SLR validation and evaluation on BDS precise orbits from 2013 to 2018

Available online at www.sciencedirect.com

ScienceDirect Advances in Space Research 64 (2019) 475–490 www.elsevier.com/locate/asr

SLR validation and evaluation on BDS precise orbits from 2013 to 2018 Honglei Yang, Tianhe Xu ⇑, Wenfeng Nie, Fan Gao, Meiqian Guan Institute of Space Science, Shandong University, Weihai, China Received 20 December 2018; received in revised form 7 March 2019; accepted 25 April 2019 Available online 7 May 2019

Abstract The objective of this paper is to validate and evaluate the orbit accuracy of the BeiDou Navigation System (BDS) using satellite laser ranging (SLR) data over a 5-year time series. The microwave-based precise orbits of BDS derived from four Analysis Centers (ACs) are validated from 2013 to 2018, including three Multi-GNSS EXperiment (MGEX) ACs from WHU, CODE and GFZ, as well as a fourth AC, known as ISC in China, with the corresponding products designated as WUM, COM, GBM and ISC. The validated orbits of BDS include the Geostationary Earth Orbit (GEO) satellite of C01, the Inclined Geo-Synchronous Orbit (ISGO) satellites of C08, C10, and C13, as well as the Medium Earth Orbit (MEO) satellite of C11. In addition, the performances of the BDS orbits during noneclipse, eclipse and Yaw Maneuver (YM) period are evaluated. Finally, the dependencies of SLR residuals on the satellite nadir angle and on the Sun elevation angle b are analyzed in detail. The results demonstrated that (1) the optimal orbit accuracies of C01, C08, C10, C11 and C13 are 522.8 mm from WUM, 53.3 mm from ISC, 54.3 mm from ISC, 38.2 mm from ISC and 51.5 mm from COM, respectively. And the orbits derived from ISC have more stable and excellent accuracy than the other ACs due to the advantages of its orbit combination algorithm. (2) Due to the deficiencies of the Solar Radiation Pressure and the YM modeling for BDS satellites from four ACs, the microwave-based orbit accuracy of BDS IGSO and MEO satellites is significantly deteriorated during the eclipse period, especially in the YM period, while the accuracy of GEO C01 during the eclipse period is better than that during the noneclipse period. (3) The dependency of SLR residuals on the satellite nadir angle has been analyzed, but limited by the number and type of all the validated BDS satellites, the nadir-dependency offset of the SLR residuals cannot be well assigned from the characteristics of the SLR detector system, or the Laser Retro-reflector Arrays. (4) By analyzing the dependency of SLR residuals on the Sun elevation angle b, some commonalities of the patterns derived from four ACs have been found for BDS IGSO and MEO satellites, and the patterns are similar to that of the GLONASS, rather than those of GPS and Galileo. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Satellite Laser Ranging (SLR); BeiDou Navigation System (BDS); Precise Orbit Validation

1. Introduction Over the past 6 years, the Chinese BeiDou Navigation System (BDS) has made important contributions worldwide, especially in the Asia-Pacific region with the special satellite types of Geostationary Earth Orbit (GEO), GeoSynchronous Orbit (ISGO) and Medium Earth Orbit (MEO). Identical to Global Positioning System (GPS) GPS35 and GPS36, GLObal NAvigation Satellite System ⇑ Corresponding author.

E-mail address: [email protected] (T. Xu). https://doi.org/10.1016/j.asr.2019.04.030 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.

(GLONASS) and Galileo satellites, all the BDS satellites are equipped with Laser Retro-reflector Arrays (LRAs) that enable Satellite Laser Ranging (SLR) measurements. As a unique optical and unambiguous space geodetic measurement technology, SLR plays an irreplaceable role in the external validation of GNSS orbits based on microwave measurements. With the continuous accumulation of SLR observations, the SLR residuals can provide more useful information that gives a richer understanding of the microwave-based GNSS orbits on long-term time series. Since the 1990s, SLR observations have been used to validate the existing GNSS satellite orbits, such as GPS35

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and GPS36 satellites, as well as GLONASS satellites (Degnan and Pavlis, 1994; Eanes et al., 1999). During this time, the research on this topic has mainly focused on comparing the orbit difference of the SLR and GNSS technologies (Pavlis, 1995; Appleby and Otsubo, 2000), combining the two tracking technologies for orbit determination (Zhu et al., 1997), as well as validating the short-term sequence microwave orbits using sparse SLR observations (Watkins et al., 1996; Eanes et al., 1999; Springer, 2000; Ineichen et al., 2001). As the time series of SLR observations increased, the long-term sequence of SLR validated residuals were analyzed. The periodic variations of the range residuals were found, which were related to the observation modeling characteristic of the SLR range system (Otsubo et al., 2001; Urschl et al., 2007) and the deficiencies of the dynamical model for the microwave orbits (Urschl et al., 2005; Urschl et al., 2007). Urschl et al. (2005) analyzed 3.3-year data of the SLR residuals for GPS and ten months of data for GLONASS, they found some pass-specific systematic errors of the SLR residuals, but these biases were not clear to be originated from the SLR sites, or the deficiencies in orbit modeling of validated satellites. In addition, Urschl et al. (2007) validated 4-year GPS and 2-year GLONASS microwave orbits from the Center for Orbit Determination in Europe (CODE), Geo Forschungs Zentrum Potsdam (GFZ), Jet Propulsion Labratorary (JPL) and International GNSS Service (IGS) (Dow et al., 2009; Johnston et al., 2017) with different orbits, arc-lengths and attitude modeling. They showed that the source of periodic variations of SLR residuals came from the deficiencies of orbit and attitude modeling (Urschl et al., 2007). Moreover, Thaller et al. (2012) discussed the pattern characteristic of SLR residuals specific to the individual SLR sites and different satellite orbit plane of GLONASS. They indicated that the stationspecific GLONASS SLR residual might be caused by the Solar Radiation Pressure (SRP) model deficiency in satellite orbit or the day-/night-time tracking issues in SLR sites (Thaller et al., 2012). As the IGS initialized the reprocessing and Multi-GNSS EXperiment (MGEX) (Montenbruck et al., 2017) campaign, more precise and more types of satellite orbits were provided in the frame of IGS. Sos´nica et al. (2015) validated 20-year GPS and 12-year GLONASS precise orbits based on the CODE reprocessed orbits. The relevant characteristics of SLR residuals were analyzed with regard to the laser beams, the shape, type, size and coating of LRAs, the SRP model, as well as the type of GNSS satellites (Sos´nica et al., 2015). Following this study, the incorrect orbits of Galileo derived from COM from January 2014 to May 2016, were validated with SLR by (Sos´nica et al., 2017). For BDS, O. Montenbruck et al. showed 3-month validation results of the BDS broadcast ephemeris (Montenbruck et al., 2013), and L. Prange et al. presented the external validation results of COM of 2014, where the classic Empirical CODE Orbit Model (ECOM) (Beutler et al., 1994; Springer et al., 1999) and the extended ECOM

