Role of Defects on Regioselectivity of Nano Pristine Graphene

Differences in GPS coordinate time series resulting from the use of individual instead of type-mean antenna phase center calibration model KAROL DAWIDOWICZ Institute of Geodesy, University of Warmia and Mazury in Olsztyn, 10-790 Olsztyn, Poland ([email protected]) Received: April 28, 2016; Revised: December 29, 2016; Accepted: May 26, 2017

ABSTRACT It is well-known that the phase center of a Global Navigation Satellite System (GNSS) antenna is not a stable point coinciding with a mechanical reference. The phase center position depends on the direction of the received signal, and is antenna- and signaldependent. Phase center corrections (PCC) models of GNSS antennas have been available for several years. The first method to create antenna PCC models was the relative field calibration procedure. Currently only absolute calibration models are generally recommended for use. In this study we investigate the differences between position estimates obtained using individual and type-mean absolute antenna calibrations in order to better understand how receiver antenna calibration models contribute to the Global Positioning System (GPS) positioning error budget. The station positions were estimated with two absolute calibration models: the igs08.atx model, which contains typemean calibration results, and individual antenna calibration models. Continuous GPS observations from selected Polish European Permanent Network (EPN) stations were used for these studies. The position time series were derived from the precise point positioning (PPP) technique using the NAPEOS scientific GNSS software package. The results show that the differences in the calibrations models propagate directly into the position domain, affecting daily as well sub-daily results. In daily solutions, the position offsets, resulting from the use of individual calibrations instead of type-mean igs08.atx calibrations, can reach up to 5 mm in the Up component, while in the horizontal one they generally stay below 1 mm. It was found that increasing the frequency of sub-daily coordinate solutions amplifies the effects of type-mean vs individual PCC-dependent differences, and also gives visible periodic variations in time series of GPS position differences. K e y w o r d s : GNSS, GPS, EPN, antenna phase center calibration

1. INTRODUCTION It has been well known almost from the beginning of the GPS era that each antenna type has its own characteristics and leads to different systematic errors. In the late 80’s to

Stud. Geophys. Geod., 62 (2018), DOI: 10.1007/s11200-016-0630-1 (in print) © 2018 Inst. Geophys. CAS, Prague

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early 90’s the impact of antenna phase center corrections (PCC) on computed coordinates was not well studied, and it was thought that by using identical equipment the associated errors could be largely reduced. Because of this measurements for the highest precision applications were carried out with identical antenna and receiver types. The mixing of receiver types proved to be less crucial, but the mixing of antenna types remained a serious problem. The precise point whose position is measured by a GNSS receiver is commonly assumed to be the electromagnetic phase center of the GNSS receiver’s antenna. However, GNSS antennas do not have a well-defined phase center, but have a phase transfer function that varies over azimuth and elevation. Additionally, this function is much more complex than a simple first degree spherical function. For any given GNSS antenna, the phase centers will change with the changing direction of the signal from a satellite. This direction-dependent phase transfer function is referred to as PCC and can be determined during antenna/radome calibration. PCCs exist for both satellite and station antennas (Schmid and Rothacher, 2003; Schmid et al., 2007) and are also antenna-type and signal-frequency dependent. A review of the antenna phase center variations problem can be found e.g. in Schupler and Clark (1991); Braun et al. (1993); Geiger (1998); Schmitz et al. (2002); Schmid et al. (2005); Wanninger (2009); Dawidowicz (2013) and Schön and Kersten (2014). Antenna PCCs can reach several centimeters. When identical antennae are used in a relative positioning, the phase center variations cancel out, particularly over short baselines. When different antennae are used, even on short baselines, ignoring these PCCs can lead to significant vertical errors (Rothacher and Mader, 1996; Mader, 1999). The GNSS antenna calibration model consists of two parts: an average phase center offset (PCO) determined with respect to the physical antenna reference point and the phase center variations (PCV) with elevation angle and azimuth dependency. PCO and PCV must be used together to correctly account for PCCs. The dominant antenna type used at the beginning in the International GNSS Service (IGS) network was the Alan Osborne AOAD/M_T antenna. Because of this, that antenna was chosen as a reference in the first developed field calibration method: relative calibration (Mader, 1999). A new approach for absolute calibration of GNSS antennas, utilizing the actual GNSS signal, has been developed by the Institut für Erdmessung (University of Hannover) and the company GEO++ (Wübbena et al., 1997). The main goal of this robot calibration method was the possibility to estimate PCCs, which are independent of a reference antenna. Another advantage is that the effect of multipath is eliminated (Wübbena et al., 2006; Schmid et al., 2007). There are several institutions which are providers of GNSS antenna/radome PCCs. Most of them are located in Germany, e.g., Geo++, Uni-Bonn, University of Hannover (Institut für Erdmessung, IfE), the state survey authorities of Berlin (SenStadt Berlin) and the Technical University of Dresden. The anechoic chamber calibration method should be also mentioned. This method has been used in the past for absolute antenna calibrations. The calibrating setup consists of a fixed transmitter on one end and a remote-controlled positioner carrying the test antenna on the other end of the test range. During calibration, the positioner rotates the test

