Hamid Reza Nankali
National Cartographic Center Of Iran(Research-Institute)
Dept of Geodesy and Geodynamics
Email: [email protected]
Global Positioning System (GPS) , which is a world-wide precise positioning system has become a popular and very useful device for geodetic survey and crystal deformation observation such as velocity filed of tectonic plate and station coordinates and their velocities.
For precise measurements, differential positioning technique is used. Two antenna located a part , receive the signals data simultaneously and the collected datasets are processed together in order to obtain relative location between to observation points. To keep the computational burden associated with the such data feasible, one technique is to determine precise ephemerid from a global distributed network(IGS). Then data from local network are analyzed by estimating receiver parameters, satellite parameter are held fix (precise ephemerid). This Precise Point Positioning(PPP) is simple and very efficient method that must be applied with dual frequency receivers and 24h observation and independent of base station and the reference frame cab be free of distortion imposed by erroneous fiducially constraint on any sites. This paper outlines the use of PPP for processing GPS data(advantages-and disadvantages)with Bernese V5 software and compare the results with relative positioning in the same point of Iranian permanent GPS observation network for crusal deformation monitoring that process with Gamit/Globk software in relative mode.
Since the inception of the Global Positioning System during the late 1970s, relative processing has dominated the filed of GPS data processing. In fact, until quite recently, it would be true to say that relative processing had a monopoly on precision GPS processing. This all changed during the late 1990s when some competition entered the market place in the form of Precise Point Positioning (PPP).
This new technique promises precisions comparable to those achievable from relative processing. The question you might be asking at this point is : ” How is this possible?” In order to answer this question. I processed the data of IPGN(Iranian Permanent GPS Observation Network) for crustal deformation monitoring and compare the results with those obtained by Gamit/Globk in relative mode. IPGN consist of 107 permanent GPS station that equipped with precise dual frequency receivers and setup in active part of the country since 2005. Fig 1
Fig 1- Iranian Permanent GPS Network
The’ relative’ part of relative processing suggests that more than one receiver is required and indeed this is the case. The minimum configuration for the determination of precise coordinates for one new point is of course two receivers. However, in order to obtain precise coordinates for a point from GPS data, a number of nuisance parameters first need to be removed from the data.
These may be classified as satellite’ errors’ atmospheric ‘errors’ and receiver’errorss’.
Satellite errors include errors in the reported satellite coordinates and satellite clocks, atmospheric errors include signal delays due to the troposphere and ionosphere while receiver errors include receiver clock errors. Let us consider for a moment how each of these errors might be removed or mitigated. Troposphere errors are largely removed by either applying a model which attempts to mathematically simulate the signal delay as in most commercial software or by estimating the signal troposphere delay along with the receiver coordinates(as in most research software). Ionosphere errors are removed by observing both GPS frequencies(L1 and L2) and combining the two observations to derive an ionosphere-free observation. Errors in satellite positions can be reduced by using precise satellite orbits available from the IGS and any remaining error(except multipath) largely cancels over short distances. That leaves satellite and receiver clock errors as the dominant errors to be death with and this is where relative positioning comes to the fore.
Precise Point Positioning
The vast majority of commercially available software utilizes the principles of relative positioning. However ,in the late 1990s, the Jet Propulsion Laboratory (NASA) pioneered a new technique that did not require differencing to obtain precise position. The labeled it Precise Point Positioning (PPP) and implemented it in their, GIPSY/OASIS II GPS processing software .(Zumberg, webb etal. 1997) The largest difference between relative processing and PPP is the way that the satellite and receiver clock errors are handled. Instead of between-receiver differencing to remove the satellite clock errors, PPP uses highly precise satellite clock estimates.
These satellite clock estimates are derived from a solution using data from a globally distributed network of GPS receivers. Instead of between –satellite differencing to remove receiver clock error, PPP estiamates theses as part of the least squares solution for the coordinates.
Consequently, precise absolute coordinates for a single receiver at an unknown location may be obtained without the need of a second receiver at a known location may by obtained without the need of a second receiver at a known location.
