PPP Standards - Revision history

Gema.Cueto: /* Site Displacements effects */

2020-06-11T10:09:03Z

Site Displacements effects

← Older revision		Revision as of 10:09, 11 June 2020
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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="~~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>. 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).		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===

Gema.Cueto: /* Compatibility and IGS Conventions */

2020-06-11T10:07:30Z

Compatibility and IGS Conventions

← Older revision		Revision as of 10:07, 11 June 2020
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	==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 <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>, 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.		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==

Gema.Cueto: /* Site Displacements effects */

2020-06-11T10:05:12Z

Site Displacements effects

← Older revision		Revision as of 10:05, 11 June 2020
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	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 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> 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.		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.

Gema.Cueto: /* Satellite Effects */

2020-06-11T10:03:45Z

Satellite Effects

← Older revision		Revision as of 10:03, 11 June 2020
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	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.		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="~~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>. 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).		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===

Gema.Cueto: /* Satellite Effects */

2020-06-11T10:02:45Z

Satellite Effects

← Older revision		Revision as of 10:02, 11 June 2020
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	*[[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="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		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~~<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>~~<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> or simply edited out.		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="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>. 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).		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="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>. 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).

Gema.Cueto: /* Site Displacements effects */

2020-06-11T10:02:08Z

Site Displacements effects

← Older revision		Revision as of 10:02, 11 June 2020
Line 45:		Line 45:
	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>Kouba, J., 2008, A simplified yaw-attitude model for eclipsing GPS satellites, GPS Solutions 2008: DOI:10.1007/s10291-008-0092-1</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.		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="Kouba">Kouba, J., 2008, A simplified yaw-attitude model for eclipsing GPS satellites, GPS Solutions 2008: DOI:10.1007/s10291-008-0092-1</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.

Gema.Cueto: /* Satellite Effects */

2020-06-11T10:00:45Z

Satellite Effects

← Older revision		Revision as of 10:00, 11 June 2020
Line 37:		Line 37:
	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.		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="~~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>. 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		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<ref>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><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> or simply edited out.		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 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><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> 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="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>. 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).		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="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>. 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).

Gema.Cueto: /* PPP Corrections Models */

2020-06-11T09:59:07Z

PPP Corrections Models

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	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="~~Handbook~~"></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.		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===

Gema.Cueto: /* Differential Code Biases effects */

2020-06-11T09:56:00Z

Differential Code Biases effects

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	===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> [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.		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==

Gema.Cueto: /* Differential Code Biases effects */

2020-06-11T09:55:25Z

Differential Code Biases effects

← Older revision		Revision as of 09:55, 11 June 2020
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	===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> [~~https://www~~.~~iers~~.~~org/IERS/EN/Home/home_node~~.~~html International Earth Rotation and Reference Systems Service~~ (~~IERS~~)]</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.		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==