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==PPP Adjustment Models and Procedures== | ==PPP Adjustment Models and Procedures== | ||
The PPP algorithm is based on the concept of parameters adjustment. At the very first step, PPP provides a pseudorange-like position estimation at meter-precision level. This position estimation is then refined over time by processing the centimeter-precision carrier-phase measurements while the estimations of receiver coordinates, clock, zenith tropospheric delay and initial phase ambiguities progressively become more and more accurate. This adjustment process can be done in a single step (with iterations), i.e., the so-called batch adjustment, or, alternatively, within a sequential adjustment/filter (either 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, such as sequential least-square filtering or Kalman filtering | The PPP algorithm is based on the concept of parameters adjustment. At the very first step, PPP provides a pseudorange-like position estimation at meter-precision level. This position estimation is then refined over time by processing the centimeter-precision carrier-phase measurements while the estimations of receiver coordinates, clock, zenith tropospheric delay and initial phase ambiguities progressively become more and more accurate. This adjustment process can be done in a single step (with iterations), i.e., the so-called batch adjustment, or, alternatively, within a sequential adjustment/filter (either 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, such as sequential least-square filtering or Kalman filtering (for GNSS positioning this is 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 parameters, can be pre-eliminated. 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 | For example, the PPP observation model and adjustment involve four types | ||
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==PPP Corrections Models== | ==PPP Corrections Models== | ||
In order to achieve the utmost cm-to-mm precision performance, PPP heavily relies on very accurate error models that are not required in case of conventional meter-level pseudorange positioning. These correction models | In order to achieve the utmost cm-to-mm precision performance, PPP heavily relies on very accurate error models that are not required in case of conventional meter-level pseudorange positioning. These correction models are discussed in the following and grouped under four categories, namely atmospheric effects, satellite effects, site displacements effects and differential code bias effects.<ref name="IGS_PPP"/><ref name="Handbook">[Kouba, Jan (et al.), Precise Point Positioning, Chapter 25, Handbook of Global Navigation Satellite Systems, 2017]</ref> | ||
===Atmospheric Effects=== | ===Atmospheric Effects=== | ||
*Higher-order ionospheric delay effects | *Higher-order ionospheric delay effects | ||
The delay introduced by atmospheric effects into the propagation of electromagnetic waves is a significant effect that needs to be taken into account even for standard meter-level pseudorange positioning. For instance, the dual-frequency linear combination of GNSS observables allows for the substantial mitigation of the first-order ionospheric effect. While this is enough for pseudorange-based meter-level positioning, whose noise is about 0.1-1m, in the case of carrier-phase based positioning aiming at cm-level accuracy, higher-order ionospheric effects are no longer negligible. Hence, these need to be included into the PPP measurements models as well. | The delay introduced by atmospheric effects into the propagation of electromagnetic waves is a significant effect that needs to be taken into account even for standard meter-level pseudorange positioning. For instance, the dual-frequency linear combination of GNSS observables allows for the substantial mitigation of the first-order ionospheric effect. While this is enough for pseudorange-based meter-level positioning, whose noise is about 0.1-1m, in the case of carrier-phase based positioning aiming at cm-level accuracy, higher-order ionospheric effects are no longer negligible. Hence, these need to be included into the PPP measurements models as well. | ||
*Tropospheric delay effects | *Tropospheric delay effects | ||