A note of caution at this point is necessary. It may be possible to get PPP confused with another from a point positioning that many GPS users will be familiar with i.e, Single Point Positioning(SPP). SPP is different to PPP in two ways. Firstly SPP does not use precise satellite clock values and secondly., only the pseudo rage observations are used. PPP uses both the pseudo range and more precise carrier phase observations.
The difference between these methods in terms of coordinate accuracy is larger; SPP producers coordinates accurate at the 1-3 m level while PPP can produce coordinates accurate at the 0.01 m level with 24hours observations.
Consequently, PPP allows coordinate determination with a precision that is comparable to relative processing.
Since no base station is required in PPP, a further question is:” what datum are the coordinates in?” For PPP , the datum is hidden in the satellite coordinates-the satellite reference frame(datum) will be the unknown ground site reference frame. This means that to obtain coordinates in a different reference frame the user needs to perform a usually straight forward coordinate transformation.
GPS Observable and PPP
The basic GPS observables used for estimating position, velocity and time are:
Pseudo range; and Carrier phase or difference of carrier phase. Precise point positioning(PPP), together with relative position, provides a significant contribution to geodynamic applications. One of the advantages of PPP is that positions are independently derived, whereas in relative positioning, an error in the base station coordinates would translate into the other stations. In PPP, dual-frequency data is essential. Therefore, there are two observation equations , for both pseudo range and carrier phase. Considering a stationA and satellite J, the linearized observations can be written as(Monico and perez, 2001: Monical 2000a):
This procedure involve four observables for each of the visible satellites in each epoch. The two pseudo range and carrier phase observables can be linearly combined, thus reducing the effects of the ionosphere refraction. The use of a troposphere model, together with parameterization techniques, can reduce the troposphere refraction effects. The IGS ephemerids supply satellite coordinates and clock errors, with accuracy in the order of 5cm and 0.3 ns, respectively, and are essential in PPP. However, variations due to geophysical phenomena should be removed using appropriate models. These corrections include (McCarthy,1996). Polar motion;
Earth body tides and ocean tide loading.
According to Zumberge et al. (1997), with PPP it is possible to obtain precision of a few millimeters and a few centimeters in the horizontal and vertical components, respectively. Such levels of accuracy can be obtained for static point position, using a period of 24 hors of data (Monico and Perez, 2001; Monico 2000a).
Once the coordinates for all stations are daily estimated using PPP, a solution for a specific epoch/can be obtained , As there is no correlation between the coordinates of different stations, such a solution may be obtained indepenendetly for each station.
The Bernese GPS Software was developed at the Astronomical Institute University of Berne (AIUB),Switzerland, in the late 1980s and is widely used around the world. The Center for Orbit Determination(CODE) analysis centre at the AIUB uses the Bernese GPS software for the analysis of the global IGS network. The software is particularly well suited for the rapid processing of small-size single and dual frequency surveys, permanent network processing, ambiguity resolution on long baselines, ionosphere and troposphere modeling, clock estimation and time transfer, combination of different receiver types, simulation studies, orbit determination and estimation of Earth rotation parameters and the generation of so –called free network solutions. In may 2004, the latest version of Bernese GPS software, version5.0, was released.
The Bernese GPS software Versions 4.2(BSW4.2) and 5(BSW5.0) are primarily focused on processing double-differenced GPS observations, however, since Version 4.2, it is also possible to carry out undifference processing, which allows precise point positioning(PPP) to be carried out.
Bernese GPS software Version 5.0 in PPP mode
The combined IGS final orbits are obtained from the individual IGS analysis center minimum constraint solutions. As a consequence of this the implied IGS orbit origin may be offset from the real geo center by up to 10mm. Therefore, when using IGS final products for PPP, the obtained daily coordinate solutions need to be corrected for these apparent geocentric variations. The final analysis approach for PPP is as follows:
- Constrain the orbits, clocks and EOP from IGS final products.
- Observations below 10-degrees elevation angle will be rejected.