(Arnold et al., 2015) were discussed emphatically (Prange et al., 2017). Furthermore, the 1.5-year orbit accuracy of the broadcast and precise orbits for BDS were validated by Peng, H. et al., where the SLR residuals during noneclipse, eclipse and Yaw Maneuver (YM) period are evaluated (Peng et al., 2016). So far, few studies have validated and evaluated the microwave-based precise orbits of BDS using SLR measurements based on long-term time series adequately. Based on this, over a 5-year time series of SLR observations from 2013 to 2018 are used to validate the microwave-based precise orbits of BDS. The precise orbits derived from four different Analysis Centers (ACs) are adopted, including the three MGEX ACs from WHU, CODE and GFZ, as well as a fourth AC, known as ISC in China, with the corresponding products designated as WUM, COM, GBM and ISC. Specifically, ISC is short for iGMAS Products Combination and Service Center, with iGMAS being the International GNSS Monitoring and Assessment System and GNSS being the Global Navigation Satellite System. Meanwhile, the validated orbits of BDS include GEO C01, ISGO C08, C10, and C13, as well as MEO C11. In order to fully understand the performances of the microwave-based precise orbits for BDS GEO, IGSO and MEO derived from four ACs, the GNSS orbits are validated and evaluated by SLR during different time period, i.e., the noneclipse, eclipse and YM period. In addition, based on the massive SLR residuals for BDS GEO, IGSO and MEO derived from four ACs, we explore the dependency of SLR residuals on the satellite nadir angle, the detectors type of SLR sites and the LRAs in the satellite body for the systematic errors, as well as the dependency of SLR residuals on the Sun elevation angle b and the argument of satellite latitude Dl for the periodic errors. The structure of this paper is as follows. Section 2 presents the SLR validation method and the concept of BDS eclipse period. Section 3 describes the processed microwave-based precise orbit of BDS derived from four ACs and the SLR normal points (NPs) data derived from the Europe Data Center (EDC). For Section 4, the statistical information and the time series patterns of SLR validation residuals are shown in Section 4.1. The dependency of SLR residuals on the satellite nadir angle and on the Sun elevation angle b are analyzed in Section 4.2. In the final section, we summarize the results and present the study’s conclusions. 2. Methodology 2.1. SLR validation method Based on the physical characteristics of the high energy laser pulse, the range accuracy of SLR can reach 1 to 3 cm in theory (Seeber, 1993). With the improvement of the satellite laser-tracking systems, the range accuracy has reached to subcentimeter and even millimeter levels in the

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last 20 years, providing an important precondition for using SLR to validate the current microwave-based orbit of GNSS satellites. The SLR validation residuals are computed as differences between laser ranges and the microwave-based positions of GNSS satellites, after the correction of the site coordinates eccentricity (https://ilrs.cddis.eosdis.nasa.gov/ network/site_procedures/eccentricity.html), the satellite LRAs offset, the general relativistic effects and the troposphere delay for SLR. The LRAs offset w.r.t the center of mass of BDS satellites are fixed as constant in Table 1. The SLR site coordinates are fixed to the priori reference frame SLRF2008 (https://ilrs.cddis.eosdis.nasa.gov/science/awg/SLRF2008.html), while the site displacement models are consistent with the International Earth Rotation and Reference System Service (IERS) Conventions 2010 (Petit and Luzum, 2010), including the ocean tidal loading, solid Earth tide and the related pole tides. Furthermore, the troposphere delay is corrected via the Mendes-Pavlis model (Mendes and Pavlis, 2004). All the above related operations are processed within the revised Bernese GNSS Software Version 5.2 (Dach et al., 2015). After the correction of the SLR observation error, a two-step engineering approach is applied to screen the initial SLR residuals. The step 1 is to exclude the largest residuals, which is 10-m level for BDS GEO, 1-m level for BDS IGSO and MEO. Afterwards, the 3-sigma rejection criterion is used as step 2. Firstly, the residual mean offset and root mean square (RMS) values are computed. Then, the SLR residuals which beyond the threshold of Mean
3  RMS, are removed to reduce the influence of the observation residuals with small RMS values but large biases. Finally, the new Mean offset and RMS are calculated once again (Sos´nica et al., 2015; Yang et al., 2016; Sos´nica et al., 2017). All the removed residuals are regarded as the observational outliers, and the final RMS corresponds to the indicator without any systematic effects. 2.2. Eclipse period of BDS The space geometric angle and position among the Sun, Earth and satellite is depicted in Fig. 1. Where Z Orbit is the normal to orbital plane of satellite, Z Earth is the polar axis of the Earth, Z Satellite is the normal in Spacecraft Fixed Coordinate, Y Satellite is the axis of rotation along the solar panels on the satellite, and X Satellite constitute right-hand rectangular coordinate system with Y Satellite and Z Satellite . Moreover, i is the inclination of satellite’s orbital plane, b is the elevation angle of the Sun above the orbital plane, Dl is the Table 1 The LRAs offset w.r.t the center of mass of BDS satellites.