Another effect that has a strong impact onto the performance of PPP solutions is the delay introduced by the troposphere. This is commonly computed by means of specific mapping functions and for a given value of the Zenith Troposphere Delay (ZTD). As far as meter-level accuracy positioning is concerned, it is enough to adopt very simple mapping functions and a single a-priori ZTD value, as an accurate ZTD estimation is normally impossible and not needed anyways. However, for PPP target accuracies, more complex mapping functions need to be implemented. These complex mapping functions, such as the Viena Mapping Function 1 (VMF1 <ref name=" | Another effect that has a strong impact onto the performance of PPP solutions is the delay introduced by the troposphere. This is commonly computed by means of specific mapping functions and for a given value of the Zenith Troposphere Delay (ZTD). As far as meter-level accuracy positioning is concerned, it is enough to adopt very simple mapping functions and a single a-priori ZTD value, as an accurate ZTD estimation is normally impossible and not needed anyways. However, for PPP target accuracies, more complex mapping functions need to be implemented. These complex mapping functions, such as the Viena Mapping Function 1 (VMF1 <ref name="Boehm"> J. Boehm, et al: Troposphere mapping functions for GPS and very long baseline interferometry from European centre for medium-range weather forecasts operational analysis data, J. Geophys. Res. 111(B02406), 1–9 (2006)</ref>), separately account for the hydrostatic (a.k.a. dry) and wet components of the ZTD. Moreover, the mapping functions need to be combined with accurate estimations of the ZTD (the dry component can be accurately computed from surface pressure, station latitude and height, while the wet one is estimated from the data), which is one of the unknown of the PPP estimation problem. | ||
===Satellite Effects=== | ===Satellite Effects=== | ||
*[[Satellite_Antenna_Phase_Centre|Satellite Antenna Offsets]] | *[[Satellite_Antenna_Phase_Centre|Satellite Antenna Offsets]] | ||
The | The need for satellite- based corrections originates from the separation between the GNSS 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 GNSS precise satellite coordinates and clock products also refer to the satellite center of mass, unlike the orbits broadcast in the GNSS 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. | ||
*[[Carrier_Phase_Wind-up_Effect|Phase Wind-Up Correction]] | *[[Carrier_Phase_Wind-up_Effect|Phase Wind-Up Correction]] | ||
GNSS 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” <ref name=" | GNSS 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” <ref name="Wu">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. 91-981</ref>. 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 | 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<ref>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.</ref><ref name="Kouba">Kouba, J., 2008, A simplified yaw-attitude model for eclipsing GPS satellites, GPS Solutions 2008: DOI:10.1007/s10291-008-0092-1</ref> 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 <ref name=" | 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 <ref name="Wu">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. 91-981</ref>. 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=== | ===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 [http://itrf.ensg.ign.fr/ International Terrestrial Reference Frame (ITRF)] “regularized” positions, from which “high-frequency” have been modelled and removed. 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 has to obtain a precise station coordinate solution consistent with the current ITRF conventions by using a PPP un-differenced approach or a relative positioning approach over long baselines (> 500 km), the above station movements must be modeled as recommended in the[http://www.iers.org/ International Earth Rotation and Reference Systems Service (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. | In a global sense, a station undergoes periodic movements (real or apparent) reaching a few dm that are not included in the corresponding [http://itrf.ensg.ign.fr/ International Terrestrial Reference Frame (ITRF)] “regularized” positions, from which “high-frequency” have been modelled and removed. 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 has to obtain a precise station coordinate solution consistent with the current ITRF conventions by using a PPP un-differenced approach or a relative positioning approach over long baselines (> 500 km), the above station movements must be modeled as recommended in the [http://www.iers.org/ International Earth Rotation and Reference Systems Service (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. | ||
*[[Solid_Tides|Solid Earth tides]] | *[[Solid_Tides|Solid Earth tides]] | ||