- Stochastic estimation of station clock(white noise) at 5min(BSW5.0) intervals(15min Prior to 5 November 2000).
- Use of the in ospherically free observable.
- No fixing of integer ambiguities
- Stepwise estimation of the radio signals delay through the troposphere at 1 hour intervals using constrains of 5mm. No inclusion of gradient vectors (the azimuth dependency in addition to the elevation dependency of the radio signals)is carried out.
- Geophysical model specific corrections in accordance with IGS and IERS conventions.
- Site specific 3D ocean loading parameters(H.G. scherneck’s table of amplitudes and phases).
- Niell mapping function for hydrostatic delay.
- No correction for atmospheric loading included in the analysis.
- Satellite and receiver specific corrections in accordance with IGS conventions.
- Reference frame Global:
- Determination of 7-parameter helmet transformation using global IGb00 network solution . Station solutions with differences of more than 15mm in the horizontal and 30mm in the vertical coordinate components are excluded from the computation of the transformation parameters.
IPGN : Iranian Permanent GPS Network
A dense and wide permanent GPS station network has been established in Iran (Tabriz-Tehran-Mashhad) and other active part of the country by National Cartographic Center of Iran (NCC). Since first of the 2005 this network and is designed both for crustal deformation monitoring and to serve as a highly precise geodetic network in Iran and consist of 107 permanent stations in first phase. Average distance between dense parts is about 25 to 30 km.
Since we have collected about 1 year data, we estimated horizontal crustal displacement and velocity field with respect to the stable Eurasian plate. This new network will bring us more precise information on crustal information and geophysical phenomena such as ionosphere disturbances and water vapour too. Finally this network serve as active controlling. The Software for processing the data is Gamit/Globk V,10.20.
GAMIT is a comprehensive GPS analysis packs developed at MIT and Scripps for the estimation of three- dimensional relative positions of ground stations and satellite orbits. The software is is designed to run under any UNIX operating system supporting X-windows. The maximum number of stations and sessions allowed is determined by dimensions set at compile time and can be tailored to fit the requirements and capabilities of the analyst’s computational environment. The primary output of GAMIT is a loosely constrained solution file of parameter estimates and covariance’s which can be passed to another software module called GLOBK for combination of data to estimate station positions and velocities and orbital and Earth-rotation parameters.
GAMIT uses double differences by differencing the between station differences also between satellites to cancel completely the effects of variations in the station clocks. GAMIT incorporate difference-operator algorithms that map the carrier beat phases into singly and doubly differenced phases. The GAMIT software uses triple differences in editing the data but not in parameter estimation. A major source of error in single-frequency GPS measurement is the this effect. To correct for the ionosphere delay and provide a check the algorithm used, GAMIT employs both the dual-frequency pseudo-ranges and phase observations.
GAMIT incorporates a weighted least squares algorithm to estimate the relative positions of a set of stations, orbital and Earth-rotation parameters, zenith delays, and phase ambiguities by fitting to doubly differenced phase observations. Since the functional(mathematical) model relating the observations and parameters is non-linear, the least- squares fit for each session may need to be iterated until convergence, i.e., until the corrections to the estimated station coordinates and other parameters estimates and covariance’s which can be passed to another software module called GLOBK for combination of data to estimate station positions and velocities and orbital and Earth-rotation parameters.
IPGN Processing Strategy
The processing strategy applied by NCC uses GAMIT software version 10.2 for IPGN (Iranian Permanent GPS Network as follow:
- IGS final orbits and IERS bulleting B values for EOPs are used.
- At least (up to 22) IGS stations are included in the processing to link between regional and global solution.
- Tight constraints on orbital parameters and EOPs.
- Solid earth tide is consistent with IERS2000.
- For radiation pressure effects, Berne mode(9-parameter)is used.
- For ocean title loading , Scherneck model (IERS standards, 1992 ) is implemented. – Sasstamoinen model for the zenith delay and Niell mapping for both the hydrostatic and wet delay are applied.
- A piece- wise linear zenith model are employed.