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Differences in GPS coordinate time series …

antenna and, in this way, simulates the different GNSS satellite directions (Schupler and Clark, 1991; Schupler et al., 1994; Gӧrres et al., 2006; Zeimetz and Kuhlman, 2008). Absolute elevation and azimuth-dependent PCCs obtained using anechoic chambers or a robot were introduced in November 2006 within the International GNSS Service (IGS) to replace elevation-only dependent receiver antenna PCCs based on relative field calibrations (Schmid et al., 2004). Currently, absolute PCCs are routinely used within both the IGS and the EUREF (IGSMAIL-6354). The absolute receiver antenna PCCs included in igs05.atx and igs08.atx files are mean values of the available individual robot calibrations for a specific antenna type or are results of converting relative PCCs to absolute PCCs (PCCs obtained using relative field calibration have been added to the absolute PCCs of AOAD/M_T antenna). This type of calibration result is indicated as antenna type-mean calibrations. This approach assumes that the PCCs of antennas of the same type can all be represented with sufficient accuracy by these type-mean calibrations. In addition to the type-mean calibrations, the EUREF Permanent Network (EPN) currently uses the individual antenna calibrations which refer to specific antenna/radome combinations. The antenna calibration file used within the EPN contains these individual antenna calibrations and (for some antennas) the type-mean calibrations. Thus, we can currently distinguish between two types of absolute PCCs: individual and type-mean. In individual calibrations one specific antenna/radome combination is calibrated several times. Then different calibration results from several sessions are combined into one unique file (as long as the combined data are comparable within a certain amount of precision). In type-mean calibrations, several antenna/radome combinations are calibrated in several sets (the same product line). The calibrations of several individual antenna/radome combinations of the same kind are then combined to one unique file. For an antenna without an individual calibration the first approximation is a type-mean. If more accurate data are needed for this specific antenna, an individual calibration is inevitable. The recent potential of satellite systems and the development of GNSS error-modeling allows the estimation of station coordinates with very high accuracy. The coordinates from weekly or daily solutions can be obtained with millimeter accuracy. The continuous re-processing of GNSS observations reveals, by decreasing the scatter in position estimates, the significant development of GNSS techniques. The associated noise reduction in derived position time-series led to the discovery of the presence of previously undetected jumps or periodic signals. The imperfection in the modeling of antenna PCCs also has the potential to contribute to the discovered jumps and periodic signals. The change from relative to absolute type-mean antenna PCC led to a significant improvement in GNSS solution results (Schmid et al., 2005, 2007; Khoda and Bruyninx, 2007; Dawidowicz, 2014). The update of receiver antenna calibrations from igs05.atx to igs.08.atx also induced a jump in the coordinates of the EPN stations (Baire et al., 2011, 2013). It can be expected that the use of individual calibrations could add further refinements to the computed solutions. To date, the impact of switching from the type-mean to the individual calibration model has been investigated in, e.g., Baire et al. (2013); Sidorov and Teferle (2013). It should be also remembered that troposheric estimates are highly correlated with the


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employed PCCs. In particular, this affects the vertical coordinate components of stations (Zhu et al., 2003; Schmid et al. 2007). In this paper, the impact of the updated receiver antenna PCCs on eight selected Polish EPN stations (Figurski et al., 2009) is investigated. The differences between type-mean and individual calibration results for selected antennas, as well as on how those differences influence the position time series were also analyzed. The period covered one year of observations collected from 1.09.2013 to 31.08.2014. Some details of the used observations are presented in the next section. The assessment is based on the NAPEOS software (Springer, 2009) using the precise point positioning (PPP) technique (Zumberge et al., 1997). PPP is a stand-alone positioning technique using undifferenced dualfrequency code and phase observations. Precise satellite products and accurate physical models are required to achieve high accuracy results. PPP provides a positioning solution in a dynamic, global reference frame, negating any local distortions associated with differential positioning techniques. Details on the achievements and limitations of PPP can be found, among others, in Zumberge et al. (1997); Kouba and Héroux (2001); Rizos et al. (2012); Dawidowicz and Krzan (2014).