X (mm) Y (mm) Z (mm)

C01

C08

C10

C11

C13

596.0 570.0 1100.0

400.0 573.0 1100.0

400.0 573.0 1100.0

419.0 538.0 1100.0

419.0 538.0 1100.0

477

argument of satellite latitude w.r.t the Sun, and E is the elongation angle of the Sun-Earth-satellite. The geometrical relationship among E, b and Dl can be expressed as cos E ¼ cos b  cos Dl

ð1Þ

During a certain period, when b becomes relatively small, the satellite will enter the shadow of the Earth, namely the eclipse period. The critical angle of beclipse can be approximated as the following: jbj  beclipse ¼ arcsin

R jjrjj

ð2Þ

where, R is the radius of the Earth, r is the major axis of satellite orbital plane, and beclipse is the Sun elevation angle during the eclipse period. The BDS satellites consist of GEO, IGSO and MEO, and their eclipse period are different from each other. The beclipse is approximately 8.7° for GEO and IGSO and approximately 12.9° for MEO. Considering the influence of the eclipse period, in Section 4.1, the threshold of the Sun elevation angle for the BDS eclipse period is set to be 9° for GEO and IGSO, and 13° for MEO. Besides, the ‘‘Noon” and ‘‘Midnight” points refer to the nearest and farthest cross nodes of the projection line of the Sun on the satellite trajectory, respectively. The YawSteering Frame is defined according to the spatial geometry of the Sun, Earth and satellite. Normally, the Yaw-Steering Frame is equivalent to the Spacecraft Fixed Coordinate. The nominal yaw angle u, which is the angle between the X-axis of Yaw-Steering Frame and the Tangential direction of the Radial-Transverse-Normal (RTN) Frame, w.r. t b and Dl is tan u ¼ 

tan b sin Dl

ð3Þ

From the Eq. (3), when b ¼0°, i.e. the satellite is running to ‘‘Noon” or ‘‘Midnight” point, the u is singular. In order to avoid the satellite extreme yaw here and to make the solar panels receive as much sunlight as possible, the satellite’s attitude is adjusted by the satellite attitude control system during its operational period. There are two kinds satellite attitude control modes for BDS satellites: Orbit Fixed Yaw (OFY) mode and Normal Yaw Steering (NYS) mode. In the OFY mode, the X-axis of satellite in the Spacecraft Fixed Coordinate is always consistent with the Tangential direction of the RTN Frame, while the NYS mode refers to the situation when u exists a slow angular rate change with the satellite running. The BDS GEO satellite always adopts the OFY mode, while the IGSO and MEO adopt the NYS mode during noneclipse periods. When b is small enough during the eclipse period, the satellite attitude of BDS IGSO and MEO changes from the NYS mode to OFY mode, which is called the Yaw Maneuver (YM). Until the angle of b becomes larger, the satellite attitude changes back to NYS mode from the OFY mode. The entire YM process will last approximately 7 to 13 days, and the extreme value

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Fig. 1. The space geometric angle and position among the Sun, Earth and satellite.

condition of the Sun elevation angle is jbmode j 4° for BDS IGSO and MEO (Lou et al., 2014; Dai et al., 2015; Peng, 2016; Peng et al., 2016).

the reference in Table 2. The ‘‘Obs. Samp.” refers to the observation sampling. 3.2. SLR NPs of BDS by EDC

3. Processed data 3.1. Microwave-based precise orbit of BDS The BDS precise orbits, as regular Multi-GNSS products, are successively provided by three MGEX ACs, WHU, known as Wuhan University, CODE, GFZ and by ISC, the iGMAS Products Combination & Service Center in China. More details regarding the iGMAS can be found in Tan et al. (2016) and the website http://www.igmas.org. Although the European Space Agency (ESA) offers short-term, discontinuous BDS precise orbit products from 2013 to 2014, it is not considered in this contribution. Based on different software platforms, the different solution strategies are used for BDS precise orbit products by different ACs. The CODE MGEX precise orbit products, namely COM, including BDS IGSO and MEO satellites, are available to the public based on the processing algorithms of Bernese GNSS software 5.3. The upgraded version of EPOS.P8 is used for GBM products, which provide the products of BDS GEO, IGSO and MEO satellites in GFZ. The WHU has provided the products of BDS satellites based on Position and Navigation Data Analyst (PANDA) software since January 1, 2013 for WUM. And the BDS precise orbit products of CODE, GFZ and ISC have been available since October 27, 2013, January 28, 2014, and October 26, 2014 respectively. The deadline for data processed in this contribution is March 10, 2018. A more detailed description of the precise orbit determination strategies and models derived from four ACs can be referred to the corresponding studies, as shown

The International Laser Ranging Service (ILRS) (Pearlman et al., 2002) provides SLR NPs data for thirteen BDS satellites until March 2018, which can be downloaded from the website of EDC and Crustal Dynamics Data Information System (CDDIS) (Noll, 2010). The SLR NPs of EDC data are selected in this contribution (ftp:// edc.dgfi.tum.de/pub/slr/data/npt_crd/compassXn). The ‘‘compassXn” refers to the ILRS name, where the X indicates the type of orbit (I, IS, M, MS, G) and n is the number in sequence of such group. Due to the deficiency of time span which derived from the SLR NPs data or the microwave-based precise orbits, five BDS satellites, i.e., GEO C01, ISGO C08, C10, and C13, as well as MEO C11, are validated as shown in Table 3. Among the remaining eight BDS satellites, the satellites of compassi1, compassi2, compassi4, and compassm1 only provide the SLR NPs data before 2013, while the precise orbit products of BDS have been provided since 2013. For the compassis1, compassis2, compassms1, and compassms2, no public microwave-based precise orbits were available until 2018. Table 3 shows the naming information, and the beginning and ending time of the validated BDS satellites. Note that the compassi6b has changed from PRN C15 to C13 on October 11, 2016. 4. Results and analysis For the five validated BDS satellites, C01 is the GEO satellite, C08, C10 and C13 are the IGSO satellites, while C11 is the MEO satellite. Fig. 2 shows their ground tracks

