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|Year of Publication||2011|
Precise point positioning (PPP) stands out as an optimal approach for providing global augmentation services using current and coming GNSS constellations. PPP requires fewer reference stations globally distributed rather than classic differential approaches (e.g. RTK), also one set of precise orbit and clock data is valid for all users everywhere, and the solution is largely unaffected by individual reference-station failures. There are always many reference stations observing the same satellite because the precise orbits and clocks are calculated from a global network of reference stations. As a result, PPP gives a highly redundant and robust position solution: mm precision level.
Precise Point Positioning (PPP) is a global precise positioning service, since it requires the availability of precise reference satellite orbit and clock products in real-time using a network of GNSS reference stations distributed worldwide.
There are not "PPP Standards" as in other GNSS systems , but there are some conventions, models and formats commonly used. To achieve the highest accuracy and consistency (mm-cm level positioning), it is customary to implement the GNSS-specific conventions and models adopted by the IGS.
Developers of GPS software are generally well aware of corrections they must apply to pseudorange or carrier-phase observations to eliminate effects such as special and general relativity, Sagnac delay, satellite clock offsets, atmospheric delays, etc. All these effects are quite large, exceeding several meters, and must be considered even for pseudorange positioning at the meter precision level. When attempting to combine satellite positions and clocks precise to a few centimeters with ionospheric-free carrier phase observations (with millimeter resolution), it is important to account for some effects that may not have been considered in pseudorange or precise differential phase processing modes.
The following sections summarize the adjustment models and procedures usually used and look at additional correction terms that are significant for carrier phase point positioning. The corrections models have been grouped under Satellite Effects, Site Displacements Effects and Compatibility and IGS conventions. A number of the corrections listed below require the Moon or the Sun positions which can be obtained from readily available planetary ephemerides files, or more conveniently from simple formulas since a relative precision of about 1/1000 is sufficient for corrections at the mm precision level. Note that for centimeter level differential positioning and baselines of less than 100 km, the correction terms discussed below can be safely neglected.
PPP Adjustment Models and Procedures
The adjustment model is a weighted least-squared estimation. This adjustment can be done in a single step, so called batch adjustment (with iterations), or alternatively within a sequential adjustment/filter (with or without iterations) that can be adapted to varying user dynamics. The disadvantage of a batch adjustment is that it may become too large even for modern and powerful computers, in particular for un-differenced observations involving a large network of stations. However, no back-substitution or back smoothing is necessary in this case, which makes batch adjustment attractive in particular for double difference approaches. Filter implementations, (for GPS positioning, equivalent to sequential adjustments with steps coinciding with observation epochs), are usually much more efficient and of smaller size than the batch adjustment implementations, at least, as far as the position solutions with un-differenced observations are concerned. This is so, since parameters that appear only at a particular observation epoch, such as station/satellite clock and even zenith path delay (zpd) parameters, can be preeliminated. However, filter (sequential adjustment) implementations require backward smoothing (back substitutions) for the parameters that are not retained from epoch to epoch, (e.g. the clock parameters). Furthermore, filter/sequential approaches can also model variations in the states of the parameters between observation epochs with appropriate stochastic processes that also update parameter variances from epoch to epoch.
For example, the PPP observation model and adjustment involve four types of parameters: station position (), receiver clock (), troposphere zenith path delay (), and non-integer carrier-phase ambiguities (). The station position may be constant or change over time depending on the user dynamics. These dynamics could vary from tens of meters per second in the case of a land vehicle to a few kilometers per second for a Low Earth Orbiter (LEO). The receiver clock will drift according to the quality of its oscillator, e.g. about 0.1 ns/sec (equivalent to several cm/sec) in the case of an internal quartz clock with frequency stability of about 10-10. Comparatively, the tropospheric zenith path delay (zpd) will vary in time by a relatively small amount, in the order of a few cm/hour. Finally, the carrier-phase ambiguities () will remain constant as long as the satellite is not being reoriented (e.g., during an eclipsing period, see the phase wind-up correction) and the carrier phases are free of cycle-slips, a condition that requires close monitoring. Note that only for double differenced data observed from at least two stations, all clocks ’s, including the receiver clock corrections are practically eliminated by the double differencing.
PPP Corrections Models
The correction terms have been grouped under Satellite Effects, Site Displacements Effects and Compatibility and IGS Conventions.