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 (<math>n, m</math>) characterized by the Love number <math>h_{nm}</math> and the Shida number <math>l_{nm}</math>. The effective values of these numbers weakly depend on station latitude and tidal frequency <ref> | 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 (<math>n, m</math>) characterized by the Love number <math>h_{nm}</math> and the Shida number <math>l_{nm}</math>. The effective values of these numbers weakly depend on station latitude and tidal frequency <ref name="Whar">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</ref> 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. | ||
*[[Pole Tide|Rotational deformation due to polar motion (polar tides)]] | *[[Pole Tide|Rotational deformation due to polar motion (polar tides)]] | ||
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 [http://itrf.ensg.ign.fr/ ITRF]. Unlike the solid earth tides and the ocean loading effects, the pole tides do not average to nearly zero over a 24h period. | 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 [http://itrf.ensg.ign.fr/ ITRF]. Unlike the solid earth tides and the ocean loading effects, the pole tides do not average to nearly zero over a 24h period. | ||
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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. | 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. | ||
*[[Transformation between Celestial and Terrestrial Frames|Earth rotation parameters (ERP)]] | *[[Transformation between Celestial and Terrestrial Frames|Earth rotation parameters (ERP)]] | ||
The Earth Rotation Parameters (i.e. pole position <math>X_p</math>, <math>Y_p</math> and <math>UT1-UTC</math>), along with the conventions for sidereal time, precession and nutation facilitate accurate transformations between terrestrial and inertial reference frames that are required in global GNSS analysis. Then, the resulting orbits in the terrestrial conventional reference frame ([http://itrf.ensg.ign.fr/ 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 [http://www.iers.org/ International Earth Rotation and Reference Systems Service (IERS)] conventions are regularized and do not include the sub-daily, tidally induced, ERP variations<ref name=" | The Earth Rotation Parameters (i.e. pole position <math>X_p</math>, <math>Y_p</math> and <math>UT1-UTC</math>), along with the conventions for sidereal time, precession and nutation facilitate accurate transformations between terrestrial and inertial reference frames that are required in global GNSS analysis. Then, the resulting orbits in the terrestrial conventional reference frame ([http://itrf.ensg.ign.fr/ 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 [http://www.iers.org/ International Earth Rotation and Reference Systems Service (IERS)] conventions are regularized and do not include the sub-daily, tidally induced, ERP variations<ref name="IERS">[https://www.iers.org/IERS/EN/Home/home_node.html International Earth Rotation and Reference Systems Service (IERS)]</ref>. 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). | ||
===Differential Code Biases effects=== | ===Differential Code Biases effects=== | ||
Measurements biases are usually not taken into account in the simplified dual-frequency PPP observation models (see PPP Fundamentals). This assumption holds true as far as the precise clock products have been generated with the same types of observations used in the PPP algorithm. As an example, GPS clock offsets are conventionally computed for an ionosphere-free combination of L1/L2 P(Y)-code observables; GLONASS clock products are referred to P-code observations on the L1 and L2 frequencies. If these same signal pairs are used as dual-frequency observations in the PPP algorithm, the conventional PPP simplified observation model can be adopted without considering any further code bias term. However, if the dual-frequency combined observation is composed by different types of signals, e.g., L2 P(Y)-code and L1 C/A-code, an additional term needs to be introduced in order to translate the satellite clock offset and make it compatible with the employed observations <ref> | Measurements biases are usually not taken into account in the simplified dual-frequency PPP observation models (see [[PPP Fundamentals]]). This assumption holds true as far as the precise clock products have been generated with the same types of observations used in the PPP algorithm. As an example, GPS clock offsets are conventionally computed for an ionosphere-free combination of L1/L2 P(Y)-code observables; GLONASS clock products are referred to P-code observations on the L1 and L2 frequencies. If these same signal pairs are used as dual-frequency observations in the PPP algorithm, the conventional PPP simplified observation model can be adopted without considering any further code bias term. However, if the dual-frequency combined observation is composed by different types of signals, e.g., L2 P(Y)-code and L1 C/A-code, an additional term needs to be introduced in order to translate the satellite clock offset and make it compatible with the employed observations <ref>O. Montenbruck, A. Hauschild: Code biases in multi-GNSS point positioning, Proc. ION ITM 2013, San Diego (ION, Virginia 2013) pp. 616–628</ref>. This additional term, commonly referred to as Differential Code Bias (DCB), improves the convergence time of filter implementations and allows for a faster and more reliable ambiguity fixing. | ||