H. Yang et al. / Advances in Space Research 64 (2019) 475–490

479

Table 2 Basic information of the precise orbit determination strategies derived from four ACs. Option

AC CODE

GFZ

WHU

iGMAS

Country Product Software Network Scheme Frequencies Elev. cutoff Obs. Samp. Art length SRP model PCV/PCO Start date Deadline Reference

Switzerland COM Bernese5.3 MGEX Double-difference B1/B2 3° 180 s 3d ECOM/ECOM2 MGEX 2013.10.27 2018.03.10 (Dach et al. 2016; Prange et al., 2016)

German GBM EPOS.P8 MGEX Un-differenced B1/B2 7° 300 s 3d ECOM MGEX 2014.01.28 2018.03.10 (Deng et al., 2014; Uhlemann et al., 2015)

China WUM PANDA MGEX Un-differenced B1/B2 7° 30 s 3d ECOM MGEX 2013.01.01 2017.06.27 (Guo et al., 2016; Guo et al., 2017)

China ISC – Comb. Comb. B1/B2 Comb. Comb. 3d Comb. Comb. 2014.10.26 2018.03.10 (Tan et al., 2016)

Table 3 The naming information, beginning and ending time of the validated BDS satellites. ILRS name

COSPAR ID

SVN

PRN

Start date

End date

compassg1 compassi3 compassi5 compassm3 compassi6b compassi6b

2010-001A 2011-013A 2011-073A 2012-018A 2016-021A 2016-021A

403 408 410 412 417 417

C01 C08 C10 C11 C15 C13

2012.04 2012.04 2012.07 2012.07 2016.06 2016.10

2018.03 2018.03 2018.03 2018.03 2016.10 2018.03

on March 1, 2018, where the red, yellow, blue, green, and magenta colors represent the C01, C08, C10, C11 and C13 satellites, respectively. To investigate the availability of the SLR residuals screening strategy, C11 is taken as an example to calculate the eliminating rate of the observations. As shown in Table 4, the percentages of the deleted observations are 1.7%, 1.3%, 1.6% and 1.3% respectively after step 1 of the SLR residuals screening strategy, while 3.2%, 3.8%,

3.2% and 3.1% after step 2. In addition, Appendix A shows all the SLR residual observations of the validated BDS GEO, IGSO and MEO satellites. For the BDS IGSO and MEO satellites, the percentage of the SLR observations during the eclipse period accounts for approximately 10% to 15% of the overall effective observations, while the percentage is about 30% for BDS GEO. The percentage of the SLR observations during the YM period is approximately 30% of the observations during the eclipse period for BDS IGSO and MEO, which means that this percentage is approximately 3% to 4.5% of the total observations. 4.1. The results of SLR validation residuals 4.1.1. Geo C01 The microwave-based precise orbit of GEO C01 is provided by WUM, GBM and ISC, but not COM. Table 5 shows the statistical information of SLR validation residuals for C01 derived from three ACs. They all have large systematic errors. The mean offset of the SLR residuals is

Fig. 2. The subsatellite tracks of C01, C08, C10, C11, and C13.

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Table 4 Observable variation of C11 satellite residual numbers. C11

Init.

Step 1

Step 2

Step 1/Init.

Step 2/Init.

Step 2/Step 1

WUM COM GBM ISC

11,362 11,473 10,700 7917

11,168 11,328 10,530 7813

10,996 11,042 10,358 7673

98.3% 98.7% 98.4% 98.7%

96.8% 96.2% 96.8% 96.9%

98.5% 97.5% 98.4% 98.2%

Table 5 The statistical information of SLR validation residuals for C01. C01

Overall

noneclipse

eclipse

WUM

Mean (mm) RMS (mm)

427.3 522.8

437.3 543.3

407.2 478.9

GBM

Mean (mm) RMS (mm)

162.9 626.7

131.1 687.8

231.3 468.8

ISC

Mean (mm) RMS (mm)

430.6 525.8

436.4 545.9

417.6 477.9

427.3 and 430.6 mm for WUM and ISC, while 162.9 mm for GBM. As presented in Peng et al. (Peng, 2016; Peng et al., 2016), the mean offset is approximately 473 mm for GBM from January 2014 to July 2015. As shown in Fig. 3, the residual scatters of GBM have an obvious upward trend, and the SLR residual mean offset decreases afterwards. We believe that a strategic improvement had been made in the microwave-based precise orbit determinations for GBM after 2015. Although the mean offset of GBM for C01 is the smallest, its RMS is worse than that of the other ACs. The RMS of the C01 SLR

residuals is 522.8, 626.7 and 525.8 mm for WUM, GBM and ISC, respectively. The difference of the statistical results between WUM and ISC is only a few millimeters. The reason is that WUM orbits are involved in the orbit combination of ISC and show an excellent performance. Fig. 3 shows the SLR validation residuals time series for C01. The red line represents the change of b, green scatters mark the residuals during the noneclipse period, and blue scatters indicate the residuals during the eclipse period. The range of b is jbmax j  22° for the C01 satellite. When b 0°, the C01 satellite is near the vernal equinox and the autumnal equinox, and the orbit accuracy does not deteriorate. When in the vicinity of the eclipse period, as jbj 10°, the residual values get obviously larger, and the accuracy becomes worse, especially for GBM. The residuals of WUM and ISC are relatively stable. Overall, C01 has a poor orbit accuracy. As C01 is always in OFY mode, a frequent maneuvering adjustment control is carried out, which makes the orbit unstable. Furthermore, one of the major reasons for the poor accuracy of GEO satellites is that GEO satellites are limited by their almost unchanged geometry from the ground station,

Fig. 3. The SLR validation residuals time series for C01.

