Satellite laser ranging to GPS and GLONASS
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Abstract
Satellite laser ranging (SLR) to the satellites of the global navigation satellite systems (GNSS) provides substantial and valuable information about the accuracy and quality of GNSS orbits and allows for the SLRGNSS colocation in space. In the framework of the NAVSTARSLR experiment two GPS satellites of BlockIIA were equipped with laser retroreflector arrays (LRAs), whereas all satellites of the GLONASS system are equipped with LRAs in an operational mode. We summarize the outcome of the NAVSTARSLR experiment by processing 20 years of SLR observations to GPS and 12 years of SLR observations to GLONASS satellites using the reprocessed microwave orbits provided by the center for orbit determination in Europe (CODE). The dependency of the SLR residuals on the size, shape, and number of corner cubes in LRAs is studied. We show that the mean SLR residuals and the RMS of residuals depend on the coating of the LRAs and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including the singlephoton and multiphoton detection modes. We also show that the SLR observations to GNSS satellites are important to validate GNSS orbits and to assess deficiencies in the solar radiation pressure models. We found that the satellite signature effect, which is defined as a spread of optical pulse signals due to reflection from multiple reflectors, causes the variations of mean SLR residuals of up to 15 mm between the observations at nadir angles of 0\(^{\circ }\) and 14\(^{\circ }\). in case of multiphoton SLR stations. For singlephoton SLR stations this effect does not exceed 1 mm. When using the new empirical CODE orbit model (ECOM), the SLR mean residual falls into the range 0.1–1.8 mm for highperforming singlephoton SLR stations observing GLONASSM satellites with uncoated corner cubes. For bestperforming multiphoton stations the mean SLR residuals are between \(12.2\) and \(25.6\) mm due to the satellite signature effect.
Keywords
SLR GNSS Precise orbit determination Satellite signature effect Corner cube coating SLR reflector types1 Introduction
1.1 Role of SLR and GNSS in space geodesy
Satellite laser ranging (SLR) observations of global navigation satellite systems (GNSS) become more and more important for satellite geodesy by providing a precise link in space between the two techniques. The strengths of SLR and GNSS solutions are different for different geophysical phenomena and for the realization of the geodetic reference frames. SLR contributes to certain datum parameters of the reference frame, i.e., to the origin and the scale. The advantage of the SLR technique lies in the observation principle based on short laser pulses with fast risetimes, resulting in a tracking precision at a level of a few millimeters. Laser range observations are free from many propagation issues related, e.g., to ionosphere delays, microwave antenna phase center variations, or phase ambiguities. Moreover, SLR observations to geodetic satellites take full advantage of a simple construction of passive satellites. Geodetic SLR satellites are dense and have spherical shapes and small areatomass ratio, which also minimizes orbit perturbations related to nongravitational forces, e.g., atmospheric drag and solar radiation pressure.
When analyzing GNSS microwave observations, modeling problems related to the uncalibrated satellite antenna phase center offsets are a major error source for the scale (Thaller et al. 2014), whereas the deficiencies in solar radiation pressure modeling affect the GNSSderived geocenter series, in particular the \(Z\) component (Meindl et al. 2013). On the other hand, the global distribution of the GNSS stations is nowadays homogeneous with a high density of observing stations, as opposed to the SLR network with merely seven observing stations in the southern hemisphere. Moreover, the Earth rotation parameters derived from GNSS and the horizontal components of station coordinates are superior to the SLRderived values (Thaller et al. 2011). GNSS solutions are crucial for the densification of the international terrestrial reference frame (ITRF) to regional and national reference frames. The high consistency and a good connection between SLR and GNSS are, thus, indispensable.
The International Laser Ranging Service (ILRS, Pearlman et al. 2002) coordinates all operational and scientific activities of the institutions involved in scientific satellite and lunar laser ranging since 1998 (Gurtner et al. 2005). The Center for Orbit Determination (CODE), hosted by the Astronomical Institute of the University of Bern (AIUB) is one of the ILRS associated analysis centers. CODE provides the GNSS quicklook residual analysis reports on a daily basis, which compare the SLR observations to GLONASS and GPS satellites with the microwave orbits. The reports assess thus the consistency level between GNSS and SLR solutions.
1.2 GNSS satellites tracked by SLR
In the NAVSTARSLR experiment two GPS satellites of BlockIIA were equipped with laser retroreflector arrays (LRAs) dedicated to SLR, namely GPS36 launched on March 10, 1994 and GPS35 launched on August 30, 1993. GPS36 was observed continuously by SLR stations between 1994 and 2014. The satellite was deactivated in February 2014.^{1} GPS35 was continuously observed until 2009, when the satellite was decommissioned. Between 2010 and 2013 GPS35 was reactivated several times for short periods. In 2011 the ILRS decided to remove this satellite from the official list of tracked satellites. Afterwards, only one SLR station, Zimmerwald, continued to track GPS35 in 2012–2013 with SLR.
The basic objectives of the NAVSTARSLR experiment were the accurate independent orbit determination of the satellites and the separation of the orbital errors from the onboard clock errors (Beard 2014).
As opposed to the GPS system, all satellites of the Russian GLONASS, the European Galileo, and the Chinese BeiDou are equipped with laser retroreflectors. It is also planned that the GPSIII satellites will carry laser retroreflectors in the future (Thomas and Merkovitz 2014).
Although all GLONASS satellites are equipped with SLR retroreflectors, only three GLONASS satellites were recommended for tracking by the ILRS in the period of 2002–2010—typically one satellite per plane. In 2010 the ILRS decided to increase the number of officiallytracked GLONASS satellites to six—two per plane. Exceeding the ILRS recommendations, several of the more able SLR stations started tracking the full constellation of GLONASS in 2010–2011. The first station tracking the full GLONASS constellation was Herstmonceux (Wilkinson 2012; Appleby 2013), followed by Zimmerwald (Ploner et al. 2012), Graz, Yarragadee, Potsdam, Changchun, Shanghai, Simeiz, Altay, Arkhyz, and some other ILRS stations.
Today, all active GLONASS satellites are tracked by many SLR stations. This results in a very good tracking record of different GNSS satellites, which allows us to validate the GNSS microwave orbits (Zhu et al. 1997; Appleby et al. 1999; Urschl et al. 2007; Fritsche et al. 2014; Montenbruck et al. 2015, Steigenberger et al. 2015), to generate precise satellite orbits using SLR data (e.g., Rodriguez and Appleby 2013), and to combine SLR and GNSS techniques using the colocations in space. The space colocations allow, e.g., improving the quality of the GNSS orbits, estimating the satellite microwave antenna offsets, and the scale transfer from the SLR to GNSS solutions (Thaller et al. 2011, 2012a, b). The satellite colocations are independent of the local ties on ground, which are often affected by systematic errors (Altamimi et al. 2011). Moreover, the increasing number of SLR observations to GNSS satellites will strengthen, in the near future, the realization of the international terrestrial reference system (ITRS) due to better established SLR station coordinates and improved observation geometry in SLR solutions.
1.3 Increasing importance of SLR to the improvement of GNSS solutions
The 18th international workshop on laser ranging, which was held in Fujiyoshida (Japan) in November 2013,^{2} recognized the “increasing importance of SLR to the improvement of GNSS performance”. The resolution of the workshop paid special attention to “the necessity of the SLR technique to the improvement of time, frequency, and ephemeris data products from GNSS” and to “the significant contribution of the global geodetic observing system (GGOS) to the development of GNSS measurement accuracy through colocation with SLR and other measurement techniques”. The laser ranging to GNSS s/c experiment (LARGE) group was established in the aftermath of this workshop as an official study group of the ILRS.^{3} The primary objectives of the LARGE group include a definition of an operational GNSS tracking strategy for the ILRS and improving the consistency between products provided by the ILRS and the International GNSS Service (IGS, Dow et al. 2009).
1.4 Goal of this study
The future realization of the ITRF will probably comprise also SLR observations of GNSS satellites. This paper summarizes the results of the NAVSTARSLR experiment and the outcome from the campaign of intensive SLR tracking of GLONASS satellites as a preparation for the future ITRF. We process 20 years of SLR observations to GPS and 12 years of SLR observations to GLONASS satellites using the reprocessed microwave orbits provided by CODE. The solution strategy in this paper is similar to that of the daily CODE quicklook residual analysis reports. We investigate the SLR residuals to GPS and GLONASS microwave orbits without estimating any parameters. This study provides thus the information about the consistency between SLR and GNSS solutions and about the SLR efficiency for the quality assessment of GNSS orbits.
2 Method of analysis
2.1 GNSS solutions
We use GPS and GLONASS orbits determined in the second IGS reprocessing campaign for the preparation of the ITRF2014. The CODE solutions follow the IGS requirements for reprocessed IGS products,^{4} including the use of the IERS Conventions 2010 (Petit and Luzum 2011) for mean pole definition and tidal displacements, the IGb08 reference frame with updated absolute antenna calibrations, and the use of higherorder ionospheric corrections from the IERS Conventions, and Earth radiation pressure modeling by RodriguezSolano et al. (2012). The blockdependent transmitter thrust values were used for the GPS satellites, whereas for all GLONASS satellites a thrust assumption of 100 W was applied. The CODE solutions were based on GPSonly observations in 1994–2001 and on combined GPS and GLONASS observations in 2002–2013. The GNSS stations tracking only GLONASS satellites were not used in the analysis. The solution was generated with the development version of Bernese GNSS Software v. 5.3 (Dach et al. 2007).