==Compatibility and IGS Conventions== | ==Compatibility and IGS Conventions== | ||
Positioning and GNSS analyses that constrain or fix any external solutions/products need to apply consistent conventions, orbit/clock weighing and models. As mentioned above, this is particularly true for PPP and clock solutions/products. However, even for cm-level precision differential positioning over continental baselines, the consistency with the IGS global solutions needs to be ensured. This includes issues such as the respective version of ITRF, the IGS ERP corresponding to the used IGS orbit and station solutions, station logs (antenna offsets) etc. Note that, in general, all IGS Analysis Centers solutions, and thus the IGS combined products, follow common standards such as the current [http://www.iers.org/ IERS] conventions | Positioning and GNSS analyses that constrain or fix any external solutions/products need to apply consistent conventions, orbit/clock weighing and models. As mentioned above, this is particularly true for PPP and clock solutions/products. However, even for cm-level precision differential positioning over continental baselines, the consistency with the IGS global solutions needs to be ensured. This includes issues such as the respective version of ITRF, the IGS ERP corresponding to the used IGS orbit and station solutions, station logs (antenna offsets) etc. Note that, in general, all IGS Analysis Centers solutions, and thus the IGS combined products, follow common standards such as the current [http://www.iers.org/ IERS] conventions <ref name="IERS">[https://www.iers.org/IERS/EN/Home/home_node.html International Earth Rotation and Reference Systems Service (IERS)]</ref>, reference frames (currently ITRF2008/IGS08) and antenna phase-center calibration models (currently igs08.atx). Thus, all the error-modeling effects discussed above are generally implemented with little or no approximation with respect to the current IERS conventions. For specific and detailed information on each IGS Analysis Center global solution strategy, modeling and departures from the conventions, in a standardized format, please refer to the IGS CB archives. | ||
==IGS Formats== | ==IGS Formats== | ||
| Line 71: | Line 71: | ||
! Format name | ! Format name | ||
! IGS Product/Sampling | ! IGS Product/Sampling | ||
! Sampling | |||
|- align="center" | |- align="center" | ||
| RINEX | | RINEX | ||
| | | GNSS Data | ||
| 30 s | |||
|- align="center" | |- align="center" | ||
| RINEX Clock | | RINEX Clock | ||
| Sat./ | | Sat. / Station Clock | ||
| 30 s / 5 min | |||
|- align="center" | |- align="center" | ||
| sp3 | | sp3 | ||
| Orbits/Clocks | | Orbits / Clocks | ||
| 15 min | |||
|- align="center" | |- align="center" | ||
| IGS ERP Format | | IGS ERP Format | ||
| IGS ERP | | IGS ERP | ||
| 1 day | |||
|- align="center" | |- align="center" | ||
| SINEX | | SINEX | ||
| | | Station Pos. / ERP | ||
| 7 days / 1 day | |||
|- align="center" | |||
| SINEX Bias | |||
| GNSS biases | |||
| 5 min | |||
|- align="center" | |- align="center" | ||
| SINEX-tropo ext. | | SINEX-tropo ext. | ||
| Tropo. ZPD 2 h/5 min | | Tropo. ZPD | ||
| 2 h/5 min | |||
|- align="center" | |- align="center" | ||
| IONEX | | IONEX | ||
| Iono. maps/ | | Iono. maps/Sat DCB | ||
| 2 h | |||
|- align="center" | |||
| ANTEX | |||
| Ant. Calibr. | |||
| - | |||
|- align="center" | |||
| Site log | |||
| Site installation history | |||
| - | |||
|} | |} | ||
Access to Real-Time (RT) IGS products is possible through the NTRIP protocol upon registration. In alternative, high-rate data in RINEX format for nearly-real or post-processed applications can be accessed without any registration from the IGS archive. | |||
[[Interfaces and Protocols| More information on formats and communication protocols]]. | [[Interfaces and Protocols| More information on formats and communication protocols]]. | ||
==Real-Time PPP== | ==Real-Time PPP== | ||