H. Yang et al. / Advances in Space Research 64 (2019) 475–490

which leads to serious correlations between orbit, clock error and phase-ambiguity in precise orbit determinations (Peng, 2016; Peng et al., 2016). Interestingly, the SLR validation accuracy of C01 during the eclipse period is better than that during the noneclipse period. This indicates that there is a significant deficiency of non-conservative force models in each AC for the microwave-based precise orbit determination of BDS GEO satellites, especially for the SRP model. In addition, for GBM, the SLR residuals pattern have obvious oscillations and drift when jbj 10°, which leads to a worse statistical result., which may be caused by the inaccuracy of the satellite orbit dynamic model, as well as the data preprocessing strategy issues when the microwave-based precise orbit determination is performed. 4.1.2. IGSO Tables 6, 7 and 8 show the accuracy statistics of C08, C10, and C13, respectively. For C08, the mean offset is 13.8, –32.7, 11.3 and 10.5 mm for WUM, COM, GBM and ISC, respectively. The overall mean offset of C10 is no more than 5 mm for all four ACs. However, during the eclipse period, especially in the YM period, the mean offset shows an obvious change, but with an unclear rule. The overall optimal RMS of C08, C10, and C13 is 53.3 mm from ISC, 54.3 mm from ISC and 51.5 mm from COM, respectively. By comparing the RMS of WUM and ISC, the SLR residuals accuracy has been improved 15.6, 19.4 and 6.7 mm for C08, C10 and C13, respectively. This indicate the advantages of the combined algorithm derived from ISC. Table 6 The statistical information of SLR validation residuals for C08. C08

Overall

noneclipse

eclipse

NYS

YM

WUM

Mean (mm) RMS (mm)

13.8 68.9

15.9 66.8

3.9 84.1

4.8 68.3

2.2 106.7

COM

Mean (mm) RMS (mm)

–32.7 75.6

–32.6 61.8

–33.3 144.1

21.6 113.3

59.5 196.6

GBM

Mean (mm) RMS (mm)

11.3 70.6

9.4 68.2

23.9 85.0

27.1 69.5

19.0 104.0

ISC

Mean (mm) RMS (mm)

10.5 53.3

11.0 50.4

6.9 69.6

5.7 53.0

27.9 90.5

Table 7 The statistical information of SLR validation residuals for C10. C10

Overall

noneclipse

eclipse

NYS

YM

WUM

Mean (mm) RMS (mm)

0.4 73.7

2.2 72.1

20.4 84.8

21.2 80.9

18.8 92.4

COM

Mean (mm) RMS (mm)

2.3 66.0

2.0 57.0

5.4 119.5

12.9 93.5

12.0 164.7

GBM

Mean (mm) RMS (mm)

1.4 62.5

0.5 59.3

14.8 82.0

3.9 67.4

29.5 98.3

ISC

Mean (mm) RMS (mm)

5.0 54.3

3.6 50.3

14.7 76.2

7.2 61.8

25.7 93.3

481

Table 8 The statistical information of SLR validation residuals for C13. C13

Overall

noneclipse

eclipse

NYS

YM

WUM

Mean (mm) RMS (mm)

19.3 62.2

19.1 60.0

20.6 74.4

7.5 48.6

65.3 128.1

COM

Mean (mm) RMS (mm)

6.3 51.5

8.1 48.7

8.1 70.0

4.8 59.3

17.9 94.7

GBM

Mean (mm) RMS (mm)

15.6 66.4

16.2 61.2

12.2 90.8

2.9 60.3

32.7 136.0

ISC

Mean (mm) RMS (mm)

5.4 55.5

4.3 50.8

11.8 76.7

17.4 63.6

0.6 98.3

By analyzing the SLR residuals statistical information of the eclipse period and the noneclipse period for the three IGSO satellites, we find that: (1) the microwave-based orbit accuracy decreases substantially during the eclipse period. Notably, the difference of RMS between the noneclipse and the NYS of eclipse period is stable at approximately 10 mm, except for C08 and C10 derived from COM. This shows that the SRP model which adopted by each AC in the microwave-based precise orbit determination still has the potential for further improvement. (2) The poor orbit accuracy further deteriorated sharply when the satellite enters the YM period. The difference of RMS values between the noneclipse and YM period can even reach more than 70–100 mm and is more serious for C08 and C10 derived from COM, as well as for C13 derived from WUM and GBM. It indicates that there is a deficiency of YM model construction for BDS satellites up to now. For the worse orbit accuracy of C08 and C10 from COM, both during the NYS of the eclipse period and the YM period, it may be caused by the deficiency of special consideration for estimating the SPR parameters of BDS IGSO satellites. In Figs. 4, 5 and 6, the red line, green scatters, blue scatters, and yellow scatters represent the angle of b, the SLR residuals during the noneclipse period, the NYS of eclipse period, and the YM period, respectively. Note that, for C13, the magenta scatters refer to the SVN 417 satellite in the period of PRN C15. The angle of bmax shows a slow decay for C08, and a slow increase for C10. The jbmax j is no more than 58°, 41°, and 53° for C08, C10 and C13. The patterns of SLR residuals derived from four ACs have a clear correlation with the change of b, where these scatters always oscillate and drift in a regular way. Furthermore, from the stable SLR residuals time series, it is found that the orbit performance of SVN 417 satellite is not affected during the entire satellite conversion period from PRN C15 to C13. 4.1.3. MEO C11 The validated orbit accuracy statistical results of the C11 satellite are shown in Table 9. The residuals have a stable negative systematic bias, and the overall mean offsets do not exceed 20.0 mm for all four ACs. Among them, the mean offset of COM is greatly affected by the eclipse

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Fig. 4. The SLR validation residuals time series for C08.