a constant acceleration in the Sun direction \(D_0\),

a constant acceleration along the axis of the satellites’ solar panels \(Y_0\),

a constant and two onceperrevolution accelerations in the direction \(X\): \(X_0, X_S. X_C\). The \(X\) direction completes righthanded coordinate system.
As opposed to other analysis centers, CODE provided two solutions for the IGS repro2 campaign: clean oneday solutions (CF2) and the threeday longarc solutions (CO2) with the satellite orbits and Earth rotation parameters referring always to the middle day of 3day satellite arcs. Both solutions are validated in our analysis.
Two different models of solar radiation pressure are tested in Sect. 5: the classical ECOM and the extended ECOM which is used for operational CODE IGS products since January 2015. A test based on 2year solutions is performed to demonstrate the SLR potential for validating and assessing the quality of the microwavebased orbits of GNSS satellites.
2.2 SLR solutions
The SLR range residuals are computed as differences between laser ranges and the microwavebased positions of GNSS satellites. The consistent GNSSderived Earth rotation parameters from the CO2 or CF2 solutions are used for the transformation between the Earthfixed and inertial reference frames. The station coordinates are fixed to the a priori reference frame SLRF2008.^{6} The SLR observations are corrected for relativistic effects, troposphere delays, and for the offset of the LRAs w.r.t. the satellites’ centers of mass. The official ILRS values of LRA offsets are used^{7} without any time dependencies. The a priori range bias corrections are applied as recommended by the Analysis Working Group of the ILRS for the ITRF2014 reprocessing of LAGEOS and Etalon data.^{8} The station displacement models, including solid Earth tides, ocean tidal loading, and nontidal station displacements are consistent with the IERS Conventions 2010 and thus also with the microwavebased GNSS solutions. Moreover, the same version 5.3 of the Bernese GNSS Software is used to ensure a full consistency between GNSS and SLR solutions. The SLR residuals constitute good proxies for the radial accuracy of the microwavederived orbits, because the maximum angle of incidence of a laser pulse is only about \(13^\circ \) and \(14^\circ \) for GPS and GLONASS satellites, respectively.
Almost every SLR station has a different technology, including different detectors, using different laser pulse widths, laser repetition rates, and edit levels for the normal point formation. This broad spectrum of uniquely developed stations impacts upon the different qualities of data provided.
Because of the differences in quality and quantity of SLR observations, we apply a twostep procedure of SLR data screening: In the first step, only the largest outliers of hundreds of meters are removed. Then we perform an analysis of 20 years of SLR data with the estimation of the mean value of SLR residuals w.r.t. GNSS microwavebased orbits and the RMS of residuals for each individual stationsatellite pair. RMS denotes here a standard deviation of SLR residuals around mean value, without removing any systematic effects. In the second step of the residual screening, we reject all observations exceeding the threshold: mean \(\pm 3 \cdot \) RMS. In this way we avoid a removal of the observations with small RMS values but large biases to GNSS satellites in our analysis. We are thus able to keep as many measurements as possible especially in the analysis of sparse observations collected by lowerperforming SLR stations in the nineties.
2.3 SLR stations observing GNSS satellites
List of SLR stations observing GNSS satellites with a colocation with other techniques of space geodesy and a number of SLR observations to GPS and GLONASS after screening
Station  Code  Site  DOMES  GNSS  VLBI  DORIS  SLR@GPS  SLR@GLO 

