- Email: [email protected]
Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations
Available online at www.sciencedirect.com
ScienceDirect Advances in Space Research xxx (2014) xxx–xxx www.elsevier.com/locate/asr
Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations Zhong-Ping Zhang a,⇑, Hai-Feng Zhang a, Wan-Zhen Chen a, Pu Li a, Wen-Dong Meng a, Yuan-Ming Wang a, Jie Wang b, Wei Hu b, Fu-Min Yang a a
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China b China Academy of Space Technology, Beijing 100094, China
Received 6 August 2012; received in revised form 17 December 2013; accepted 20 December 2013
Abstract Beidou is the regional satellite navigation system in China, consisting of three kinds of orbiting satellites, MEO, GEO and IGSO, with the orbital altitudes of 21500–36000 km. For improving the accuracy of satellites orbit determination, calibrating microwave measuring techniques and providing better navigation service, all Beidou satellites are equipped with laser retro-reflector arrays (LRAs) to implement high precision laser ranging. The paper presents the design of LRAs for Beidou navigation satellites and the method of inclined installation of LRAs for GEO satellites to increase the effective reflective areas for the regional ground stations. By using the SLR system, the observations for Beidou satellites demonstrated a precision of centimeters. The performances of these LRAs on Beidou satellites are very excellent. Ó 2013 Published by Elsevier Ltd. on behalf of COSPAR. Keywords: Beidou navigation satellites; Satellite laser ranging (SLR); Laser retro-reflector arrays (LRAs)
1. Introduction The China’s Beidou Navigation Satellite System (BDS) is one of Global Navigation Satellite Systems (GNSS), which consists of three kinds of satellite orbits, GEO, IGSO and MEO, similar in principle to GPS with wide positioning applications (Jin et al., 2007; 2010 and 2013) and remote sensing potentials (Jin et al., 2008; 2009 and 2011). The orbital altitudes for GEO and IGSO are 36000 km, and 21500 km for MEO. For improving the accuracy of satellites orbit determination to calibrate the microwave measuring techniques and provide better navigation service, Satellite Laser Ranging (SLR) technique is applied to the Beidou navigation satellite system (BDS), like GPS, GLONASS and GALILEO system. ⇑ Corresponding author. Tel./fax: +86 21 64696290.
E-mail address: [email protected] (Z.-P. Zhang).
The laser retro-reflector arrays (LRAs) are the key onboard equipment for SLR system, installed on the outside surface of the satellite. For increasing the effective reflective area, generally the LRAs will consist of many corner cubes to reflect backward the laser pulses that are transmitted from ground laser ranging stations and increase the returning laser photons as many as possible to enter into the telescope at the ground station. The roundtrip flight time of laser pulse to LRAs will be measured to obtain the range between satellite and station with the precision of centimeters or millimeters. The design and structure of LRAs will impact on the laser returns and measuring precision. There are mainly three types of LRAs as follows: (1) Spherical ball fully covered with corner cubes on its surface, such as Lageos, Starlette, GFZ and Etalon. This kind of satellite is dedicated for geodesy and geodynamics research. There is nothing other than the LRAs onboard the satellites (Arnold, 1978).
0273-1177/$36.00 Ó 2013 Published by Elsevier Ltd. on behalf of COSPAR. http://dx.doi.org/10.1016/j.asr.2013.12.025
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
2
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
(2) Semi-spherical base mounted with 4–9 sets of corner cubes. This kind of LRAs are implemented onboard the remote sensing, oceanography and gravity satellites such as ERS, Envisat, Champ, Grace, Jason and Icesat for the need of precise orbit determination (POD) (Francis et al., 1991; Neubert et al., 1998; Grunwaldt et al., 2000; Femenias, 2004; Yang et al., 1991). (3) Planar base covered with a lot of corner cubes for high orbit satellites, such as GPS, Glonass, Galileo/Giove, Beidou-M1, etc. and some geostationary satellites Optus B1, B3, ETS-VIII, Beidou-GEO, etc. (James et al.,1991; Sawabe et al., 2009). Shanghai Astronomical Observatory (SHAO) began to design LRAs since 1999 and many sets of LRAs for different Earth orbiting satellites in China have been manufactured and launched into space. Since 2006, SHAO have been designing and manufacturing the LRAs for Beidou satellites and up to now the total of sixteen Beidou satellites with LRAs are on orbit and the Beidou regional navigation system has been established. Since December 2008 and April 2012, the total of five Beidou satellites, MEO-1, GEO-1, IGSO-3/-4, MEO-3, have been participating in global SLR tracking campaign and a good opportunity of comparison of LRAs for laser measurement with other GNSS satellites is provided for those who design, investigate and manufacture LRAs. A lot of SLR tracking data has been obtained by using SLR stations with centimeter precision. The laser data have played an important role in orbit determination and calibration of microwave measuring techniques for Beidou navigation satellites. This paper introduces in detail LRAs for Beidou satellites in China designed by SHAO and laser measuring results. 2. LRAs for Beidou satellites
orbit) with an orbital altitude of 21500 km launched on April, 2007. Fig. 1 and Table 1 show the photos and parameters of LRAs for Beidou-M1 (MEO) and Beidou GEO/IGSO satellites with the orbital height of 36000 km. The diameter of the corner cubes we chose for all of LRAs on Beidou satellites is 33 mm to insure the reflective area. For compensation of the velocity aberration, the 0.6 arc-seconds dihedral offsets with uncertainty of about 0.3 arc-seconds were adopted for the Beidou-M1’s corner cube and the 0.5 arc-seconds for the Beidou-GEO/IGSO’s. The LRAs of Beidou MEO and GEO/IGSO have 42 and 90 corner cubes, and the weight of 2.45 kg and 4.85 kg, respectively. Due to the small incidence angle of laser beam and no critical angle happened, all the surfaces of the corner cubes were without coating that can prolong its working life in space. The optical reflectivity in 532 nm of the corner cubes using the fused silica was above 92%. Each corner cube was installed into an independent chamber and the small gap will be kept surrounding corner cube to avoid damage caused by expanding when heated. The single corner cube component was fixed into the planar base made of aluminum alloy material. We chose the plane hexagon array base for Beidou’s LRAs, because it is a little close to circular shape in order to reduce the returned pulse spread and to achieve better ranging precision. The optical performances of each corner cube were carefully measured by the ZYGO interferometer in our laboratory (Fig. 2) and the testing results agree with the design (Fig. 3). In addition, the LRAs had passes all of the space environmental simulation testing to insure the stability of the products.