Fig. 5. The SLR validation residuals time series for C10.

period, while the mean offset of ISC is stable during both the eclipse and the noneclipse period. The validated orbit accuracy of SLR residuals can reach to 38.2 mm for ISC, and 43.3, 44.1 and 47.9 mm for WUM, GBM and COM.

Like the BDS IGSO satellites, the orbit accuracy does not decrease significantly during the NYS of eclipse period for all four ACs, while the accuracy sharply decreases in the YM period, especially for COM.

H. Yang et al. / Advances in Space Research 64 (2019) 475–490

483

Fig. 6. The SLR validation residuals time series for C13.

Table 9 The statistical information of SLR validation residuals for C11. C11

Overall

noneclipse

eclipse

NYS

YM

WUM

Mean (mm) RMS (mm)

12.8 43.3

13.3 41.2

9.8 53.6

11.4 42.5

4.2 80.9

COM

Mean (mm) RMS (mm)

18.9 47.9

18.2 40.1

–23.2 83.5

17.9 54.8

45.4 153.3

GBM

Mean (mm) RMS (mm)

8.5 44.1

9.6 42.4

1.8 54.0

3.8 42.3

4.2 79.3

ISC

Mean (mm) RMS (mm)

13.4 38.2

13.2 35.4

14.6 51.9

13.7 42.6

17.7 74.2

Fig. 7 shows the time series of validation residuals for C11. After 5 years of on-orbit operation, the bmax is obviously attenuated by approximately 20° for C11, from 64° to 43°, while the validated accuracy of SLR residuals is hardly affected. Compared with the validated three IGSO satellite, the patterns of SLR residuals time series are more stable, denser and smoother. The patterns do not have a significantly correlation with the change of b for C11. Same as IGSO, the patterns also show obvious oscillation and drift during the eclipse period, especially during the YM period, which means that the inaccurate dynamic model problem still exists for C11. 4.2. Correlation analysis The purpose of this section is to explore the dependency of SLR residuals on the satellite nadir angle, the detectors

type of SLR sites and the LRAs in the satellite body for the systematic errors, as well as the dependency of SLR residuals on the Sun elevation angle b and the argument of satellite latitude Dl for the periodic errors. The correlation analysis of SLR residuals for GPS, GLONASS and Galileo constellations has been done (Otsubo et al., 2001; Urschl et al., 2005; Urschl et al., 2007; Sos´nica et al., 2015; Sos´nica et al., 2017; Zajdel et al., 2017). However, all of them belong to MEO satellites, with almost only one AC’s precise orbit products have been analyzed for these correlations. In this contribution, these correlations of SLR validation residuals are analyzed based on three types of BDS GEO, IGSO and MEO satellites, as well as four ACs. 4.2.1. Dependency on the satellite nadir angle The satellite nadir angle refers to the incident angle of a laser beam on the LRAs, and it does not point strictly in the radial direction of the RTN Frame. The variation characteristics of the SLR residuals in different nadir angle are related to satellite types. Fig. 8 shows the dependency among SLR residuals, the nadir angle and the angle of b for the three types of BDS satellites derived from four ACs. The color bar corresponds to the change of b, the red line refers to the regression coefficient of the SLR residuals as a linear function of the nadir angle, and the corresponding equation. Therefore, the linear term means regression slope of SLR residuals as a function of the nadir angle (mm/°). In Fig. 8, the span of nadir angle is from 5° to 8° for GEO C01, 1° to 9° for three IGSO, and 0° to 13° for

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H. Yang et al. / Advances in Space Research 64 (2019) 475–490

Fig. 7. The SLR validation residuals time series for C11.

MEO C11. For C01, the slope of linear functions has a great difference for three ACs, its slope can reach 118.0 and 92.6 mm/° for WUM and ISC, and only 11.3 mm/° for GBM. The SLR residuals of C01 have data gaps between the nadir angle of 6° and 7°, and there are a strong correlation between the nadir angle and b in these SLR residuals patterns. For the three IGSO satellites, the steepest slope is 2.4, 5.6 and 5.3 mm/° for C08, C10 and C13, while the gentlest slope is 0.8, 1.5 and 1.6 mm/°, respectively. As the nadir angle changes from 1° to 9°, the nadir-dependency offset of the SLR residuals has at least 6.4, 12 and 12.8 mm for the three IGSO satellites. No significant correlation is found between the nadir angle and b for BDS IGSO and MEO satellites. For C11, the steepest slope is no more than 1.8 mm/°, and there is a strong consistency for all four ACs. Among the four ACs, the slope of the SLR residuals as a linear function of the nadir angle from ISC is always smoothest, especially for the three IGSO satellites. The slope from GBM always has special characteristic, such as an opposite linear term or constant term offset compared with other three ACs for C01, C08, as well as C13. It indicates that the microwave-based precise orbit determination strategy of the different ACs can cause significant interference to systematic errors which related to the satellite nadir angle. The interrelationship from multiple SLR sites can contaminate the dependency of SLR residuals on the satellite nadir angle. Three high-performing SLR sites of Yarragadee (7090, Australia), Changchun (7237, China), and