No standard for Real-Time PPP has yet been defined. Nonetheless, a standarisation effort is being carried by the [http://www.rtcm.org/ Radio Technical Comission for Maritime Services](RTCM) Special | No standard for Real-Time PPP has yet been defined. Nonetheless, a standarisation effort is being carried by the [http://www.rtcm.org/ Radio Technical Comission for Maritime Services](RTCM) Special Committee 104 (SC-104), which also defines the standard message formats currently employed by PPP services (among others) for the communication between users and reference stations <ref name="Committe">Special Committee 104, RTCM Recommended Standards for Differential GNSS (Global Navigation Satellite Systems) Service, Version 3.3, Radio Technical Commission for Maritime Services, Alexandria, VA, October 7, 2016.</ref> | ||
== | ==Related Articles== | ||
*[[Precise Point Positioning]] | |||
*[[PPP Fundamentals]] | |||
*[[Linear observation model for PPP]] | |||
*[[Precise modelling terms for PPP]] | |||
*[[Parameters adjustment for PPP]] | |||
*[[Real Time Kinematics]] | |||
*[[PPP Systems]] | |||
*[[Precise GNSS Satellite Coordinates Computation]] | |||
*[[Antenna Phase Centre]] | |||
*[[Interfaces and Protocols]] | |||
*[[DGNSS Standards]] | |||
*[[RTK Standards]] | |||
==References== | ==References== | ||
Latest revision as of 10:09, 11 June 2020
| Fundamentals | |
|---|---|
| Title | PPP Standards |
| Edited by | GMV |
| Level | Intermediate |
| Year of Publication | 2011 |
Precise Point Positioning (PPP) stands out as an optimal approach for providing global augmentation services using all the available GNSS constellations. By combining precise orbit and clock products with un-differenced, dual-frequency, code and carrier-phase measurements, PPP algorithm is able to achieve cm-level precision, or even mm-level precision in the case of static mode and post-processing mode. PPP requires fewer reference stations globally distributed as compared with classic differential approaches (e.g. RTK), and one set of precise orbit and clock data is valid for all users everywhere. 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 provides position solutions that are largely unaffected by individual reference-station failures.
PPP Standards
Precise Point Positioning (PPP) is a global precise positioning service, which 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.[1]
Developers of GNSS software are generally well aware of corrections they must be applied to pseudorange or carrier-phase observations in order 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 correction models have been grouped under four different categories, namely atmospheric effects, satellite effects, site displacements effects and differential code bias effects. Furthermore, compatibility issues and IGS conventions are discussed as well. Part of the corrections listed below requires the Moon or the Sun positions, which can be obtained from readily available planetary ephemerides files or, more conveniently, from simple analytical formulas. In fact, the latter provide a relative precision of about 1/1000, which is sufficient for mm-level corrections. Note that the correction terms discussed below mandatorily need to be considered when targeting sub-centimeter precision level. In contrast, for centimeter level differential positioning and baselines of less than 100 km, such correction terms can be safely neglected.
PPP Adjustment Models and Procedures
The PPP algorithm is based on the concept of parameters adjustment. At the very first step, PPP provides a pseudorange-like position estimation at meter-precision level. This position estimation is then refined over time by processing the centimeter-precision carrier-phase measurements while the estimations of receiver coordinates, clock, zenith tropospheric delay and initial phase ambiguities progressively become more and more accurate. This adjustment process can be done in a single step (with iterations), i.e., the so-called batch adjustment, or, alternatively, within a sequential adjustment/filter (either 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, such as sequential least-square filtering or Kalman filtering (for GNSS positioning this is 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 parameters, can be pre-eliminated. 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 ([math]\displaystyle{ x, y, z }[/math]), receiver clock ([math]\displaystyle{ dT }[/math]), troposphere zenith path delay ([math]\displaystyle{ zpd_w }[/math]), and non-integer carrier-phase ambiguities ([math]\displaystyle{ N }[/math]). 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 [math]\displaystyle{ 10^{10} }[/math]. Comparatively, the tropospheric zenith path delay will vary in time by a relatively small amount, in the order of a few cm/hour. Finally, the carrier-phase ambiguities ([math]\displaystyle{ N }[/math]) 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 [math]\displaystyle{ dT }[/math]’s, including the receiver clock corrections are practically eliminated by the double differencing.