The requirement for satellite based corrections originates from the separation between the GPS satellite center of mass and the phase center of its antenna. Because the force models used for satellite orbit modeling refer to its center of mass, the IGS GPS precise satellite coordinates and clock products also refer to the satellite center of mass, unlike the orbits broadcast in the GPS navigation message that refer to satellite antenna phase center. However, the measurements are made to the antenna phase center, thus one must know satellite phase center offsets and monitor the orientation of the offset vector in space as the satellite orbits the Earth. The phase centers for most satellites are offset both in the body z coordinate direction (towards the Earth) and in the body x coordinate direction which is on the plane containing the Sun.
GPS satellites transmit Right Hand Circularly Polarized (RHCP) radio waves and therefore, the observed carrierphase depends on the mutual orientation of the satellite and receiver antennas. A rotation of either receiver or satellite antenna around its bore (vertical) axis will change the carrier-phase up to one cycle (one wavelength), which corresponds to one complete revolution of the antenna. This effect is called “phase wind-up” . A receiver antenna, unless mobile, does not rotate and remains oriented towards a fixed reference direction (usually north). However, satellite antennas undergo slow rotations as their solar panels are being oriented towards the Sun and the station-satellite geometry changes. Further, in order to reorient their solar panels towards the Sun during eclipsing seasons, satellites are also subjected to rapid rotations, so called “noon” (when a straight line, starting from the Sun, intersects the satellite and then the center of the Earth) and “midnight turns” (when the line intersects the center of the Earth, then the satellite). This can represent antenna rotations of up to one revolution within less than half an hour. During such noon or midnight turns, phase data needs to be corrected for this effect or simply edited out.
The phase wind-up correction has been generally neglected even in the most precise differential positioning software, as it is quite negligible for double difference positioning on baselines/networks spanning up to a few hundred kilometers. However, it has been shown to reach up to 4 cm for a baseline of 4000 km  . This effect is significant for un-differenced point positioning when fixing IGS satellite clocks, since it can reach up to one half of the wavelength. Since about 1994, most of the IGS Analysis Centers (and therefore the IGS orbit/clock combined products) apply this phase wind-up correction. Neglecting it and fixing IGS orbits/clocks will result in position and clock errors at the dm level. For receiver antenna rotations (e.g. during kinematic positioning/navigation) the phase wind-up is fully absorbed into station clock solutions (or eliminated by double differencing).
Site Displacements effects
In a global sense, a station undergoes periodic movements (real or apparent) reaching a few dm that are not included in the corresponding ITRF “regularized” positions, from which “high-frequency” have been removed using models. Since most of the periodical station movements are nearly the same over broad areas of the Earth, they nearly cancel in relative positioning over short (<100 km) baselines and thus need not be considered. However, if one is to obtain a precise station coordinate solution consistent with the current International Terrestrial Reference Frame (ITRF) conventions in PPP, using un-differenced approaches, or in relative positioning over long baselines (> 500 km), the above station movements must be modeled as recommended in the IERS Conventions. This is accomplished by adding the site displacement correction terms listed below to the regularized ITRF coordinates. Site displacement effects with magnitude of less than 1 centimeter, such as atmospheric and ground water and/or snow build-up loading, have been neglected and are not considered here.
The “solid” Earth is in fact pliable enough to respond to the same gravitational forces that generate the ocean tides. The periodic vertical and horizontal site displacements caused by tides are represented by spherical harmonics of degree and order () characterized by the Love number and the Shida number . The effective values of these numbers weakly depend on station latitude and tidal frequency  and need to be taken into account when a position precision of 1 mm is desired. It should be noted that error produced due to solid Earth tides is larger than the errors due to polar tides or ocean loading.
Much like deformations due to Sun and Moon attractions that cause periodical station position displacements, the changes of the Earth’s spin axis with respect to Earth’s crust, i.e. the polar motion, causes periodical deformations due to minute changes in the Earth centrifugal potential. They are obtained with the second degree Love and Shida numbers. For sub-centimeter position precision the polar tide corrections need to be applied to obtain an apparent station position; that is, these corrections have to be subtracted from the position solutions in order to be consistent with ITRF. Unlike the solid earth tides and the ocean loading effects, the pole tides do not average to nearly zero over a 24h period.