Shanghai (7821, China) are selected for further analysis. Fig. 9 shows the dependency of SLR residuals on the nadir angle for C01 derived from three selected SLR sites. The range of the nadir angle of GEO C01 is between 0.3° and 0.4° for the three selected SLR sites. Due to their unique geographical position, different SLR sites have different observational ranges for C01. The span of the nadir angle is from 5.8° to 6.1° for Yarragadee, 6.7° to 7° for Changchun, and 5.5° to 5.9° for Shanghai. With a slight increase in the nadir angle, the angle of b changed from positive to negative for Yarragadee in the southern hemisphere, and from negative to positive for the Changchun and Shanghai in the northern hemisphere. Interestingly, the slope of the linear fitting function for C01 derived from the single SLR site is much steeper than the slope derived from all multi-SLR sites. Among the three selected SLR sites, the slope of Shanghai is always the smoothest while that of Yarragadee is the steepest. With the change of 0.3° for the nadir angle, the nadir-dependency offset of the SLR residuals derived from the three SLR sites can reach up to 100 mm for the same AC. For BDS IGSO and MEO satellites, the dependency of SLR residuals on the satellite nadir angle of COM derived from three selected SLR sites is shown in Fig. 10. For these satellites, the pattern of SLR residuals is somewhat like the results of GEO C01. when the nadir angle is relatively small, the SLR residuals are focused on the negative values of b for Yarragadee, and on the positive values of b for Changchun and Shanghai. The slope of the SLR residuals

H. Yang et al. / Advances in Space Research 64 (2019) 475–490

485

Fig. 8. The dependency of SLR residuals on the nadir angle.

as a linear function of the nadir angle are complicated no matter for the same satellite or for the same SLR site. Among them, the slope of Changchun is always the steep-

est for COM. Besides, the track of sub-satellite points (see Fig. 2) of C10 and C13 are close, with many SLR residuals concentrated in the vicinity of the nadir angle at 5°.

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Fig. 9. The dependency of SLR residuals on the nadir angle for C01 derived from three selected SLR sites.

Fig. 10. The dependency of SLR residuals on the satellite nadir angle for BDS IGSO and MEO satellites derived from three selected SLR sites by COM.

H. Yang et al. / Advances in Space Research 64 (2019) 475–490

Table 10 shows the slope of SLR residuals on the satellite nadir angle and the mean offset derived from the three selected SLR sites by all four ACs. The mean offset of Changchun is the largest either for the three selected SLR sites or for the validated IGSO and MEO satellites. The steepest slope of C08, C10, C11 and C13 are 3.1, 3.1, 2.4 and 7.1 mm/° for Yarragadee, 1.7, 6.4, 2.1 and 7.6 mm/° for Shanghai, and 7.1, 5.3, 3.7 and 16.6 mm/° for Changchun, respectively. Usually, the steep slope is accompanied by large mean offset of the SLR residuals, but it is not absolute. The mean offsets of Changchun are negative and stable in the three selected sites for all four ACs though it has the steeper slope. Among the three selected SLR sites, the SLR detector system belongs to the high-energy Micro-Channel Plate (MCP) for Yarragadee, while it belongs to Compensated

487

Single-Photon Avalanche Diode (C-SPAD) for Changchun and Shanghai. Due to the extremely rare or even none SLR observations for BDS satellites, no SLR detector system of Photo-Multiplier Tube (PMT) can be chosen in this contribution. Even for MEO C11, the slope of SLR residuals on the satellite nadir angle has an opposite sign for all four ACs derived from the SLR sites of Changchun and Shanghai, although they have the same detector types. So far, unlike GLONASS and Galileo satellites, the common characteristics of the SLR residuals cannot be well reflected in BDS satellites based on the same SLR detector system. Moreover, the sizes, shapes, types and coating of the LRAs can affect the SLR residuals, including the center of mass of LRAs offset. The LRAs of C01 consists of 90 corner cubes, while 42 corner cubes for C08, C10, C11 and C13. Limited by the number and type of the SLR validated satellites, the

Table 10 The slope of SLR residuals on the satellite nadir angle and the mean offset for BDS IGSO and MEO satellites. 7090

7237

7821

Satellite C08

AC WUM COM GBM ISC

Slope 0.4 3.1 2.7 2.6

Mean (mm) 2.3 27.8 22.4 8.0

Slope 6.7 7.1 0.5 6.9

Mean (mm) 36.6 57.5 17.7 –33.7

Slope 0.2 1.7 1.1 0.5

Mean (mm) 8.7 20.1 26.8 4.8

C10

WUM COM GBM ISC

2.9 1.0 3.1 2.5

7.1 7.8 3.9 0.6

4.5 5.2 3.9 5.3

10.6 16.0 10.9 16.7

0.4 6.4 0.4 1.2

37.9 13.7 22.8 26.2

C11

WUM COM GBM ISC

2.4 0.7 1.3 1.4

19.0 25.9 17.7 –22.6

2.4 3.7 2.9 2.8

39.8 51.1 37.3 41.2

1.2 0.5 1.6 2.1

13.1 17.8 7.0 9.1

C13

WUM COM GBM ISC

7.1 5.3 5.8 2.8

18.0 7.7 22.0 7.4

12.8 14.7 16.6 12.5

34.4 –23.4 11.6 31.1

2.6 5.6 7.6 4.6

0.9 3.7 40.3 18.4

Fig. 11. The dependency of SLR residuals on the Sun elevation angle b and the argument of satellite latitude.Dl