1824  GLSL  Golosiv, Ukraine  12356S001  \(\times \)  0  477  
1863  MAID  Maidanak 2, Uzbekistan  12340S001  3  19  
1864   Maidanak 1, Uzbekistan  12340S002  774  1307  
1868  KOML  Komsomolsk, Russia  12341S001  76  5281  
1873  SIML  Simeiz, Crimea  12337S003  \(\times \)  \(\times \)  62  1945  
1879  ALTL  Altay, Russia  12372S001  64  8646  
1884  RIGL  Riga, Latvia  12302S002  \(\times \)  740  0  
1886  ARKL  Arkhyz, Russia  12373S001  0  3314  
1887  BAIL  Baikonur, Kazakhstan  25603S001  0  3241  
1888  SVEL  Svetloe, Russia  12350S002  \(\times \)  \(\times \)  0  78  
1889  ZELL  Zelenchukskya, Russia  12351S002  \(\times \)  \(\times \)  0  1801  
1890  BADL  Badary, Russia  12338S004  \(\times \)  \(\times \)  \(\times \)  0  519 
1893  KTZL  Katzively, Crimea  12337S006  265  5498  
7080  MDOL  McDonald Observatory, Texas  40442M006  \(\times \)  3505  3796  
7090  YARL  Yarragadee, Australia  50107M001  \(\times \)  \(\times \)  23,284  83,135  
7105  GODL  Greenbelt, Maryland  40451M105  \(\times \)  \(\times \)  \(\times \)  1036  10,259 
7110  MONL  Monument Peak, California  40497M001  \(\times \)  5865  12,863  
7124  THTL  Tahiti, French Polynesia  92201M007  \(\times \)  \(\times \)  0  1479  
7210  HALL  Haleakala, Hawaii  40445M001  \(\times \)  7009  1526  
7231  WUHL  Wuhan, China  21602S004  \(\times \)  \(\times \)  15  0  
7237  CHAL  Changchun, China  21611S001  \(\times \)  1214  27,692  
7249  BEIL  Beijing, China  21601S004  \(\times \)  104  3435  
7308  KOGC  Koganei, Japan  21704S002  \(\times \)  \(\times \)  745  4393  
7335  KASL  Kashima, Japan  21701M002  \(\times \)  \(\times \)  4  0  
7339  TATL  Tateyama, Japan  21740M001  \(\times \)  77  0  
7355  URUL  Urumqi, China  21612M002  \(\times \)  \(\times \)  23  55  
7358  GMSL  Tanegashima, Japan  21749S001  \(\times \)  336  721  
7405  CONL  Concepción, Chile  41719M001  \(\times \)  \(\times \)  1369  6642  
7406  SJUL  San Juan, Argentina  41508S003  6266  20,402  
7501  HARL  Hartebeesthoek, South Africa  30302M003  \(\times \)  \(\times \)  \(\times \)  141  11,064 
7810  ZIML  Zimmerwald, Switzerland  14001S007  \(\times \)  9695  61,670  
7811  BORL  Borówiec, Poland  12205S001  \(\times \)  5  0  
7820  KUNL  Kunming, China  21609S002  \(\times \)  197  60  
7821  SHA2  Shanghai, China  21605S010  \(\times \)  \(\times \)  183  8152  
7824  SFEL  San Fernando, Spain  13402S007  \(\times \)  0  1231  
7825  STL3  Mt Stromlo, Australia  50119S003  \(\times \)  \(\times \)  2647  13,352  
7832  RIYL  Riyadh, Saudi Arabia  20101S001  \(\times \)  9482  7945  
7835  GRSL  Grasse, France  10002S001  \(\times \)  139  66  
7836  POTL  Potsdam, Germany  14106S009  \(\times \)  123  137  
7837  SHAL  Shanghai, China  21605S001  \(\times \)  \(\times \)  0  266  
7838  SISL  Simosato, Japan  21726S001  99  2365  
7839  GRZL  Graz, Austria  11001S002  \(\times \)  10,376  45,533  
7840  HERL  Herstmonceux, UK  13212S001  \(\times \)  6351  20,171  
7841  POT3  Potsdam, Germany  14106S011  \(\times \)  102  4687  
7843  ORRL  Orroral, Australia  50103S007  1675  0  
7845  GRSM  Grasse, France  10002S002  \(\times \)  5721  6266  
7849  STRL  Mt Stromlo, Australia  50119S001  \(\times \)  \(\times \)  546  651  
7884  –  Albuquerque, New Mexico  40429S001  \(\times \)  763  0  
7918  –  Greenbelt, Maryland  40451M120  \(\times \)  \(\times \)  \(\times \)  65  0 
7941  MATM  Matera, Italy  12734S008  \(\times \)  \(\times \)  1334  19,657  
8834  WETL  Wettzell, Germany  14201S018  \(\times \)  \(\times \)  5320  18,164 
3 SLR validation of GPS orbits
The GPS LRAs were constructed by the Russian Institute for Space Device Engineering and are similar in design to those used on the GLONASS satellites. However, the total reflecting area is much smaller due to the limited mounting space on the GPS satellites. GPS35 and GPS36 were deployed with LRAs in the framework of the NAVSTARSLR experiment. The first satellites that will be deployed with LRAs in the operational mode are GPSIII, which will replace the current GPS satellites. The first launch of a GPSIII satellite is planed for 2016, but the launch of the first vehicle equipped with LRA will take place not earlier than in 2019 (Thomas and Merkovitz 2014).
Each retroreflector of GPS35/36 is coated on the back reflective surfaces with aluminum. The GPS retroreflector array consists of merely 32 fusedquartz corner cubes (for GLONASS the number of corner cubes varies between 112 and 396), which are arranged in a flat panel in alternating rows of either four or five cubes. The array size is \(239 \times 194 \times 37\) mm in length, width, and height, respectively.
The small size of the LRAs causes difficulties of tracking GPS satellites for many SLR stations, especially in the nineties, due to the low energy of returning pulses. On the other hand, the optical center (effective reflection point) of the smaller arrays is better defined. Smaller LRAs are subject to smaller variations of the effective reflection points for different incidence angles.
3.1 RMS of residuals for GPS and GLONASS
The RMS of SLR residuals to GLONASS is 46 and 57 mm in 2002 for the CO2 and CF2 solutions, respectively, and it is reduced to 37 mm in 2013, implying that even in the last years the accuracy of GLONASS orbits did not reach that of the GPS orbits. However, the number of SLR observations to GLONASS substantially grew in 2011, when more and more ILRS stations started tracking the full GLONASS constellation. The yearly average number of SLR observations to the two GPS satellites is 5400 with a maximum in 2005 of 8700. The number of SLR observations to all GLONASS satellites varies from 10,700 observations in 2004 (3 GLONASS satellites were tracked in this period) to 87,000 in 2013, when the full constellation was tracked.
Figure 2 also shows that the RMS of SLR residuals is typically smaller for the 3day CO2 solutions than for the 1day CF2 solutions, on average by 4 % for GPS and from 30 % in 2002–2005 to 1 % in 2013 for GLONASS. For GPS the differences between CO2 and CF2 are largest in 1994 and in the period 1999–2003. In the 3day GNSS solutions, the satellite orbits are continuous, the Earth rotation parameters have imposed continuities at the day boundaries, and as a result, the 3day solutions are much more stable than the 1day GNSS solutions. Lutz et al. (2015) studied different arc lengths of GPS and GLONASS orbits and they found that the generation of the 3day arc solutions improves in particular the estimates of polar rates and geocenter coordinates. Figure 2 shows that the 3day arc definition is advantageous in particular for incomplete satellite constellations observed by the sparse and inhomogeneously distributed ground network of GLONASS receivers in the early years of GLONASS solutions (i.e., before 2009).