- LC relax combination is used.
- Elevation-Dependent Model for antenna phase-centers.
- Ambiguity-fixed and free solutions will be produced for each day.
- Reference frame Global:
- Daily solutions are combined with global solutions from SOPAC.
- Combined daily solutions are transformed into ITRF2000 by minimizing the correction of 8 IGS core stations by estimating 7-parameter transformation with GLOBK.
Observation (Data Set) for PPP
This research used data from 22stations of IPGON which one of them is belong to IGS (tehn). These stations are located on the active part of the country. Data was collected over a period one GPS week (1358) . The initial observation were made on 15jan2006 and the final observation on 21Jan2006 . The reference epoch for processing was 1.1.2000 which the final solution will be referenced to ITRF2000 epoch (2006/0397) . All stations equipped with Ashtech UZ-12(ICGRS)receivers and Ash 701945 B_M precise antenna that collect data in 30″ interval.
The strategy adopted for the processing of GPS data of IPGON in PPP mode with Bernese were mentioned in the previous section:
So used IGS final orbit (ITRF 2000) and the epoch refers to each day of observations, and also final clocks and EOP. The basic observable was ionosphere free with 30 second recording interval and elevation musk of 10 deg. The ambiguity weren’t solved as integers. Geophysical model specific correction in accordance with IGS and IERS(ocean tide –body tide-pole tide).
Analysis of the Results:
The precision and accuracy of the coordinate of the stations in terms of local geodetic coordinate system (N,E,U) are analyzed.
The precession analysis is based on two criteria
- The formal standard deviations of the coordinates.
- The repeat abilities of the estimated coordinates.
The formal standard deviation of parameters is obtained from (variance and covariance matrix) of parameters. The daily repeatability provide a more realistic measure of precession for station coordinates. It is given by the expression:
n: number of occupation days, Ri is the estimated coordinate and ∑i is the formal error of the coordinates for day i and Rm is the weighted mean of the coordinates of the station. Fig 3,4 illustrate the precession of the station coordinate components(N,E,U)in term of and repeatability respectively.
Fig 2- precession of the station coordinates
Fig 3- repeatability
Comparison(Relative Positioning and PPP)
The main benefit of PPP is that its strengths are exactly in the areas of the weaknesses of relative processing and vice versa. Rather that being competitors, they complement each other perfectly.
The accuracies of relative positioning degrade with distance from the base station . Of course, this is not the case with PPP since it does not relay on a base station.
The main draw back with PPP is that there is a delay of approximately two weeks from the time of data collection to the availability of the precise satellite coordinates and clocks. Consequently, the most precise positions are not available until two weeks after the data were collected. A less precise solution is possible however, using the rapid satellite position and clock solutions. Due to double-differencing, the degradation of the coordinate accuracy is less when using the rapid products in relative positioning.
Relative positioning is a more logical choice for this task since it takes advantage of the cancellation effect when double differencing. That is, any errors common to the network partially or totally cancel- troposphere, ionosphere, tidal and non-tidal loading each fall into this category. This many not be the case with PPP since each point is processing independently of the others. Ambiguity resolution is also simpler in relative processing. Great care must be taken, however, to ensure that correct antenna .
Phase centre models are employed when mixing antenna type in relative processing, while PPP relies only on a single antenna. Fig4 shows the coordinate difference between two processing mode for IPGN.
In this research 22 stations of IPGN were processed with Bernese V.5 software and compare the result with those obtain in ITRF2000 with. The result shows the general agreement. The results shows that the standard deviation of the PPP for this GPS week (1358). Solution is better than 4mm for daily solutions, and the repeatability is about 2mm, 3.5mm,4.5mm for N,E,U components. The difference between the coordinates of PPP and those obtain in relative mode in ITRF 2000 are due to the ambiguity resolution for PPP and combination of solution in Gamit/Globk software. The difference between baseline computed by PPP and relative mode is better than 3mm. Farther analysis recommend for longer observation and also velocity estimation and plate rotation vector with the PPP.
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