Table 1 Parameters of Beidou-M1 (MEO) and Beidou GEO/IGSO.
2.1. Characteristics of LRAs of Beidou satellites Due to the high orbits of Beidou satellites, the maximum incident angle of the laser beam to LRAs is less than 13 degrees when the MEO/GEO/IGSO satellites at the elevation of 20 degrees. So the planar array is suitable for these satellites. The first planar array designed and manufactured by SHAO was for the Beidou-M1 (MEO
Size Diameter of corner cube Number of corner cube Reflective area Material Dihedral offset Weight
M1(MEO)
GEO/IGSO
31.6*28*3.0 cm 33 mm 42 360 cm2 Fused silica 0.600 2.45 kg
49*43*3.0 cm 33 mm 90 770 cm2 Fused silica 0.500 4.85 kg
Fig. 1. LRAs on Beidou MEO and GEO/IGSO.
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
3
Fig. 2. The ZYGO interferometer in SHAO’s laboratory.
Fig. 3. Optical performances testing for a single cube corner with ZYGO interferometer in SHAO.
2.2. Inclined installation of LRAs for Beidou GEO satellites According to the following equation of the relative reflective area of corner cubes incised by the circular to the incidence angle of laser beam, the relative effective area increases with the decreasing incidence angle of laser beam. g¼
pffi 2 ðsin1 ðlÞ 2l tanðir ÞÞ cosði0 Þ p
ð1Þ
where, 2
l ¼ ð1 2 tan ðir ÞÞ
1=2
;
ir ¼ sin
1
sinði0 Þ n
where, g is the reflective area of corner cubes, i0 is the incidence angle of laser beam, ir is refractive angle, n is the refractive index of corner cubes. Considering that GEO satellites are stationary for the station on ground and the stations to track Beidou GEO satellites are mainly located in the Chinese region, the method of inclined installation of LRAs is adopted to make the normal direction of the plane of LRAs pointing to the Chinese continent rather than the earth’s center so as to reduce the incidence angle of laser beam from ground stations. But the normal direction of the plane of GEO satellites with micro-wave antenna is also pointing to the center of Earth. Fig. 4 shows the relative place of satellite (S), ground station (O) and the
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
4
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
RSO ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 R2E þ ðRE þ hS Þ 2RE ðRE þ hS Þcosð\OESÞ;
lCO ¼ 2RE sinðOC=2Þ cosðOCÞ ¼ cosð90 bO Þ cosð90 bC Þ þ sinð90 bO Þ sinð90 bC Þ cosðaC aO Þ ¼ sin bO sin bC þ cos bO cos bC cosðaC aO Þ
Fig. 4. Diagram of the relative place of satellite, ground station and the intersection of the normal of the plane of LRAs and ground.