Ocean loading is similar to solid Earth tides: it is dominated by diurnal and semi diurnal periods, but it results from the load of the ocean tides on the underlying crust. While the displacements due to ocean loading are almost an order of magnitude smaller than those due to solid Earth tides, ocean loading is more localized, and by convention it does not have a permanent part. For single epoch positioning at the 5-cm precision level or mm static positioning over 24h period and/or for stations that are far from the oceans, ocean loading can be safely neglected. On the other hand, for cm precise kinematic point positioning or precise static positioning along coastal regions over observation intervals significantly shorter than 24h, this effect has to be taken into account. Note that when the tropospheric or clock solutions are required, the ocean load effects also have to be taken into account even for a 24h static point positioning processing, unless the station is far (> 1000 km) from the nearest coast line. Otherwise, the ocean load effects will map into the solutions for tropospheric and station clocks.
The Earth Rotation Parameters (i.e. pole position , and ), along with the conventions for sidereal time, precession and nutation facilitate accurate transformations between terrestrial and inertial reference frames that are required in global GPS analysis. Then, the resulting orbits in the terrestrial conventional reference frame (ITRF), much like the IGS orbit products, imply, quite precisely, the underlying ERP. Consequently, IGS users who fix or heavily constrain the IGS orbits and work directly in ITRF need not worry about ERP. However, when using software formulated in an inertial frame, the ERP, corresponding to the fixed orbits, augmented with the so called sub-daily ERP model, are required and must be used. This is so, since ERP, according to the IERS convention are regularized and do not include the sub-daily, tidally induced, ERP variations. The sub-daily ERP is also dominated by diurnal and sub-diurnal periods of ocean tide origin, and can reach up to 0.1 mas (milli-arc seconds).
Compatibility and IGS Conventions
Positioning and GPS analyses that constrain or fix any external solutions/products need to apply consistent conventions, orbit/clock weighing and models. This is in particular true for PPP and clock solutions/products, however even for cm precision differential positioning over continental baselines, the consistency with the IGS global solutions also needs to be considered. This includes issues such as the respective version of ITRF, the IGS ERP corresponding to the IGS orbit and station solutions used, station logs (antenna offsets) etc. Note that, in general, all IGS Analysis Centers solutions and thus IGS combined products follow the current IERS conventions (2003). Thus, all the error-modeling effects discussed above are generally implemented with little or no approximation with respect to the current IERS conventions. The only exceptions are the atmospheric and snow loading effects, which currently (2009) are neglected by all IGS Analysis Centers. For specific and detail information on each IGS Analysis Center global solution strategy, modeling and departures from the conventions, in a standardized format, refer to the IGS CB archives.
IGS has adopted and developed a number of standard formats, which for convenience are listed below. Note that some formats, like RINEX, SP3 and SINEX undergo regular revisions to accommodate receiver/satellite upgrades, or multi-technique solutions, respectively.
|Format name||IGS Product/Sampling|
|RINEX||GPS Data/ 30 s|
|RINEX Clock||Sat./Sta. Clock/5 min/30s|
|sp3||Orbits/Clocks/ 15 min.|
|IGS ERP Format||IGS ERP/ 1 day|
|SINEX||Sta. Pos.(ERP) / 7(1) day|
|SINEX-tropo ext.||Tropo. ZPD 2 h/5 min|
|IONEX||Iono. maps/sat DCB 2 h|
No standard for Real-Time PPP has yet been defined. Nonetheless, a standarisation effort is being carried by the Radio Technical Comission for Maritime Services(RTCM) Special committee 104.
- ^ a b Guide to Use IGS Products
- ^ a b Wu, J.T., S,C. Wu, G.A. Hajj, W.I. Bertiger, and S.M. Lichten, 1993, Effects of antenna orientation on GPS carrier phase, Man. Geodetica 18, pp. 91-98
- ^ Bar-Sever, Y. E., 1996, A new module for GPS yaw attitude control, Proceedings of IGS Workshop-Special Topics and New Directions, eds. G.Gendt and G. Dick, GeoforschunsZentrum, Potsdam, pp. 128-140.
- ^ Kouba, J., 2008, A simplified yaw-attitude model for eclipsing GPS satellites, GPS Solutions 2008: DOI:10.1007/s10291-008-0092-1
- ^ Wahr, J.M., 1981, The forced nutation of an elliptical, rotating, elastic, and ocean less Earth, Geophys. J. Roy. Astron. Soc., 64, pp. 705-727.