PPP Corrections Models
In order to achieve the utmost cm-to-mm precision performance, PPP heavily relies on very accurate error models that are not required in case of conventional meter-level pseudorange positioning. These correction models are discussed in the following and grouped under four categories, namely atmospheric effects, satellite effects, site displacements effects and differential code bias effects.[1][2]
Atmospheric Effects
- Higher-order ionospheric delay effects
The delay introduced by atmospheric effects into the propagation of electromagnetic waves is a significant effect that needs to be taken into account even for standard meter-level pseudorange positioning. For instance, the dual-frequency linear combination of GNSS observables allows for the substantial mitigation of the first-order ionospheric effect. While this is enough for pseudorange-based meter-level positioning, whose noise is about 0.1-1m, in the case of carrier-phase based positioning aiming at cm-level accuracy, higher-order ionospheric effects are no longer negligible. Hence, these need to be included into the PPP measurements models as well.
- Tropospheric delay effects
Another effect that has a strong impact onto the performance of PPP solutions is the delay introduced by the troposphere. This is commonly computed by means of specific mapping functions and for a given value of the Zenith Troposphere Delay (ZTD). As far as meter-level accuracy positioning is concerned, it is enough to adopt very simple mapping functions and a single a-priori ZTD value, as an accurate ZTD estimation is normally impossible and not needed anyways. However, for PPP target accuracies, more complex mapping functions need to be implemented. These complex mapping functions, such as the Viena Mapping Function 1 (VMF1 [3]), separately account for the hydrostatic (a.k.a. dry) and wet components of the ZTD. Moreover, the mapping functions need to be combined with accurate estimations of the ZTD (the dry component can be accurately computed from surface pressure, station latitude and height, while the wet one is estimated from the data), which is one of the unknown of the PPP estimation problem.
Satellite Effects
The need for satellite- based corrections originates from the separation between the GNSS 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 GNSS precise satellite coordinates and clock products also refer to the satellite center of mass, unlike the orbits broadcast in the GNSS 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.
GNSS 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” [4]. 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[5][6] 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 [4]. 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 International Terrestrial Reference Frame (ITRF) “regularized” positions, from which “high-frequency” have been modelled and removed. 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 has to obtain a precise station coordinate solution consistent with the current ITRF conventions by using a PPP un-differenced approach or a relative positioning approach over long baselines (> 500 km), the above station movements must be modeled as recommended in the International Earth Rotation and Reference Systems Service (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 ([math]\displaystyle{ n, m }[/math]) characterized by the Love number [math]\displaystyle{ h_{nm} }[/math] and the Shida number [math]\displaystyle{ l_{nm} }[/math]. The effective values of these numbers weakly depend on station latitude and tidal frequency [7] 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 [math]\displaystyle{ X_p }[/math], [math]\displaystyle{ Y_p }[/math] and [math]\displaystyle{ UT1-UTC }[/math]), along with the conventions for sidereal time, precession and nutation facilitate accurate transformations between terrestrial and inertial reference frames that are required in global GNSS 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 International Earth Rotation and Reference Systems Service (IERS) conventions are regularized and do not include the sub-daily, tidally induced, ERP variations[8]. 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).
Differential Code Biases effects
Measurements biases are usually not taken into account in the simplified dual-frequency PPP observation models (see PPP Fundamentals). This assumption holds true as far as the precise clock products have been generated with the same types of observations used in the PPP algorithm. As an example, GPS clock offsets are conventionally computed for an ionosphere-free combination of L1/L2 P(Y)-code observables; GLONASS clock products are referred to P-code observations on the L1 and L2 frequencies. If these same signal pairs are used as dual-frequency observations in the PPP algorithm, the conventional PPP simplified observation model can be adopted without considering any further code bias term. However, if the dual-frequency combined observation is composed by different types of signals, e.g., L2 P(Y)-code and L1 C/A-code, an additional term needs to be introduced in order to translate the satellite clock offset and make it compatible with the employed observations [9]. This additional term, commonly referred to as Differential Code Bias (DCB), improves the convergence time of filter implementations and allows for a faster and more reliable ambiguity fixing.