intersection of the normal of the plane of LRAs and ground surface (C) in the geographic coordinate system. The coordinates are signed as ðaS ; bS Þ; ðaO ; bO Þ; ðaC ; bC Þ, respectively while a is the longitude and b is the latitude. For the normal of the plane of LRAs oriented to the Earth’s center, the incidence angle (i) can be calculated by the following formula: i ¼ arcsin
RE sin ðarccosðcos bO cosðaS aO ÞÞÞ RSO
ð2Þ
where, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 RSO ¼ R2E þ ðRE þ hS Þ 2RE ðRE þ hS Þ cosð\OESÞ where, RE is the radius of the Earth, RSO is the slant distance from ground station to satellite, hS is the satellite height above sea level, ðaO ; bO Þ are the coordinates of ground station, ðaS ; bS Þ (for GEO satellite, bS ¼ 0) are the coordinates of the satellite.If the normal of the plane of LRAs of Beidou GEO satellites points to the intersection C (aC ; bC ), the incidence angle can be calculated by using formulas of spherical triangle: iC ¼ arccos R2SC þ R2SO l2CO =2RSC RSO
ð3Þ
where, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 RSC ¼ R2E þ ðRE þ hS Þ 2RE ðRE þ hS Þ cosðbC Þ cosðaS aC Þ
Table 2 The increasing ratio of effective reflective areas for different GEO satellites and different stations. GEO Satellite GEO Satellite GEO Satellite A (58.75° Long.) B (80° Long.) C (110.5° Long.) (%) (%) (%) Beijing station in 20.62 the north China Kashi station in 13.41 the west China Sanya station in 8.74 the south China
15.71
10.46
7.16
1.52
7.16
12.37
where, iC is the incidence angle between ground station (O) and the satellite (S), RSC is the slant distance from the intersection (C) to the satellite, lCO is the curve distance from station to the intersection (C). For the stations located in the Chinese region, the incidence angle (i) calculated from the formula (2) will be smaller than the one from the formula (1). So the relative effective area of LRAs for ground stations will be increased. Due to the dedicated laser tracking network for Beidou satellites consists of several independent SLR systems only in China, so the geometrical center of those SLR stations on ground is chosen as the normal of LRA directing to point (C). Based on the coordinates of the intersection point and Beidou GEO satellites, the inclined angle of LRA of all GEO satellites is less than 7 degree. Table 2 shows the increasing rate of effective reflective area for different position GEO satellites and different ground stations in China after the inclined installation of LRAs for GEO satellites. The effective reflective areas are increased up to 20.6% at the maximum. Although the increasing rate is not very much for each satellite, it is considerable significant for the ground stations. The advantages of inclined installation of LRAs on Beidou GEO satellites will be presented in the measuring results during the tracking campaign task. 3. SLR Observations and measurement results 3.1. Beidou-M1 observations The laser ranging to the Beidou-M1 was carried out at Changchun SLR station since its launch in 2007. The first attempt of observation to Beidou-M1 was on April 29, 2007 and the laser returns were successfully obtained. The ranging precision was about 2 cm. The comparison of the returned signal strengths among the GNSS satellites had been done during several nights at Changchun SLR station in May 2007. The returned signal strengths from Beidou-M1 were much higher than those from GPS-36 and GLOVE-A when those satellites were at the same elevations. Since the end of 2008, COMPAS-M1 was tracked by global SLR stations. The international SLR observation campaign for comparison of the returned signal strengths from different GNSS satellites started in December 2008. Some results have been obtained and presented on the International Laser Workshop on SLR Tracking of GNSS Constellations held in Metsovo, Greece on September 14–19, 2009. Fig. 5 was provided by G. Kirchner of the Graz SLR station in Austria (Pearlman, 2009). The
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
5
parts of the returned FFDP from the Beidou-M1’s LRAs, but is still able to get enough signal strengths due to the shorter distances of satellite and better atmospheric transmission. Therefore we think the smaller FFDP of the Beidou-M1’s LRAs is adequate and the dihedral offsets were controlled accurately for compensation of the velocity aberration. 3.2. Beidou GEO/IGSO satellites observations, daylight measurement and kHz SLR tracking
Fig. 5. Comparison of the returned signal strengths from different GNSS satellites during 2008–2009.
horizontal axis represents the elevation of the satellite, and the vertical axis is the received returns per second. The statistics are for the ranging data of the Graz station only during 2008–2009. Although the return numbers in the figure were not corrected for the different range factors of different satellites, the better performance of the Beidou-M1’s LRAs is obvious. Therefore some of the SLR stations, such as Yarragadee, Zimmerwald, Mt.Stromlo, found that it was not difficult to obtain ranging data for the Beidou-M1 in the daytime. In addition, the size and weight of the Beidou-M1’s LRAs is much smaller than the Glonass’ LRAs and also smaller than the GIOVEA’s ones. It is well known that the more compact size of the LRAs, the better ranging precision. We try to understand the results shown by the Fig. 5. We think the Far Field Diffraction Pattern (FFDP) from the corner cubes of Beidou-M1 are smaller than other satellites, so the stronger returned signals from the Beidou-M1 can be obtained at lower elevations. In many cases, at higher elevations the velocity aberration effects are bigger; the ground station cannot be well covered by the stronger
The Beidou GEO-2/-1/-3/-4/-5 satellites were launched into different positions over the equator in 2009 and 2010. The Beidou IGSO-1/-2/-3/-4/-5 satellites were launched in 2010 and 2011 and Beidou MEO-3/-4/-5/-6 satellites launched in 2011 and 2012. The laser ranging experiments for those satellites have been done at a new dedicated Beidou SLR station in north China with the aperture of 1 m receiving telescope and a powerful laser since April 2009. The above mentioned station has had the capability of daylight laser ranging since August 2009. The quite strong returned signals from the Beidou GEO-1 were received at the elevation of 27 degrees and at the range of 38910 km and about 30 returns per second were obtained during the pass. On April 1, 2010, the daylight tracking to Beidou GEO-1 was successfully performed for the first time in the world by using the dedicated Beidou SLR system (Fig. 6) and the Beidou IGSO could also be tracked in daylight. The ranging precision for the Beidou satellites is about 2.5 cm. The elevation of Beidou GEO-5 for Beijing city in China is only 17 degrees, the range about 39990 km and by using the above mentioned laser ranging system, the laser returns can be also obtained. The above good measuring results of Beidou GEO satellites benefit from the inclined installation of LRAs. Shanghai SLR station also tracked some passes of these satellites with the new kHz laser ranging system (1.0 mJ
Fig. 6. Laser tracking to Beidou-GEO1 in daylight on April 1, 2010 (local time 04:47:36 pm).