2. RESEARCH STRATEGY In this study, one year of GPS observations from eight Polish EPN stations which are also a part of ASG-EUPOS network (Bosy et al., 2008) were used. Table 1 contains some information on the selected stations. In this study PCCs generated by Geo++ and SenStadt (Table 1) were used. It should be noted that so far there is no type-mean PCC for the TRM57971.00 TZGD antenna/radome (station KATO). For this reason, a type-mean PCC for TRM57971.00 NONE antenna/radome was applied, as recommended (igs08_1842.atx). The type-mean calibration distributed by the IGS in the so-called ANTEX format was used. These files contain PCC models derived from absolute field or relative field (converted to absolute) calibration. The type-mean values are provided to the IGS by calibration facilities together with information on the number of individual calibrations and the number of different antenna/radome pairs used to compute the mean.

Table 1. Characteristics of stations used in the analysis. No. Station 1 2 3 4 5 6 7 8

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BPDL GWWL LODZ REDZ SWKI USDL WROC KATO

Stations Hardware

Antenna Calibration Service

Antenna Type

Receiver Type

Type-Mean

Individual

TRM55971.00 TZGD TRM55971.00 TZGD TRM55971.00 TZGD TRM55971.00 TZGD TRM55971.00 TZGD TRM55971.00 TZGD LEIAR25.R4 LEIT TRM57971.00 TZGD

TRIMBLE NETR5 TRIMBLE NETR5 TRIMBLE NETR5 TRIMBLE NETR5 TRIMBLE NETR5 TRIMBLE NETR5 LEICA GR25 TRIMBLE NETR5

Geo++ Geo++ Geo++ Geo++ Geo++ Geo++ Geo++ ---

SenStadt SenStadt SenStadt SenStadt SenStadt SenStadt Geo++ SenStadt



Figure 1 presents the stations used in the investigation. Almost all the ASG-EUPOS stations are located on the roofs of public buildings. Antenna locations were chosen so as to ensure the best possible observation conditions, as well as to have the possibility to locate a 19-inch rack with a GNSS receiver and a communication module at a short distance from the antenna (not exceeding 30 m of antenna cable). The location of the eight chosen stations met the following requirements: -

good visibility of satellites for the entire horizon above the elevation angle of 5; the station antenna mounting has been stabilized by being installed on a special mast fixed to the chimney or roof; no electromagnetic interferences or bounces of signals have been found in the place of installation; the distance between the antenna and the nearest fixed elements (surface of the chimney or roof) is at least 0.6 m.

Therefore, it can be assumed that near-field conditions are similar at all test stations. The processing was done using the NAvigation Package for Earth Observation Satellites ver. 3.3.1 (NAPEOS) (Springer, 2009). Two parallel PPP runs were performed, leaving all processing options identical except the antenna/radome calibrations: -

Fig. 1.

a PPP run using the type-mean PCC (igs08_1842.atx); a PPP run using the individual PCC; computation of the difference (individual minus type-mean results).

Stations used in the investigation. See Table 1 for their codes and characteristics.


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Because all error sources can be considered identical in both PPP runs, the differences in the final solutions are only affected by variations in the antenna/radome calibrations. For a selected station and installed antenna/radome pair, the differences between the daily positions obtained using two PPP post-processing provide the position offset caused by the changed antenna calibration model. In the computations a standard processing strategy was used. The European Space Agency’s (ESA) precise orbit and clock information were applied. As data, a zerodifference GPS code and phase observations were used with a 30-s sampling interval. Additionally, a 10 elevation angle mask was adopted with an elevation-dependent weighting function ( sin e2 ). A priori zenith path delays (ZPDs) were computed with the formula of Saastamoinen using the Global Pressure and Temperature (GPT) model (Boehm et al., 2007); ZPDs were mapped into slant delays using the hydrostatic Global Mapping Function (GMF). The first-order Ionosphere effect was eliminated by forming ionosphere-free linear combination; higher-order effects were not corrected (Springer, 2009). The computations were based on the float as well as the fixed ambiguity solution (Tregoning and Watson, 2009; King and Watson, 2010). NAPEOS strictly follows the International Earth Rotation Service (IERS) convention and used the IAU2000 transformation routines. Ocean loading values are obtained from the ONSALA ocean loading service of M.S. Bos’ and H.-G. Scherneck’s. NAPEOS used the Finite Element Solution 2004 (FES2004) with center of mass corrections (CMCs) (Lyard et al., 2006). The tidal variations due to the Earth’s rotations are fully implemented using the IERS subroutine (Springer, 2009).