After 2008, CO2 and CF2 show a similar performance for GPS satellites. Figure 2 shows that after 2008 the RMS of residuals increases in both solutions, which can be related on the one hand to an increasing number of newly established SLR stations which were not taken into account in the ITRF2008 solution and have only approximate coordinates in SLRF2008, and on the other hand, it can be related to the aging process of GPS satellites. GPS satellites of Block IIA were designed for 7.5 years, whereas their real lifetime was three times longer (about 21 years). The center of mass of GPS satellites was expected to change its position by 4.6 mm^{9} in the \(Z\) direction over the 7.5year life time of the mission due to the fuel combustion during satellite maneuvers. In this study we use the average value of the LRA offset w.r.t. the satellite center of mass for the entire period, which may also contribute to the increased RMS of SLR residuals in the most recent years of the mission.
Only the CO2 results are discussed in the following sections, because of the better performance of the CO2 solutions as compared to CF2.
3.2 Stationrelated residuals
The mean residual of all stations (see Fig. 4, right most column) assumes a maximum value between 1999 and 2002 (about \(23\) mm) and after 2010 (\(14\) mm), whereas it is smallest in 1995 (\(3\) mm). One would expect a linear change of the SLR mean due to the change of satellite center of mass over the lifetime of a satellite, rather than a signature with two minima and two maxima. The variations of the mean offsets are, therefore, mostly related to the equipment changes at SLR stations, but they may also be related to some mismodeled higherorder ionosphere delay terms in the GNSS microwave solutions. From the analysis of GOCE data, it was found that the modeling of highorder ionosphere delay as proposed by the IERS 2010 Conventions cannot fully account for large microwave signal delays in the ionosphere during periods of high solar activity (Jäggi et al. 2015). The GNSS highorder ionosphere signal delay may be underestimated when using a priori ionosphere maps of the insufficient space and time resolution, resulting in the averaging out the large shortterm signal delays in the ionosphere. The periods of maximum negative SLR means correspond to the periods of the highest solar and thus also the highest ionosphere activities. The issues related to the modeling of the highorder ionosphere delays in GNSS microwave solutions should be further analyzed.
3.3 Satellite signature effect
The size of the flat onboard laser arrays and the spread of optical pulses due to reflection from several reflectors is one of the major error sources in SLR and it is often called the satellite signature effect (Otsubo et al. 2001).
For singlephoton systems, the average reflection point coincides with the array center, because it corresponds to the centroid of the residual histogram. As each detected photon may originate from anyone of the retroreflectors, the spatial distribution of the whole array is mapped over many detections (Otsubo et al. 2015). Thus, the SLR stations operating in the singlephoton mode are free of the issues related to different incidence angles of a laser beam for flat LRAs. Herstmonceux (7840) is the only station working strictly at the singlephoton level using a Geigermode such that it is able to make only one detection per laser shot after having been armed by the gating subsystem (Wilkinson and Appleby 2011). Graz (7839) and Zimmerwald (after 2008) are also using CSPAD detectors at low return rate, which allow the laser ranges from these stations to minimize the satellite signature effect.
The NASA SLR stations, e.g., McDonald (7080), Yarragadee (7090), Greenbelt (7105), and Monument Peak (7110), are typically equipped with microchannel plates with a high detection level (multiphoton mode). The effective array size, which is the measure of the spread of optical pulse signals due to the reflection from multiple reflectors, is higher for highenergy detection systems, because the detection timing is defined at some threshold level at the leading edge of the return pulse. Otsubo et al. (2001) found that the effective array size for olderclass GLONASS satellites with large LRAs (396 corner cubes) is between +0.1 and +0.3 m for multiphoton systems, whereas it is \(0.1\) and +0.1 m for single photon systems. This difference is equivalent to measured ranges 15–45 mm shorter than expected for the multiphoton detection systems observing GLONASS satellites at low and high elevation angles.
Figure 4 shows that the NASA SLR stations (7080, 7090, 7105, 7110) observing in the multiphoton mode have larger negative SLR means, typically between \(10\) and \(35\) mm, whereas the stations operating at low return rate (7810 after 2008, 7839, 7840) have SLR means between +10 and \(15\) mm. This clearly shows that systemdependent LRA offset corrections, similar to those used by the ILRS Analysis Working Group for LAGEOS and Etalon (Otsubo and Appleby 2003) and in future also for Ajisai (Otsubo et al. 1999), LARES, Stella, and Starlette (Otsubo et al. 2015), are urgently needed for GNSS satellites.
Taking only the residuals from Herstmonceux (7840) operating strictly at the singlephoton mode, the SLR mean for the period 1995–2010^{10} is \(4.2\) mm with the slope of \(0.65\) mm/year, which is slightly larger than the expected change of satellite centerofmass over the satellite’s lifetime (nominal value of \(0.61\) mm/year assuming 7.5 years of satellite lifetime, and \(0.23\) mm/year assuming 21 years of satellite lifetime). This small value of SLR mean indicates that the microwavebased GNSS and opticalbased SLR observations currently agree at a few mmlevel. The consistency between both space geodetic techniques can further be increased by taking into account both, geophysical and technical differences, between microwave and optical spacegeodetic techniques (see next Section).
3.4 GPSSLR mean residuals: a summary
 modeling of the Earth albedo and infrared reradiation pressure (about 10 mm) (RodriguezSolano et al. 2012),Table 2
SLR observation characteristics to GPS satellites
Satellite
Plane
No. obs
Mean (mm)
RMS (mm)
GPS35
2
52,868
\(12.8\)
22.8
GPS36
3
57,797
\(13.5\)
23.6