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
6
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
Fig. 7. Measuring results of Beidou GEO-1 and IGSO-1 satellites by Shanghai kHz SLR system.
energy in 532 nm, 20 ps pulse width, 1 kHz repetition). Fig. 7 shows the measuring results of Beidou GEO-1 and IGSO-1 by using Shanghai kHz SLR system. For Beidou GEO-1 satellite, the average returns per minute are about 580 points. It is shown from the observation results that the performances of the Beidou GEO/IGSO’s LRAs are much excellent. According to David Arnold’s recent research, it is better to have the corner cubes without any dihedral offsets for the MEO and GEO orbits (Arnold, 2008). We are planning to verify his idea in near future missions. 4. Conclusions SHAO has designed and manufactured many sets of LRAs for the China-made satellites with different orbital altitudes for the purpose of precise orbit determination. Now there are 16 sets of LRAs on Beidou satellites launched into the different orbits. A great amount of laser tracking data was obtained by using the dedicated Beidou SLR system and they have played significant role in calibrating the microwave, radio measuring techniques and Beidou satellite precise orbit determination. It was shown from the measurement results of the international laser ranging campaign for the GNSS satellites during 2008– 2009 that the returned signal strengths from the Beidou M1’s LRAs were stronger than those from other GNSS satellites at low elevations. For GEO satellites, the method of inclined installation of LRAs is adopted to make its normal direction point to the stations on ground, not to the Earth’s center. This original way of installation makes the reflective area and returns increased effectively for the ground dedicated SLR stations. Measurement results show that the performances of LRAs on Beidou satellites are very good. The ranging precision for the Beidou MEO and GEO/IGSO satellites were about 2 cm and 2.5 cm (single-shot RMS), respectively with laser pulse width of 150 picoseconds. The methods of design of LRAs on Beidou satellites have been successfully applied to other satellites in China.
Acknowledgements The work was supported by the Center of the Satellite Navigation Engineering and the China Academy of Space Technology, as well as by the Science & Technology Commission of Shanghai Municipality No.06DZ22101. We would like to thank ILRS stations observing Beidou-M1 satellite and David Arnold for helpful discussions. References Arnold, D., 1978. Optical and infrared transfer function of the Lageos retro reflector array. Tech. Rep., 1–191, NASA-CR-157182. Arnold, D., 2008, Signal Strength Measurements and Retroreflector Array Design, In: 16th International Workshop on Laser Ranging, Poznan, Poland, October 12–17. Femenias, P.F., 2004, ESA EO Envisat and Cryosat Missions Status, In: 14th International Workshop on Laser Ranging, San Fernando, Spain, June 7–11. Francis, R., Graf, G., Edwards, P.G., et al., 1991. The ERS-1 Spacecraft and Its Payload, Magazine-ESA Bulletin1, 65, 26–48. Fumin Yang, Wanzhen Chen, Zhongping Zhang, et al., 1991. Design of Laser Retro-Reflector Array and Laser Ranging Experiment for Shenzhou-IV Satellite, In: 14th International Workshop on Laser Ranging, San Fernando, Spain, June 7–11. Grunwaldt, L., Neubert, R., and Lapushka, K., 2000. First Results of Laser Ranging to the CHAMP Retroreflector, In: 12th International Workshop on Laser Ranging, Matera, Italy, November 13–17. James, W., Steel, W., Evans, N., 1991. Design and testing of a cube-corner array for laser ranging. SPIE 1400, 129–136. Jin, S.G., van Dam, T., Wdowinski, S., 2013. Observing and understanding the Earth system variations from space geodesy. J. Geodyn. 72, 1–10. Jin, S.G., Feng, G.P., Gleason, S., 2011. Remote sensing using GNSS signals: current status and future directions. Adv. Space Res. 47 (10), 1645–1653. Jin, S.G., Luo, O.F., Ren, C., 2010. Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates. Adv. Space Res. 46 (2), 190–195. Jin, S.G., Luo, O.F., Gleason, S., 2009. Characterization of diurnal cycles in ZTD from a decade of global GPS observations. J. Geod. 83 (6), 537–545. Jin, S.G., Luo, O.F., Park, P., 2008. GPS observations of the ionospheric F2-layer behavior during the 20th November 2003 geomagnetic storm over South Korea. J. Geod. 82 (12), 883–892.
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx Jin, S.G., Park, P., Zhu, W.Y., 2007. Micro-plate tectonics and kinematics in Northeast Asia inferred from a dense set of GPS observations. Earth Planet. Sci. Lett. 257 (3–4), 486–496. Neubert, R., Grunwaldt, L., Neubert, J., 1998. The Retro-Reflector for the CHAMP Satellite: Final Design and Realization, In: 11th International Workshop on Laser Ranging, Deggendorf, Germany, September 21–25.
7
Pearlman, M.R., 2009. Technological Challenges of SLR Tracking of GNSS Constellations, International Laser Workshop on SLR Tracking of GNSS Constellations, Metsovo, Greece, September 14–19. Sawabe, M., T. Uchimura, A. Suzuki, H. Noda., 2009. Laser Retroreflector Array of Geostationary Satellite, ETS-VIII, In: 14th International Workshop on Laser Ranging, San Fernando, Spain, June 7–11.