3. ANALYSIS In this section, the differences between type-mean and individual PCCs for selected stations are analyzed, as well as the differences in North, East, Up coordinates caused by the switch from type-mean to individual calibration tables in daily and sub-daily GPSonly processing. 3.1. PCC comparison Figure 2 presents the individual versus type-mean PCC differences calculated for ionosphere-free linear combination. For the purposes of this comparison, the PCCs were converted to a common PCO (obtained via type-mean calibration), then the differences between PCCs were calculated and displayed. In analyzing the PCC differences for the ionosphere-free linear combination (Fig. 2), it can be observed that the influence of calibration type on PCC for selected antennas has a magnitude up to ±5 mm. It is also visible that all differences change, depending on elevation and azimuth. Generally, the largest magnitude of the differences between the individual and type-mean solutions occur at low elevation angles. These differences should be minimized in positioning results through the application of the 10 elevation mask and the elevation-dependent weighting during processing. In analyzing the PCC differences for six stations where the same type TRM55971.00 TZGD antenna was mounted (BPDL, GWWL, LODZ, REDZ, SWKI, USDL), it was observed that the antenna/radome combinations have different characteristics.

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Fig. 2. Phase center correction differences (dPCC) between type-mean and individual calibration obtained for the ionosphere-free linear combination. See Table 1 for codes of the stations.


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3.2. Position differences from daily solutions Each daily RINEX data set was processed once using the individual PCC models and the IGS08 type-mean (igs08_1842.atx) calibration models in float as well as fixed ambiguity mode. The North, East and Up differences are presented in Fig. 3. In analyzing the results presented in Fig. 3 (float solution), it is visible that for the horizontal components, the position offsets induced by the differences between both PCC models are below 1 mm. Greater differences can be seen for the Up component. These differences range from 5 to 5 mm depending on the station. It was found that for stations with the same type of antenna/radome combination (TRM55971.00 TZGD) the

Fig. 3. Daily North, East and Up differences caused by the use of different calibration models in daily processing over 01/09/201331/08/2014. See Table 1 for codes of the stations.

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differences also significantly differ and range from 4 mm (BPDL station) to 2 mm (GWWL station). This indicates that all antennas of the same type cannot necessarily be represented confidently by a unique type-mean calibration. For some stations, the periods where some jumps occurred can be observed. This is especially visible for WROC, where the observed changes achieve the greatest value, although such jumps have also been found for other stations. Detailed analysis of the observation files and post-processing results shows that during the period of these incidental residuals some gaps in data occurred. In the author’s opinion, these gaps made the PPP processing more difficult, which resulted in lower precision of the position. Additionally, the PCC can have an different impact on the coordinates calculated for days with incomplete data. Figures 4 and 5 presents box whiskers plots for obtained float and fixed solutions. For fixed solutions the results are characterized by bigger scattering (especially for the Up component). This phenomenon also applies to original time series. It should be remembered that fixing ambiguity is especially important, and recommended, for short observing intervals. Daily static PPP is capable of providing millimeter positioning accuracy in float solution. In Geng et al. (2010) it was demonstrated that using 4-hour observation periods allows to obtain the same accuracy in fixed as well as in float PPP solutions. Additionally, Geng et al. (2009) showed that correct ambiguity resolution may lead to degraded, rather than improved, positioning accuracy in the fixed solutions compared with the float ones. This may be the reason of slightly bigger scattering visible in fixed solutions. The changing calibration models in post-processing from individual to type-mean mostly affect the Up component. In analyzing the first six stations where the same type of antenna was mounted, the previously described differences are translated in the results. These differences should be considered as caused by differences visible in type-mean and individual PCC. The estimated mean position offsets range from 0.1 to 0.7 mm in the North, from 0.0 to 0.7 mm in the East and from 4.1 to 4.5 mm in the Up components. For station WROC, the maximum value of the position component differences exceeds 5 mm and for the East and Up they reach 10 mm. The effect of scattering in differences for WROC stations is also visible in the standard deviation. The highest values were clearly obtained for the WROC station. The analysis of the observation files shows that WROC observations were burdened with more gaps in data. These gaps are characteristic for days where outliers in solution occurred. The WROC observation data problem coincides with December 2013 and January 2014 and, consequently, may also be associated with snow accumulation on the antenna. Historical meteorological data for the regions of station location were checked, and the snow cover is presented in Fig. 6. As shown in Fig. 6 there is no correlation between the WROC observation data (results) problem and snow accumulation on the antenna. First of all, the snow accumulation coincides with the middle of December as well as with January and February 2014. Additionally, in the region of the WROC station the snow cover was very small compared to other station regions (e.g., SWKI, KATO), where there was no such large scattering in position differences.