modeling the antenna thrust (5–10 mm),

use of consistent reference frame (identical scales of reference frames in IGb08 and SLRF2008) and improved phase center modeling in igs08.atx.

atmospheric pressure loading corrections to remove systematic effects related to the weatherdependency of SLR solutions, i.e., the socalled BlueSky effect,

modeling temporal changes of satellite center of mass over a satellite’s lifetime,

modeling variations of the effective reflection points for different incidence angles for different SLR detectors and satellite retroreflectors,

improved modeling of solar radiation pressure on GNSS satellites,

improved modeling of higherorder ionosphere delays for GNSS signals,

improved values of microwave satellite antenna offsets.
Sośnica et al. (2013) showed that the BlueSky effect amounts on average to 1 mm and can reach up to 4.4 mm for continental SLR stations. Arnold et al. (2015) showed that the mean SLR residuals to GPS satellites are reduced by about 2 mm using the extended ECOM model for the impact of solar radiation pressure. The change of the satellite center of mass may be responsible for a bias of up to 5 mm, whereas the variations of the effective reflection points for different incidence angles for different receiving systems depend on the effective size of retroreflector and can even reach values of up to 22 mm for largesize GLONASS LRAs Otsubo et al. (2001).
Thaller et al. (2012b) found that the microwave antenna offsets of IGS08 are not consistent with the SLR scale of the reference frame ITRF2008. The estimated satellite antenna offsets amount to \(86\) and \(110\) mm for GPS and GLONASS satellites, respectively. Springer et al. (2009) found antenna offset corrections w.r.t. the official igs05.atx values exceeding values of \(300\) mm for some GNSS satellites using an analysis of GNSSonly and GNSSSLR solutions. The large values of satellite antenna offset corrections (even of \(300\) mm) compared to the small SLR mean w.r.t. GNSS orbits (about \(13\) mm) indicate that inaccurate microwave antenna offsets must be being absorbed by GNSSderived parameters other than satellite orbits, e.g., by satellite or receiver clocks, troposphere delays, phase ambiguities, or the vertical component of the station coordinates. We, therefore, conclude that the remaining offsets between SLR and GNSS solutions originate to the greatest extent from the variations of the effective reflection points for different SLR receiving systems, modeling of highorder ionosphere delays, the BlueSky effect, and GNSS models of solar radiation pressure. The latter will be addressed in Sect. 5.
4 SLR validation of GLONASS orbits
Since December 2010, the full constellation of GLONASS satellites has been tracked by the SLR stations. Moreover, the ILRS initiated a campaign of intensive SLR tracking of all active GNSS satellites equipped with LRAs. This resulted in a substantial amount of highquality SLR data to a large number of GLONASS satellites of different types and generations.
GLONASS satellites are equipped with LRAs of different types and coating. LRAs form rectangular regular arrays (GLONASS95, 99, and above up to 131, except for 125), circular arrays (GLONASS84, 86, 87, 89), regular ring arrays (GLONASSK1125), or irregular arrays covering the front side of the satellites (GLONASS82). GLONASS LRAs consist of 112, 123, 124, 132 or 396 corner cubes. The olderclass GLONASS satellites are typically equipped with aluminum (AL) coated corner cubes, whereas the recently launched satellites have typically uncoated corner cube retroreflectors. Different types of GLONASS LRAs are characterized by different numbers of returning photons and by different RMS of SLR normal points (Ploner et al. 2012), as well as by different mean offsets and residual characteristics between SLR and microwave orbit solutions.
Characteristics of the GLONASS satellites tracked by the ILRS stations
Type  ILRS  SVN  Slot  COSPAR  Plane  Coating  LRA shape  No. cc  From  To  No. obs  Mean  RMS 