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
ScienceDirect Advances in Space Research xxx (2014) xxx–xxx www.elsevier.com/locate/asr
Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations Zhong-Ping Zhang a,⇑, Hai-Feng Zhang a, Wan-Zhen Chen a, Pu Li a, Wen-Dong Meng a, Yuan-Ming Wang a, Jie Wang b, Wei Hu b, Fu-Min Yang a a
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China b China Academy of Space Technology, Beijing 100094, China
Received 6 August 2012; received in revised form 17 December 2013; accepted 20 December 2013
Abstract Beidou is the regional satellite navigation system in China, consisting of three kinds of orbiting satellites, MEO, GEO and IGSO, with the orbital altitudes of 21500–36000 km. For improving the accuracy of satellites orbit determination, calibrating microwave measuring techniques and providing better navigation service, all Beidou satellites are equipped with laser retro-reflector arrays (LRAs) to implement high precision laser ranging. The paper presents the design of LRAs for Beidou navigation satellites and the method of inclined installation of LRAs for GEO satellites to increase the effective reflective areas for the regional ground stations. By using the SLR system, the observations for Beidou satellites demonstrated a precision of centimeters. The performances of these LRAs on Beidou satellites are very excellent. Ó 2013 Published by Elsevier Ltd. on behalf of COSPAR. Keywords: Beidou navigation satellites; Satellite laser ranging (SLR); Laser retro-reflector arrays (LRAs)
1. Introduction The China’s Beidou Navigation Satellite System (BDS) is one of Global Navigation Satellite Systems (GNSS), which consists of three kinds of satellite orbits, GEO, IGSO and MEO, similar in principle to GPS with wide positioning applications (Jin et al., 2007; 2010 and 2013) and remote sensing potentials (Jin et al., 2008; 2009 and 2011). The orbital altitudes for GEO and IGSO are 36000 km, and 21500 km for MEO. For improving the accuracy of satellites orbit determination to calibrate the microwave measuring techniques and provide better navigation service, Satellite Laser Ranging (SLR) technique is applied to the Beidou navigation satellite system (BDS), like GPS, GLONASS and GALILEO system. ⇑ Corresponding author. Tel./fax: +86 21 64696290.
E-mail address: [email protected] (Z.-P. Zhang).
The laser retro-reflector arrays (LRAs) are the key onboard equipment for SLR system, installed on the outside surface of the satellite. For increasing the effective reflective area, generally the LRAs will consist of many corner cubes to reflect backward the laser pulses that are transmitted from ground laser ranging stations and increase the returning laser photons as many as possible to enter into the telescope at the ground station. The roundtrip flight time of laser pulse to LRAs will be measured to obtain the range between satellite and station with the precision of centimeters or millimeters. The design and structure of LRAs will impact on the laser returns and measuring precision. There are mainly three types of LRAs as follows: (1) Spherical ball fully covered with corner cubes on its surface, such as Lageos, Starlette, GFZ and Etalon. This kind of satellite is dedicated for geodesy and geodynamics research. There is nothing other than the LRAs onboard the satellites (Arnold, 1978).
0273-1177/$36.00 Ó 2013 Published by Elsevier Ltd. on behalf of COSPAR. http://dx.doi.org/10.1016/j.asr.2013.12.025
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
2
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
(2) Semi-spherical base mounted with 4–9 sets of corner cubes. This kind of LRAs are implemented onboard the remote sensing, oceanography and gravity satellites such as ERS, Envisat, Champ, Grace, Jason and Icesat for the need of precise orbit determination (POD) (Francis et al., 1991; Neubert et al., 1998; Grunwaldt et al., 2000; Femenias, 2004; Yang et al., 1991). (3) Planar base covered with a lot of corner cubes for high orbit satellites, such as GPS, Glonass, Galileo/Giove, Beidou-M1, etc. and some geostationary satellites Optus B1, B3, ETS-VIII, Beidou-GEO, etc. (James et al.,1991; Sawabe et al., 2009). Shanghai Astronomical Observatory (SHAO) began to design LRAs since 1999 and many sets of LRAs for different Earth orbiting satellites in China have been manufactured and launched into space. Since 2006, SHAO have been designing and manufacturing the LRAs for Beidou satellites and up to now the total of sixteen Beidou satellites with LRAs are on orbit and the Beidou regional navigation system has been established. Since December 2008 and April 2012, the total of five Beidou satellites, MEO-1, GEO-1, IGSO-3/-4, MEO-3, have been participating in global SLR tracking campaign and a good opportunity of comparison of LRAs for laser measurement with other GNSS satellites is provided for those who design, investigate and manufacture LRAs. A lot of SLR tracking data has been obtained by using SLR stations with centimeter precision. The laser data have played an important role in orbit determination and calibration of microwave measuring techniques for Beidou navigation satellites. This paper introduces in detail LRAs for Beidou satellites in China designed by SHAO and laser measuring results. 2. LRAs for Beidou satellites
orbit) with an orbital altitude of 21500 km launched on April, 2007. Fig. 1 and Table 1 show the photos and parameters of LRAs for Beidou-M1 (MEO) and Beidou GEO/IGSO satellites with the orbital height of 36000 km. The diameter of the corner cubes we chose for all of LRAs on Beidou satellites is 33 mm to insure the reflective area. For compensation of the velocity aberration, the 0.6 arc-seconds dihedral offsets with uncertainty of about 0.3 arc-seconds were adopted for the Beidou-M1’s corner cube and the 0.5 arc-seconds for the Beidou-GEO/IGSO’s. The LRAs of Beidou MEO and GEO/IGSO have 42 and 90 corner cubes, and the weight of 2.45 kg and 4.85 kg, respectively. Due to the small incidence angle of laser beam and no critical angle happened, all the surfaces of the corner cubes were without coating that can prolong its working life in space. The optical reflectivity in 532 nm of the corner cubes using the fused silica was above 92%. Each corner cube was installed into an independent chamber and the small gap will be kept surrounding corner cube to avoid damage caused by expanding when heated. The single corner cube component was fixed into the planar base made of aluminum alloy material. We chose the plane hexagon array base for Beidou’s LRAs, because it is a little close to circular shape in order to reduce the returned pulse spread and to achieve better ranging precision. The optical performances of each corner cube were carefully measured by the ZYGO interferometer in our laboratory (Fig. 2) and the testing results agree with the design (Fig. 3). In addition, the LRAs had passes all of the space environmental simulation testing to insure the stability of the products.