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SLR residuals cannot be effectively classified by different categories, the dependency of SLR residuals on LRAs characteristics also cannot be assigned well for BDS satellites. 4.2.2. Dependency on the Sun elevation angle Fig. 11 shows the dependency of SLR residuals on the Sun elevation angle b and the argument of satellite latitude Dl for BDS IGSO and MEO satellites derived from four ACs. All the four patterns have a strong symmetry as Dl ¼180° and b ¼0°. For the sparse and blank area, the negative SLR residuals are abundant in the vicinity of this region. As jbj 0° and Dl 0°, it is almost collinear among the Sun, the observed satellite, and the sight direction of SLR site, which is unrealistic for the optical SLR measurement based on visible light band. When Dl 2 (0°, 60°) [ (300°, 360°) , the scatters for b 2 (20°, 60°) are more intense than those for b 2 (20°, 60°). The reason is that more SLR sites locate in the Northern Hemisphere than in the Southern Hemisphere. These SLR sites have more probability to avoid collinearity among the Sun, the observed satellite, and the sight direction of SLR site in the range of b 2 (20°, 60°). In the remaining area, the major positive values exist when jbj <40° and Dl 2 (90°, 270°). Moreover, the effect of the YM mode during the eclipse period is reflected when jbj <4°, especially for COM. This is caused by the definition of ECOM SRP model, which is designed for a NYS-operated satellite, not an OFY-operated satellite. The dependency of SLR residuals on b and Dl is always used to investigate the deficiency of the SRP model, which has been discussed for the GPS, GLONASS and Galileo (Urschl et al., 2007; Sos´nica et al., 2015; Sos´nica et al., 2017). Although the body of BDS satellite is closer to the GPS and Galileo, the X-surface and Z-surface areas in the satellite body are 3.4 and 3.8 m2 for BDS, 2.7 and 2.9 m2 for GPS-IIA, 4.2 and 1.7 m2 for GLONASS, as well as 1.3 and 3.0 m2 for Galileo. However, the wing is 40.0, 30.9, 11.9 and 10.8 m2 for BDS, GLONASS, GPS-IIA and Galileo, respectively (Garcia-Serrano et al., 2016). Therefore, the dependency of SLR residuals on b and Dl for BDS is more similar to the dependency for GLONASS due to the more similarity of the overall surface area, taking wings into consideration. 5. Summary and conclusions As an irreplaceable technique, SLR can provide an absolute accuracy for satellite orbit external validation and reflect the deficiencies of dynamic models in the microwave-based precise orbit determination, especially with long-term time series of SLR residuals. In this contribution, the SLR data from 2013 to 2018 are used to validate the microwave-based precise orbit for BDS GEO, ISGO and MEO satellites derived from four ACs. Specifically, the performances of the BDS orbits during the noneclipse, the eclipse and the YM periods are evaluated. Furthermore, the dependency of the SLR residuals on the

satellite nadir angle, the Sun elevation angle b and argument of satellite latitude Dl are analyzed. The main conclusions are the following: (1) The optimal SLR validated orbit accuracy of C01, C08, C10, C11 and C13 are 522.8 mm from WUM, 53.3 mm from ISC, 54.3 mm from ISC, 38.2 mm from ISC and 51.5 mm from COM, respectively. Due to the advantages of the orbit combination algorithm, the orbit accuracy of ISC is more stable and excellent for each of the validated BDS satellites. In view of the advantages of ISC products by iGMAS in China, the combination of separate MGEX orbit products is much appreciated in the near future. (2) For all the validated BDS IGSO and MEO satellites, the microwave-based orbit accuracy of all ACs is significantly deteriorated during the eclipse period, especially in the YM period. In the case of BDS GEO, the accuracy of C01 during the eclipse period is better than that during the noneclipse period. Among the four ACs, the accuracy of COM is the most deterioration in the YM period, and the pattern of SLR residuals of GBM always stand out due to its data preprocessing strategy when the microwave-based precise orbit determination is performed. All situations indicate that there is a deficiency of YM model construction for BDS satellites up to now, and the SRP model adopted by each AC in the microwave-based precise orbit determination still has the potential for further improvement. (3) By analyzing the dependencies of SLR residuals on the satellite nadir angle, and on the Sun elevation angle b, some systematic and periodic errors are reflected. But limited by the number and type of all the validated BDS satellites, the nadir-dependency offset of the SLR residuals cannot be well assigned from the SLR detector system, or the LRAs characteristics. Among the selected three SLR sites, the slope of the SLR residuals as a linear function of the nadir angle are messy for the four ACs no matter for the same satellite or for the same SLR site. In addition, the pattern of the dependency of SLR residuals on b and Dl have some commonalities for the four ACs, where the SRP model based on ECOM model is adopted in all of them. And the patterns of BDS IGSO and MEO satellites is similar to that of the GLONASS due to their similar overall surface area. With the global distribution of BDS3 satellites and the continuous observation of SLR, the correlation analysis of BDS will surely be further improved using SLR measurement. Acknowledgements The study is funded by the National Natural Science Foundation of China (41574013, 41731069 and 41874032) and the National Key Research and Development Program of China (2016YFB0501701 and 2016YFB0501902). Thanks are due to ILRS, CDDIS, EDC, IGS ACs and iGMAS for providing the SLR data and orbits of BeiDou Navigation System.

H. Yang et al. / Advances in Space Research 64 (2019) 475–490

Appendix A. Number of SLR observations of the five BDS satellites PRN AC

Step1 Step2 noneclipse eclipse NYS YM

C01 WUM 6508 GBM 5887 ISC 5510

6476 5794 5473

4321 3956 3783

2155 1838 1690

– – –

– – –

C08 WUM COM GBM ISC

6240 6516 5957 4840

6180 6407 5877 4735

5516 5694 5112 4110

664 713 765 625

425 494 458 389

239 219 307 236

C10 WUM COM GBM ISC

8516 7636 7030 5296

8437 7474 6939 5209

7452 6726 6078 4552

985 748 861 657

664 523 495 390

321 225 366 267

C11 WUM COM GBM ISC

11,168 11,328 10,530 7813

10,996 11,042 10,358 7673

9389 9616 8991 6571

1607 1426 1367 1102

1245 1150 1024 839

362 276 343 263

C13 WUM COM GBM ISC

1209 2177 2368 2355

1190 2128 2332 2324

1026 1894 1987 1971

164 234 345 353

127 175 238 237

37 59 107 116

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