–  82  779  R01  1998077A  1  AL  Irregular planar  396  2002  2002  1194  2.6  44.9 
–  86  790  R06  2001053C  1  AL  Irregular circle  132  2002  2002  4643  8.5  46.4 
–  87  789  R03  2001053B  1  AL  Irregular circle  132  2002  2007  38,546  \(\)0.6  42.4 
–  89  791  R22  2002060A  3  AL  Irregular circle  132  2003  2007  32,509  \(\)3.4  40.8 
M  95  712  R08  2004053B  1  AL  Rectangular  112  2005  2013  23,005  6.9  37.0 
M  99  713  R24  2005050B  3  AL  Rectangular  112  2007  2009  18,883  \(\)2.5  40.8 
M  100  714  R18  2005050A  3  AL  Rectangular  112  2009  2011  1686  11.2  55.2 
M  101  715  R14  2006062C  2  AL  Rectangular  112  2009  2013  5345  4.2  38.0 
M  102  716  R15  2006062A  2  AL  Rectangular  112  2007  2013  48,798  12.1  37.5 
M  103  717  R10  2006062B  2  AL  Rectangular  112  2009  2013  6002  13.0  40.4 
M  105  719  R20  2007052B  3  AL  Rectangular  112  2009  2013  5108  6.5  33.3 
M  106  720  R19  2007052A  3  AL  Rectangular  112  2009  2013  5248  5.8  28.5 
M  107  721  R13  2007065A  2  AL  Rectangular  112  2009  2013  5757  \(0.3\)  29.7 
M  109  723  R11  2007065C  2  AL  Rectangular  112  2008  2013  41,748  \(12\).8  39.8 
M  110  724  R18  2008046A  3  AL  Rectangular  112  2009  2013  17,985  0.8  32.5 
M  111  725  R21  2008046B  3  AL  Rectangular  112  2009  2013  4535  3.0  35.9 
M  113  728  R03  2008067A  1  AL  Rectangular  112  2009  2013  4603  \(18.5\)  28.4 
M  115  729  R08  2008067B  1  NO  Rectangular  112  2009  2012  37,183  \(15.5\)  30.5 
M  116  730  R01  2009070A  1  AL  Rectangular  112  2010  2013  5781  3.4  35.6 
M  117  733  R06  2009070B  1  AL  Rectangular  112  2010  2013  4797  4.7  32.9 
M  118  734  R05  2009070C  1  AL  Rectangular  112  2010  2013  19,813  6.3  33.1 
M  119  731  R22  2010007A  3  AL  Rectangular  112  2010  2013  4679  \(0.4\)  29.9 
M  120  732  R23  2010007C  3  AL  Rectangular  112  2010  2013  13,249  1.2  33.1 
M  121  735  R24  2010007B  3  AL  Rectangular  112  2010  2013  5535  6.6  32.7 
M  122  736  R09  2010041C  2  NO  Rectangular  112  2011  2013  2856  2.3  33.8 
M  123  737  R12  2010041B  2  NO  Rectangular  112  2010  2013  9769  \(2.1\)  31.7 
M  124  738  R16  2010041A  2  NO  Rectangular  112  2011  2013  8780  1.3  33.7 
K1  125  801  R26  2011009A  3  NO  Ring Array  123  2011  2013  2969  \(6.2\)  30.7 
M  126  742  R04  2011055A  1  NO  Rectangular  112  2011  2013  7204  1.8  32.5 
M  127  743  R05  2011065C  1  NO  Rectangular  112  2012  2013  3068  2.1  33.4 
M  128  744  R03  2011065A  1  NO  Rectangular  112  2011  2013  7678  \(0.5\)  33.9 
M  129  745  R07  2011065B  1  NO  Rectangular  112  2011  2013  13,820  \(0.8\)  31.2 
M  130  746  R17  2011071A  3  NO  Rectangular  112  2011  2013  16,738  \(4.8\)  31.7 
M  131  747  R02  2013019A  1  NO  Rectangular  112  2013  2013  1655  6.6  38.7 
4.1 Coating of LRA corner cubes
Summary on the GLONASS satellites tracked by the ILRS stations
Type  No. obs  Mean  RMS  

GLONASS  76,892  \(\)1.2  42.0  
GLONASSM  351,308  \(\)0.4  34.9  
GLONASSK1  2969  \( \)6.2  30.7  
GLONASSM  Coated  242,557  2.1  36.3 
GLONASSM  Uncoated  108,751  \(\)5.9  31.8 
GLONASSM  Plane 1  126,952  \(\)2.6  32.8 
GLONASSM  Plane 2  123,053  0.6  37.1 
GLONASSM  Plane 3  93,646  0.4  34.4 
The means of SLR residuals are at a level of \(1\) to \(+2\) mm for the olderclass GLONASS and the GLONASSM with coated LRAs, and at a level of \(6\) mm for the GLONASSM with uncoated LRAs and the GLONASSK1 satellite (see Table 4). The uncoated corner cubes, as opposed to the cubes with coating, are characterized by a higher return rate of laser pulses (Wilkinson and Appleby 2011), but, on the other hand, they are subject to polarization effects that affect their total crosssection.
SLR mean residuals to GLONASSM satellites as a function of the nadir angle for selected SLR stations in 2012–2013
Site  Uncoated  Coated  