Table 1 Parameters of Beidou-M1 (MEO) and Beidou GEO/IGSO.
2.1. Characteristics of LRAs of Beidou satellites Due to the high orbits of Beidou satellites, the maximum incident angle of the laser beam to LRAs is less than 13 degrees when the MEO/GEO/IGSO satellites at the elevation of 20 degrees. So the planar array is suitable for these satellites. The first planar array designed and manufactured by SHAO was for the Beidou-M1 (MEO
Size Diameter of corner cube Number of corner cube Reflective area Material Dihedral offset Weight
M1(MEO)
GEO/IGSO
31.6*28*3.0 cm 33 mm 42 360 cm2 Fused silica 0.600 2.45 kg
49*43*3.0 cm 33 mm 90 770 cm2 Fused silica 0.500 4.85 kg
Fig. 1. LRAs on Beidou MEO and GEO/IGSO.
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
3
Fig. 2. The ZYGO interferometer in SHAO’s laboratory.
Fig. 3. Optical performances testing for a single cube corner with ZYGO interferometer in SHAO.
2.2. Inclined installation of LRAs for Beidou GEO satellites According to the following equation of the relative reflective area of corner cubes incised by the circular to the incidence angle of laser beam, the relative effective area increases with the decreasing incidence angle of laser beam. g¼
pffi 2 ðsin1 ðlÞ 2l tanðir ÞÞ cosði0 Þ p
ð1Þ
where, 2
l ¼ ð1 2 tan ðir ÞÞ
1=2
;
ir ¼ sin
1
sinði0 Þ n
where, g is the reflective area of corner cubes, i0 is the incidence angle of laser beam, ir is refractive angle, n is the refractive index of corner cubes. Considering that GEO satellites are stationary for the station on ground and the stations to track Beidou GEO satellites are mainly located in the Chinese region, the method of inclined installation of LRAs is adopted to make the normal direction of the plane of LRAs pointing to the Chinese continent rather than the earth’s center so as to reduce the incidence angle of laser beam from ground stations. But the normal direction of the plane of GEO satellites with micro-wave antenna is also pointing to the center of Earth. Fig. 4 shows the relative place of satellite (S), ground station (O) and the
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
4
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
RSO ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 R2E þ ðRE þ hS Þ 2RE ðRE þ hS Þcosð\OESÞ;
lCO ¼ 2RE sinðOC=2Þ cosðOCÞ ¼ cosð90 bO Þ cosð90 bC Þ þ sinð90 bO Þ sinð90 bC Þ cosðaC aO Þ ¼ sin bO sin bC þ cos bO cos bC cosðaC aO Þ
Fig. 4. Diagram of the relative place of satellite, ground station and the intersection of the normal of the plane of LRAs and ground.