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Fig. 4. Box-whisker plots (median value, upper and lower quartiles, maximum and minimum values, outliers) for daily North, East and Up differences for float solution. See Table 1 for codes of the stations.

Fig. 5.

The same as in Fig. 4, but for daily fixed solution.

Finally, the calculation of the Lomb-Scargle spectrum (Scargle, 1982; Townsend, 2010) for the data was performed. In Sidorov and Teferle (2013) the impact of switching from type-mean to individual PCCs was investigated, based on the float ambiguity PPP solution. The periodic signals are identified at frequencies matching the overtones of the GPS draconitic year (1.04  n cpy, where n = 2, 3, 4, …). To check whether for the tested dataset similar signals will occure, or whether the observed draconitic signatures will be reduced if ambiguity fixing is performed, spectral analysis was done. For daily solutions

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Fig. 6. Snow cover in the regions of station locations over 01/09/201331/08/2014. See Table 1 for codes of the stations.

the power spectral density (PSD) unit is mm2/cpy. For sub-daily solutions the PSD unit is mm2/cpd. A good guideline for interpreting Lomb-Scargle power is provided in Hatzes (2016), i.e. PSD < 6 - most likely not real; 6 < PSD < 10 - possibly real but probably not; 10 < PSD < 14 - might be real; worth investigating more; 14 < PSD < 20 - most likely real; PSD > 2030 - definitely real. If we take into account only the frequencies above 2 cpy, where normalized PSD exceeds 10, one can observe only a few cases with periodic signals (Fig. 7). Considering the eight stations and three position components, for float solutions 11 cases occur (45.8%) where one can talk about periodicity. For fixed solutions there are only six similar cases (25.0%). Generally, the periodic signals are identified at about 2 cpy frequency, which matching the overtones of the GPS draconitic year. GPS draconitic signal (351.6 ± 0.2 days) and its higher harmonics are observed at almost all IGS products such as position time series of IGS permanent stations. Orbital error and multipath are known as two possible sources of these signals. The effect of Earth shadow crossing of GPS satellites is another suspect for this signal (Allahverdi-Zadeh et al., 2016). The results reveal that the imperfections in the applied antenna/radome PCCs may also contribute to the draconitic harmonics observed in the GPS coordinate time series. On the other hand, the observed draconitic signatures are clearly reduced if ambiguity fixing is performed. 3.3. Position differences from sub-daily solutions This part of the study investigates the differences between position estimates obtained using individual and type-mean (igs08.atx, https://igscb.jpl.nasa.gov/igscb /station/general/igs08.atx) antenna calibration models in GPS pseudo-kinematic processing (that means independent position solutions at each, very short, observation


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Fig. 7. Lomb-Scargle periodograms for daily position differences. PSD - power spectral density. See Table 1 for codes of the stations.

window). 15-min observation windows were used to study the short-period oscillations. The results are presented in Fig. 8. For the readability of the graphs, only the results of the first seven days of the analyzed period are presented. Analyzing the float solutions, the differences in all three position components have visible periodicity. The differences reveal the following: -

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the presented stations exhibit position component shifts up to 5 mm; the differences experience rapid changes within short time periods; the amplitudes of these differences reach up to 10 mm; variations in differences have periods close to 24 hours, which corresponds to the orbital period of the GPS satellites. Stud. Geophys. Geod., 62 (2018)


For fixed solutions, the periodicity it is not so evident, but it is also observable. It can be also observed that the amplitude of differences in the height are greater than for other two position components. Figures 9 and 10 present box-whisker plots of obtained results. Generally the position offsets in the height component are evidently greater than for horizontal components. For BPDL and LODZ stations, the Up component bias reaches up to 5 mm. For North and East components the differences are visibly smaller. The results of the float as well as the fixed solution showed that the differences in the calibration models directly propagate into the position domain, affecting sub-daily results. It was demonstrated that the mean position offsets (one week of pseudo-kinematic