Nadir (mm)  Slope (mm/\({^\circ }\))  Nadir (mm)  Slope (mm/\({^\circ }\))  
7080  \(\)15.1  \(\)1.10  \(\)9.6  \(\)1.06 
7090  \(\)5.6  \(\)0.67  \(\)11.8  \(\)0.46 
7105  \(\)22.0  \(\)0.40  \(\)5.1  \(\)0.79 
7110  \(\)4.8  \(\)0.64  20.7  \(\)1.31 
7810\(^\mathrm{a}\)  \(\)1.3  0.07  \(\)13.7  1.08 
7839\(^\mathrm{a}\)  1.4  0.06  \(\)5.1  0.65 
7840\(^\mathrm{a}\)  0.2  0.09  \(\)2.8  0.61 
8834  \(\)4.0  \(\)1.09  1.2  \(0.97\) 
GLONASSM satellites with coated LRAs in Table 5 also show negative slopes of the nadir angles for the multiphoton stations and positive slopes for CSPAD stations. The estimated slope is, however, larger for the CSPAD stations, reaching 1.08 mm/\({^\circ }\) for Zimmerwald. This large slope for coated LRAs can be explained, on the one hand, by a lower return rate and a lower efficiency of coated corner cubes at the altitude of GNSS satellites, and, on the other hand, by the nature of the CSPAD detectors. CSPAD may introduce time walk effects as a function of the return energy, but this effect should be compensated by an additional circuit. The compensation electronics can be realized using a terrestrial target which should not broaden the laser pulse. However, during satellite ranging, the signature effect broadens the return pulse, and as a result, the CSPAD cannot entirely compensate the intensity dependence due to varying energy (Appleby 1996; Otsubo et al. 2015). Moreover, when a station does not control the signal strength, the detection energy tends to change at low elevation angles due to atmospheric attenuation and the long range, resulting in nadirdependency of SLR residuals. Eventually, the large slopes can also be related to a lower quality of GLONASS orbits as the GLONASS satellites with coated LRAs are older than the satellites without coating.
The ILRS recommends uncoated cubes in the design of the GNSS satellites as noted by Wilkinson and Appleby (2011). Such a design with singlephoton detectors minimizes the offsets and reduces elevationdependent systematic effects in geodetic products.
4.2 GLONASS orbital planes
The SLR residuals should be in principle independent from the orbital planes of the GLONASS satellites. Table 4 shows, however, small variations of the SLR RMS of residuals and SLR means. They can be explained by satelliterelated issues. The GLONASSM satellites orbiting in the plane 1 have a mean offset smaller by 2–3 mm than the satellites in the planes 2 and 3, because the majority of the new satellites with uncoated LRAs, which typically have negative values of SLR means, were placed in the orbital plane 1.
The larger RMS of the residuals in plane 2 (Table 4) can be explained by a different orientation of this plane w.r.t. the ecliptic, and thus, by a different impact of solar radiation pressure on the satellites orbiting in the plane 2. The maximum elevation angle of the Sun (\(\beta \)) is 43\(^{\circ }\) for plane 2, whereas for planes 1 and 3 the maximum values of \(\beta \) may exceed 83\(^{\circ }\). When the \(\beta \) angle over an orbital plane is small the satellites are more subject to modeling deficiencies in solar radiation pressure than the satellites orbiting at high \(\beta \) angles, because at small \(\beta \) angles the Sun illuminates four surfaces of the satellite “box” body, whereas for maximum \(\beta \), close to 90\(^{\circ }\), only one surface is illuminated for most of the time. Large variations occur in particular for the eclipsing satellites (e.g., Arnold et al. 2014). We conclude that the differences of the SLR residuals in the GLONASS orbital planes can be explained both in terms of the different coating of satellite LRAs and by issues related to solar radiation pressure modeling.
4.3 Stationdependent biases
Figure 7 shows the RMS values to GLONASS satellites for the best performing SLR stations. The RMS values are similar for most of the SLR stations with the exception of San Juan (7406) showing larger variations starting in January 2012. Similar issues of SLR data provided by San Juan were also found by the ILRS Analysis Working Group^{11} in LAGEOS data.
The RMS of residuals falls into the range 32–58 mm for olderclass GLONASS (SVN 779–791), 19–55 mm for the older GLONASSM (SVN 712–724), and 15–35 mm for the newlylaunched, typically GLONASSM with uncoated LRAs (SVN 725–747). For GLONASSK1 (SVN 801), the RMS is larger for Wettzell (8834) and Monument Peak (7110). However, this satellite was being observed mainly in 2011, when Wettzell and Monument Peak had some engineering issues leading to a decreased stability of station biases.
5 Validation of GNSS orbit models
The extended ECOM is better suited to absorb the impact of direct solar radiation pressure, and as a result, the GNSSderived parameters become more stable. The extended ECOM reduces the peaks of the draconitic year harmonics in GNSSderived geocenter coordinates, in the polar motion components, and in the lengthofday parameter, and reduces the misclosures of the GPS and GLONASS orbits at the day boundaries. The new ECOM is used by CODE for generating the official IGS products since January 2015. For details related to the extended ECOM consult Arnold et al. (2015).
The extended ECOM includes more empirical parameters than the classical ECOM. The twiceperrevolution (\(D_{S2}, D_{C2}\)) and fourfoldperrevolution parameters (\(D_{S4},\) \( D_{C4}\)) are estimated in the satelliteSun direction \(D\) with the angular argument \(\Delta u\), which is satellite’s argument of latitude related to the argument of latitude of the Sun.
5.1 Extended empirical code orbit model (ECOM)
GNSS orbit validation of the classical (old) ECOM and the extended (new) ECOM using SLR observations
Solution  SLR@GPS  SLR@GLONASS  