intersection of the normal of the plane of LRAs and ground surface (C) in the geographic coordinate system. The coordinates are signed as ðaS ; bS Þ; ðaO ; bO Þ; ðaC ; bC Þ, respectively while a is the longitude and b is the latitude. For the normal of the plane of LRAs oriented to the Earth’s center, the incidence angle (i) can be calculated by the following formula: i ¼ arcsin
RE sin ðarccosðcos bO cosðaS aO ÞÞÞ RSO
ð2Þ
where, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 RSO ¼ R2E þ ðRE þ hS Þ 2RE ðRE þ hS Þ cosð\OESÞ where, RE is the radius of the Earth, RSO is the slant distance from ground station to satellite, hS is the satellite height above sea level, ðaO ; bO Þ are the coordinates of ground station, ðaS ; bS Þ (for GEO satellite, bS ¼ 0) are the coordinates of the satellite.If the normal of the plane of LRAs of Beidou GEO satellites points to the intersection C (aC ; bC ), the incidence angle can be calculated by using formulas of spherical triangle: iC ¼ arccos R2SC þ R2SO l2CO =2RSC RSO
ð3Þ
where, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 RSC ¼ R2E þ ðRE þ hS Þ 2RE ðRE þ hS Þ cosðbC Þ cosðaS aC Þ
Table 2 The increasing ratio of effective reflective areas for different GEO satellites and different stations. GEO Satellite GEO Satellite GEO Satellite A (58.75° Long.) B (80° Long.) C (110.5° Long.) (%) (%) (%) Beijing station in 20.62 the north China Kashi station in 13.41 the west China Sanya station in 8.74 the south China
15.71
10.46
7.16
1.52
7.16
12.37
where, iC is the incidence angle between ground station (O) and the satellite (S), RSC is the slant distance from the intersection (C) to the satellite, lCO is the curve distance from station to the intersection (C). For the stations located in the Chinese region, the incidence angle (i) calculated from the formula (2) will be smaller than the one from the formula (1). So the relative effective area of LRAs for ground stations will be increased. Due to the dedicated laser tracking network for Beidou satellites consists of several independent SLR systems only in China, so the geometrical center of those SLR stations on ground is chosen as the normal of LRA directing to point (C). Based on the coordinates of the intersection point and Beidou GEO satellites, the inclined angle of LRA of all GEO satellites is less than 7 degree. Table 2 shows the increasing rate of effective reflective area for different position GEO satellites and different ground stations in China after the inclined installation of LRAs for GEO satellites. The effective reflective areas are increased up to 20.6% at the maximum. Although the increasing rate is not very much for each satellite, it is considerable significant for the ground stations. The advantages of inclined installation of LRAs on Beidou GEO satellites will be presented in the measuring results during the tracking campaign task. 3. SLR Observations and measurement results 3.1. Beidou-M1 observations The laser ranging to the Beidou-M1 was carried out at Changchun SLR station since its launch in 2007. The first attempt of observation to Beidou-M1 was on April 29, 2007 and the laser returns were successfully obtained. The ranging precision was about 2 cm. The comparison of the returned signal strengths among the GNSS satellites had been done during several nights at Changchun SLR station in May 2007. The returned signal strengths from Beidou-M1 were much higher than those from GPS-36 and GLOVE-A when those satellites were at the same elevations. Since the end of 2008, COMPAS-M1 was tracked by global SLR stations. The international SLR observation campaign for comparison of the returned signal strengths from different GNSS satellites started in December 2008. Some results have been obtained and presented on the International Laser Workshop on SLR Tracking of GNSS Constellations held in Metsovo, Greece on September 14–19, 2009. Fig. 5 was provided by G. Kirchner of the Graz SLR station in Austria (Pearlman, 2009). The
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
5
parts of the returned FFDP from the Beidou-M1’s LRAs, but is still able to get enough signal strengths due to the shorter distances of satellite and better atmospheric transmission. Therefore we think the smaller FFDP of the Beidou-M1’s LRAs is adequate and the dihedral offsets were controlled accurately for compensation of the velocity aberration. 3.2. Beidou GEO/IGSO satellites observations, daylight measurement and kHz SLR tracking
Fig. 5. Comparison of the returned signal strengths from different GNSS satellites during 2008–2009.
horizontal axis represents the elevation of the satellite, and the vertical axis is the received returns per second. The statistics are for the ranging data of the Graz station only during 2008–2009. Although the return numbers in the figure were not corrected for the different range factors of different satellites, the better performance of the Beidou-M1’s LRAs is obvious. Therefore some of the SLR stations, such as Yarragadee, Zimmerwald, Mt.Stromlo, found that it was not difficult to obtain ranging data for the Beidou-M1 in the daytime. In addition, the size and weight of the Beidou-M1’s LRAs is much smaller than the Glonass’ LRAs and also smaller than the GIOVEA’s ones. It is well known that the more compact size of the LRAs, the better ranging precision. We try to understand the results shown by the Fig. 5. We think the Far Field Diffraction Pattern (FFDP) from the corner cubes of Beidou-M1 are smaller than other satellites, so the stronger returned signals from the Beidou-M1 can be obtained at lower elevations. In many cases, at higher elevations the velocity aberration effects are bigger; the ground station cannot be well covered by the stronger
The Beidou GEO-2/-1/-3/-4/-5 satellites were launched into different positions over the equator in 2009 and 2010. The Beidou IGSO-1/-2/-3/-4/-5 satellites were launched in 2010 and 2011 and Beidou MEO-3/-4/-5/-6 satellites launched in 2011 and 2012. The laser ranging experiments for those satellites have been done at a new dedicated Beidou SLR station in north China with the aperture of 1 m receiving telescope and a powerful laser since April 2009. The above mentioned station has had the capability of daylight laser ranging since August 2009. The quite strong returned signals from the Beidou GEO-1 were received at the elevation of 27 degrees and at the range of 38910 km and about 30 returns per second were obtained during the pass. On April 1, 2010, the daylight tracking to Beidou GEO-1 was successfully performed for the first time in the world by using the dedicated Beidou SLR system (Fig. 6) and the Beidou IGSO could also be tracked in daylight. The ranging precision for the Beidou satellites is about 2.5 cm. The elevation of Beidou GEO-5 for Beijing city in China is only 17 degrees, the range about 39990 km and by using the above mentioned laser ranging system, the laser returns can be also obtained. The above good measuring results of Beidou GEO satellites benefit from the inclined installation of LRAs. Shanghai SLR station also tracked some passes of these satellites with the new kHz laser ranging system (1.0 mJ
Fig. 6. Laser tracking to Beidou-GEO1 in daylight on April 1, 2010 (local time 04:47:36 pm).