Compatibility and IGS Conventions
Positioning and GNSS analyses that constrain or fix any external solutions/products need to apply consistent conventions, orbit/clock weighing and models. As mentioned above, this is particularly true for PPP and clock solutions/products. However, even for cm-level precision differential positioning over continental baselines, the consistency with the IGS global solutions needs to be ensured. This includes issues such as the respective version of ITRF, the IGS ERP corresponding to the used IGS orbit and station solutions, station logs (antenna offsets) etc. Note that, in general, all IGS Analysis Centers solutions, and thus the IGS combined products, follow common standards such as the current IERS conventions [8], reference frames (currently ITRF2008/IGS08) and antenna phase-center calibration models (currently igs08.atx). Thus, all the error-modeling effects discussed above are generally implemented with little or no approximation with respect to the current IERS conventions. For specific and detailed information on each IGS Analysis Center global solution strategy, modeling and departures from the conventions, in a standardized format, please refer to the IGS CB archives.
IGS Formats
IGS has adopted and developed a number of standard formats for GNSS observation data and the derived products, which for convenience are listed below [10]. 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 | Sampling |
|---|---|---|
| RINEX | GNSS Data | 30 s |
| RINEX Clock | Sat. / Station Clock | 30 s / 5 min |
| sp3 | Orbits / Clocks | 15 min |
| IGS ERP Format | IGS ERP | 1 day |
| SINEX | Station Pos. / ERP | 7 days / 1 day |
| SINEX Bias | GNSS biases | 5 min |
| SINEX-tropo ext. | Tropo. ZPD | 2 h/5 min |
| IONEX | Iono. maps/Sat DCB | 2 h |
| ANTEX | Ant. Calibr. | - |
| Site log | Site installation history | - |
Access to Real-Time (RT) IGS products is possible through the NTRIP protocol upon registration. In alternative, high-rate data in RINEX format for nearly-real or post-processed applications can be accessed without any registration from the IGS archive.
More information on formats and communication protocols.
Real-Time PPP
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 (SC-104), which also defines the standard message formats currently employed by PPP services (among others) for the communication between users and reference stations [11]
Related Articles
- Precise Point Positioning
- PPP Fundamentals
- Linear observation model for PPP
- Precise modelling terms for PPP
- Parameters adjustment for PPP
- Real Time Kinematics
- PPP Systems
- Precise GNSS Satellite Coordinates Computation
- Antenna Phase Centre
- Interfaces and Protocols
- DGNSS Standards
- RTK Standards
References
- ^ a b Guide to Use IGS Products
- ^ [Kouba, Jan (et al.), Precise Point Positioning, Chapter 25, Handbook of Global Navigation Satellite Systems, 2017]
- ^ J. Boehm, et al: Troposphere mapping functions for GPS and very long baseline interferometry from European centre for medium-range weather forecasts operational analysis data, J. Geophys. Res. 111(B02406), 1–9 (2006)
- ^ 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. 91-981
- ^ 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
- ^ a b International Earth Rotation and Reference Systems Service (IERS)
- ^ O. Montenbruck, A. Hauschild: Code biases in multi-GNSS point positioning, Proc. ION ITM 2013, San Diego (ION, Virginia 2013) pp. 616–628
- ^ IGS Format
- ^ Special Committee 104, RTCM Recommended Standards for Differential GNSS (Global Navigation Satellite Systems) Service, Version 3.3, Radio Technical Commission for Maritime Services, Alexandria, VA, October 7, 2016.