Fig. 8. Sub-daily North, East and Up coordinate differences caused by the use of different calibration models in 15-min observation windows over 01/09/201331/08/2014. See Table 1 for codes of the stations. Stud. Geophys. Geod., 62 (2018)

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observations), resulting from the use of individual calibrations instead of type-mean igs08.atx calibrations, can reach up to 5 mm in the Up component, while the offsets in the horizontal components generally remain below 1 mm. It was also observed that the obtained mean differences significantly differ, even for stations where antennas/radomes of the same model were mounted. This indicates that all antennas of the same type cannot necessarily be represented confidently by a unique type-mean calibration. To detect the periodicity in the obtained results, the Lomb-Scargle spectrum was calculated. Figure 11 presents the power of detected periodic signals in cpd.

Fig. 9. Box-whisker plots of sub-daily North, East, Up differences for the float solution. See Table 1 for codes of the stations.

Fig. 10. The same as in Fig. 9, but for the fixed solution.

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Fig. 11. Lomb-Scargle periodograms for sub-daily position differences at individual stations for the float and fixed solutions. PSD - power spectral density. See Table 1 for codes of the stations.

Analyzing the results presented in Fig. 11, strong periodic signals can be identified for the float as well as the fixed solution. The obtained results reveal that variations in differences in all stations have periods close to 12 hours (2 cpd) which agree with the orbital period of the GPS satellites. Generally, this is true for all stations and all position components. However, it is visible in Fig. 11 (for almost all stations) that there is also some periodicity at 1, 3 and 4 cpd frequencies.


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4. CONCLUSIONS This paper investigated how different antenna calibration models impact estimated station positions. Position offsets were derived from the daily and sub-daily position differences between PPP runs differing only by the model used for the receiving antenna. This study focused only on the GPS part of the calibrations based on a set of 8 individually calibrated antenna/radome combinations. In analyzing the PCC differences for the ionosphere-free linear combination, it can be observed that the influence of calibration type on PCC for selected antennas has a magnitude up to ± 5 mm. Generally, the largest differences occur at low elevation angles. These differences should be minimized in positioning results through the application of the 10 degree elevation mask and the elevation-dependent weighting during processing. In analyzing GPS coordinate time series it was found that the position offsets resulting from the use of individual calibrations instead of type-mean igs08.atx calibrations can reach up to 5 mm in the Up component, while in the horizontal components the offsets generally remain below 1 mm (in daily as well as in sub-daily results). The daily results also show that there are incidental jumps in differences. This is especially visible for the WROC station, where changes achieved the greatest values, although for other stations such jumps were also found. These observation data problems coincide with December 2013 and January 2014 and, consequently, may also be associated with snow accumulation on the antenna. The historical meteorological data were checked, and it was shown that there is no correlation between the observed increased scatter in the results and snow accumulation on the antenna. Detailed analysis of observation files shows that during the period of these incidental residuals, some gaps in data occurred. The most convincing reason for these oscillations is that the PCC can have a different impact on the coordinates calculated for days with incomplete data. Calculation of the Lomb-Scargle spectrum for the data revealed only a few cases where some weak periodicity up to 2 cpy can be considered. For float solutions it occurred for 45.8% of the investigated position components, and for fixed solutions there were only 25.0% of similar cases. Generally, the periodic signals are identified at about 2 cpy frequency, which matching the second harmonic of the GPS draconitic year. The results reveal that the imperfections in the applied antenna/radome PCCs may contribute to the draconitic harmonics observed in the GPS coordinate time series. On the other hand, the observed draconitic signatures are clearly reduced if ambiguity fixing is performed. The sub-daily results show that the differences in the calibration models propagate directly into the position domain, affecting obtained position differences and giving periodic variations. The main sub-daily variations have periods close to half a sidereal day with amplitudes of up to 10 mm in position components. Some periodicity is also found at 2, 3 and 4 cpd frequencies. Clear differences, in the size of mean position bias, were also observed for the station where the same antenna/radome model was mounted. These differences are mainly related to the PCC deficiencies of a particular antenna/radome model, and may indicate that all antennas of the same type cannot necessarily be represented confidently by a unique type-

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mean calibration. Because of the very similar near-field conditions at all stations, it can be assumed that the impact of the near-field effect was insignificant. Acknowledgements: The author is grateful for GNSS data provided by the International GNSS Service, EUREF Permanent Network, and the European Space Agency. Special thanks to Grzegorz Krzan for guidance on how to use NAPEOS software.

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