NS (cm)
.NS (cm)
Science
PPP-SRPA
-15
(RMS-mm: NS-2.9, EW-2.3, UD-8.1)
True Dis. (single base, 130 m)
-20
(RMS-mm: NS-0.4, EW-0.5, UD-0.9)
-2 -4
-25
EM (cm)
20
-8
15
2009.6
2009.8
2010
2010.2
2010.4
2009.6
2009.8
2010
2010.2
2010.4
2009.6
2009.8 2010 2010.2 Decimal Year
2010.4
10
6
5
EW (cm)
0 5
UD (cm)
PPP PPP-SRPA
-6
25
0
4 2
-5
0
-10 -15 -20
-2 2009.5
2010
2010.5
2011
2011.5
Decimal Year (6/1/2009-5/31/2011)
Landslide displacement time series (red dots) in three directions (NS: north-south, EW: east-west, and UD: updown) derived from the Precise Point Positioning with Single Receiver Phase Ambiguity (PPP-SRPA) solutions. The dark dots illustrate the “true” landslide displacement time series derived from single-baseline (130 m) carrier-phase double-difference solutions.
UD (cm)
Figure 2.
0
-5
-10
true displacement time series were re-overlapped and the RMS of the residual time series was re-calculated. The nal RMS value was regarded as “accuracy” in this article. Table 1 lists the percent of outliers and the RMS accuracy of the PPP-SRPA solutions for different sessions used in this study. 4. Accuracy of PPP resolution
Figure 3.
Comparisons of landslide displacement time series for a 4-hour session (8:00 a.m.- 12:00 a.m.) derived from the conventional Precise Point Positioning (PPP) resolution and the PPP with Single Receiver Phase Ambiguity (PPPSRPA) resolution.
Figure 3 compares the conventional PPP solutions and the PPPSRPA solutions for a 4-hour session (8:00 a.m.-12:00 p.m.) of the two-year data. It appears that the PPP-SRPA method doubled the
The highest accuracy was achieved during the early morning ses-
accuracy of the EW component and slightly improved the accuracy of the UD component compared to the conventional PPP
sions (local time 0:00 a.m.-4:00 a.m., 4:00 a.m.-8:00 a.m.), which experienced the least amount of rainfall, while the lowest accuracy
method. However, there was no considerable improvement with regard to the accuracy of the NS component. Figure 4a illus-
was achieved during the early afternoon session (12:00 p.m.-4:00 p.m.), which experienced the largest amount of rainfall. Local thun-
trates 2-year accumulated precipitation within 1-h and 4-h win-
derstorms and heavy rainfall are very frequent in early afternoon
dows over a 24-hour period recorded at a local USGS weather station (USGS50115230). Figure 4b illustrates the RMS accuracy of the
throughout the year in the tropical region, particularly in summer months. Heavy rainfall accompanied by thunderstorms and the
PPP-SRPA solutions corresponding to these six 4-hour windows. Figure 4 indicates that the variation of RMS accuracy during a 24-
passage of weather fronts can cause signi cant temporal and spatial variation in atmospheric water vapor impacting the propaga-
hour period was coincident with the variation of local precipitation.
tion of GPS signals (e.g., Rocken et al., 1995; Dodson et al., 1996;
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Journal of Geodetic
26
Table 1.
Science
Outliers and Accuracy of precise point positioning with single receiver phase ambiguity (PPP-SRPA) resolution
Sessions Duration Local Time
Outliers (Total 700 samples) Accuracy (RMS, mm) V/H NS EW UD NS EW UD
24 Hours 0h-24h 12 Hours 00AM-12AM 11 Hours 00AM-11AM 10 Hours 00AM-10AM 9 Hours 00AM-9AM 8 Hours 04AM-12AM 7 Hours 04AM-11AM 6 Hours 04AM-10AM 5 Hours 04AM-09AM 4 Hours 08AM-12PM 4 Hours 00AM-04AM 4 Hours 04AM-08AM 4 Hours 08AM-12AM 4 Hours 12AM-04PM 4 Hours 04PM-08PM 4-Hour Ave. 3 Hours 08AM-11AM 2 Hours 08AM-10AM 1.5 Hours 08AM-9:30AM 1 Hours 08AM-09AM