Mean (mm)  RMS (mm)  Resid./\(\varepsilon \) (mm/\({^\circ }\))  Mean (mm)  RMS (mm)  Resid./\(\varepsilon \) (mm/\({^\circ }\))  
Old ECOM  \(12.2\)  25.3  \(\)0.43  0.6  34.6  0.92 
New ECOM  \(10.0\)  24.0  \(\)0.24  \(6.7\)  32.7  \(\)0.05 
When using the new ECOM, the SLR mean offset for singlephoton stations virtually disappears. The SLR mean for GLONASSM with uncoated LRAs is 0.1, 1.8, and 0.9 mm for Zimmerwald, Graz, and Herstmonceux, respectively. For multiphoton stations the SLR means are \(21.1\), \(12.2\), and \(25.6\) mm for McDonald, Yarragadee, and Greenbelt, respectively, due to the satellite signature effect. The GLONASS SLR mean of about \(6.7\) mm in the new ECOM is thus more reliable than the mean of \(0.6\) mm (see Table 6), because of the existence of the satellite signature effect for the highdetectionlevel stations.
5.2 Daytime and nighttime SLR tracking
Fortunately, this effect is not an engineering problem of SLR stations, but it can be simply explained by a wrong orbit model. Figure 11 (right) shows that this systematic effect disappears when using the extended ECOM for GLONASS. The nighttime and daytime observations are now randomly distributed. During the daytime tracking the Sun is close to a satellite in the sky, which corresponds to small elongation angles \(\varepsilon \). Small elongation angles are associated with negative SLR residuals when using the old ECOM as in Fig. 10 (top). The nighttime tracking is, on the other hand, associated with large \(\varepsilon \) values, and thus, with positive residuals, because the Sun and the satellite are in the opposite direction as viewed from the Earth. Using the new ECOM removes the elongationdependency and thus also the differences between SLR observations acquired during day and nighttime (Fig. 11).
6 Summary and conclusions
20 years of SLR observations to GPS and 12 years of SLR data to GLONASS were processed using the reprocessed microwavebased CODE orbits. The mean SLR residuals to GPS satellites are \(12.8\) and \(13.5\) mm for GPS35 and GPS36, respectively, with RMS values of 22.8 and 23.6 mm, respectively. The largest RMS for GPS occur in 1994, with 35 mm. In 2003 the RMS of residuals is just 16 mm.
The RMS of SLR residuals to GLONASS is 46 mm in 2002 and it is reduced to 37 mm in 2013, implying that even in the recent years the accuracy of GLONASS microwavederived orbits did not reach that of GPS orbits. However, the number of SLR observations to GLONASS has been substantially increased in 2011, when more and more ILRS stations started tracking the full GLONASS constellation. The RMS of SLR residuals is typically smaller for 3day solutions than for the 1day solutions, on average by 4 % for GPS, and from 30 % in 2002–2005 to 1 % in 2013 for GLONASS. This fact is consistent with the findings of Lutz et al. (2015) who claim a much better performance of 3day GNSS solutions in particular for the estimated rates of Earth rotation parameters.
The mean of the residuals of the SLR measurements compared to the GNSS orbits is timedependent because of equipment changes in the ground network. The SLR stations operating in the multiphoton mode have a larger negative mean offset to GPS typically in the range from \(10\) to \(35\) mm, whereas the stations operating at low return rate (CSPAD, i.e., singlephoton stations) have the SLR mean offsets between +10 and \(15\) mm.
The remaining biases between SLR and GNSS solutions originate to the greatest extent from the variations of the effective reflection points for different SLR receiving systems (about 15 mm for multiphoton stations), the BlueSky effect (up to 4.4 mm for continental stations), and modeling deficiencies of solar radiation pressure (2.2 mm for GPS and 6.1 mm for GLONASS).
For GLONASSM satellites with uncoated LRAs a clear difference between singlephoton and multiphoton stations was found. Stations operating in multiphoton mode with high detection energy have typically a large negative slope of the SLR residual w.r.t. the satellite nadir angle with a maximum slope of \(1.1\) mm/\({^\circ }\), which corresponds to a difference of the mean SLR residuals of up to 15 mm between the observations at nadir angles of 0\(^{\circ }\) and 14\(^{\circ }\). The stations with singlephoton detectors at low return rate have a positive slope of maximum up to 0.09 mm/\({^\circ }\), which corresponds to a difference of 1 mm between the SLR observations at nadir angles of 0\(^{\circ }\) and 14\(^{\circ }\). The satellite signature effect for highdetectionenergy stations, thus, introduces nadirdependent residuals in the SLR ranges up to 15 mm, whereas the singlephoton stations are free of this effect. Therefore, the laser ranges registered by multiphoton stations are shorter for high nadir angles as the pulses are reflected by the near edge of the array.
The ILRS recommends uncoated cubes for future GNSS satellites. Such a design, in a conjunction with singlephoton station detectors and the new empirical CODE orbit model, reduces the biases and elevationdependent systematic effects in geodetic products to the 1 mm level. It implies that there is no need of estimating range biases to GNSS satellites with uncoated corner cubes for the SLR stations operating in the singlephoton mode. The range biases have to be estimated or modeled only when using the highenergy detection modes due to the satellite signature effect.
SLR confirmed that CODE’s new empirical orbit model with estimating especially twiceperrevolution parameters in the \(D\) direction remarkably reduces the spurious behavior of most of GLONASS satellites, and as a result, substantially improves the GNSS solutions. The new ECOM shows no dependency of SLR residuals w.r.t. the Sunsatellite elongation. When using the new ECOM, the uncoatedLRA GLONASSM SLR mean offset is 0.1, 1.8, and 0.9 mm for Zimmerwald, Graz, and Herstmonceux, respectively, which implies that the mean offset for singlephoton stations virtually disappears. For the bestperforming multiphoton stations the mean offsets are between \(12.2\) and \(25.6\) mm due to the satellite signature effect.
The mean SLR offsets to GLONASSM at a level of 0.1–1.8 mm for singlephoton stations imply that there is no need for estimating range biases for CSPAD stations tracking the satellites with uncoated corner cubes. Thus, the formation of single, double, or triple differences with the interpolation in time as proposed by Svehla et al. (2013) is not needed for the SLR tracking of GNSS satellites in case of CSPAD stations. For multiphoton stations, the offsets and the offsetdependency on the nadir angle have to be well understood and mitigated in the future. The mean SLR offset of the order of 0.1–1.8 mm imply that there is no scale difference between SLRF2008 and IGb08, and thus, the microwavebased (GNSS) and laserbased (SLR) technique solutions of space geodesy are consistent at 1 mm level and free from scale issues.
Finally, the apparent systematic differences of SLR residuals between daytime and nighttime SLR tracking are reduced from about 50 to 3 mm when using the new extended empirical CODE orbit model. The new ECOM increases the SLR mean to GPS by 2.2 mm and reduces the SLR mean to GLONASS by 6.1 mm. It is also remarkable that with the new ECOM, the discrepancy between GPS and GLONASS mean SLR residuals is reduced from 13.2 to 3.3 mm and the mean GPS and GLONASS offsets become more consistent. Therefore, SLR observations of GNSS satellites constitute an important tool for validating GNSS orbits and for finding deficiencies in solar radiation pressure modeling.
Footnotes
 1.
 2.
 3.
 4.
 5.
 6.
SLRF2008 release from April 10, 2014 with updated coordinates for stations recently affected by the earthquakes and provisional coordinates for recently established SLR stations.
 7.
 8.
 9.
 10.
In 1995 a new CSPAD was installed in Herstmonceux, whereas in 2010 a dichroic beamsplitter inside the receiver telescope was replaced, which increased the return rate Wilkinson and Appleby (2011).
 11.
Notes
Acknowledgments
The ILRS and IGS are acknowledged for providing SLR and GNSS data. The SLR and GNSS stations are acknowledged for a continuous tracking of the geodetic satellites and for providing highquality SLR and GNSS observations. This work was partly supported by the Swiss National Science Foundation (SNSF) Grant No. 200020_157062 “Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald”.
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