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
6
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx
Fig. 7. Measuring results of Beidou GEO-1 and IGSO-1 satellites by Shanghai kHz SLR system.
energy in 532 nm, 20 ps pulse width, 1 kHz repetition). Fig. 7 shows the measuring results of Beidou GEO-1 and IGSO-1 by using Shanghai kHz SLR system. For Beidou GEO-1 satellite, the average returns per minute are about 580 points. It is shown from the observation results that the performances of the Beidou GEO/IGSO’s LRAs are much excellent. According to David Arnold’s recent research, it is better to have the corner cubes without any dihedral offsets for the MEO and GEO orbits (Arnold, 2008). We are planning to verify his idea in near future missions. 4. Conclusions SHAO has designed and manufactured many sets of LRAs for the China-made satellites with different orbital altitudes for the purpose of precise orbit determination. Now there are 16 sets of LRAs on Beidou satellites launched into the different orbits. A great amount of laser tracking data was obtained by using the dedicated Beidou SLR system and they have played significant role in calibrating the microwave, radio measuring techniques and Beidou satellite precise orbit determination. It was shown from the measurement results of the international laser ranging campaign for the GNSS satellites during 2008– 2009 that the returned signal strengths from the Beidou M1’s LRAs were stronger than those from other GNSS satellites at low elevations. For GEO satellites, the method of inclined installation of LRAs is adopted to make its normal direction point to the stations on ground, not to the Earth’s center. This original way of installation makes the reflective area and returns increased effectively for the ground dedicated SLR stations. Measurement results show that the performances of LRAs on Beidou satellites are very good. The ranging precision for the Beidou MEO and GEO/IGSO satellites were about 2 cm and 2.5 cm (single-shot RMS), respectively with laser pulse width of 150 picoseconds. The methods of design of LRAs on Beidou satellites have been successfully applied to other satellites in China.
Acknowledgements The work was supported by the Center of the Satellite Navigation Engineering and the China Academy of Space Technology, as well as by the Science & Technology Commission of Shanghai Municipality No.06DZ22101. We would like to thank ILRS stations observing Beidou-M1 satellite and David Arnold for helpful discussions. References Arnold, D., 1978. Optical and infrared transfer function of the Lageos retro reflector array. Tech. Rep., 1–191, NASA-CR-157182. Arnold, D., 2008, Signal Strength Measurements and Retroreflector Array Design, In: 16th International Workshop on Laser Ranging, Poznan, Poland, October 12–17. Femenias, P.F., 2004, ESA EO Envisat and Cryosat Missions Status, In: 14th International Workshop on Laser Ranging, San Fernando, Spain, June 7–11. Francis, R., Graf, G., Edwards, P.G., et al., 1991. The ERS-1 Spacecraft and Its Payload, Magazine-ESA Bulletin1, 65, 26–48. Fumin Yang, Wanzhen Chen, Zhongping Zhang, et al., 1991. Design of Laser Retro-Reflector Array and Laser Ranging Experiment for Shenzhou-IV Satellite, In: 14th International Workshop on Laser Ranging, San Fernando, Spain, June 7–11. Grunwaldt, L., Neubert, R., and Lapushka, K., 2000. First Results of Laser Ranging to the CHAMP Retroreflector, In: 12th International Workshop on Laser Ranging, Matera, Italy, November 13–17. James, W., Steel, W., Evans, N., 1991. Design and testing of a cube-corner array for laser ranging. SPIE 1400, 129–136. Jin, S.G., van Dam, T., Wdowinski, S., 2013. Observing and understanding the Earth system variations from space geodesy. J. Geodyn. 72, 1–10. Jin, S.G., Feng, G.P., Gleason, S., 2011. Remote sensing using GNSS signals: current status and future directions. Adv. Space Res. 47 (10), 1645–1653. Jin, S.G., Luo, O.F., Ren, C., 2010. Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates. Adv. Space Res. 46 (2), 190–195. Jin, S.G., Luo, O.F., Gleason, S., 2009. Characterization of diurnal cycles in ZTD from a decade of global GPS observations. J. Geod. 83 (6), 537–545. Jin, S.G., Luo, O.F., Park, P., 2008. GPS observations of the ionospheric F2-layer behavior during the 20th November 2003 geomagnetic storm over South Korea. J. Geod. 82 (12), 883–892.
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025
Z.-P. Zhang et al. / Advances in Space Research xxx (2014) xxx–xxx Jin, S.G., Park, P., Zhu, W.Y., 2007. Micro-plate tectonics and kinematics in Northeast Asia inferred from a dense set of GPS observations. Earth Planet. Sci. Lett. 257 (3–4), 486–496. Neubert, R., Grunwaldt, L., Neubert, J., 1998. The Retro-Reflector for the CHAMP Satellite: Final Design and Realization, In: 11th International Workshop on Laser Ranging, Deggendorf, Germany, September 21–25.
7
Pearlman, M.R., 2009. Technological Challenges of SLR Tracking of GNSS Constellations, International Laser Workshop on SLR Tracking of GNSS Constellations, Metsovo, Greece, September 14–19. Sawabe, M., T. Uchimura, A. Suzuki, H. Noda., 2009. Laser Retroreflector Array of Geostationary Satellite, ETS-VIII, In: 14th International Workshop on Laser Ranging, San Fernando, Spain, June 7–11.
Please cite this article in press as: Zhang, Z.-P., et al. Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations. J. Adv. Space Res. (2014), http://dx.doi.org/10.1016/j.asr.2013.12.025