Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations

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.     

Design and experiment of onboard laser time transfer in Chinese Beidou navigation satellites

High-precision time synchronization between satellites and ground stations plays the vital role in satellite navigation system. Laser time transfer (LTT) technology is widely recognized as the highest accuracy way to achieve time synchronization derived from satellite laser ranging (SLR) technology. Onboard LTT payload has been designed and developed by Shanghai Astronomical Observatory, and successfully applied to Chinese Beidou navigation satellites. By using the SLR system, with strictly controlling laser firing time and developing LTT data processing system on ground, the high precise onboard laser time transfer experiment has been first performed for satellite navigation system in the world. The clock difference and relative frequency difference between the ground hydrogen maser and space rubidium clocks have been obtained, with the precision of approximately 300 ps and relative frequency stability of 10E−14. This article describes the development of onboard LTT payload, introduces the principle, system composition, applications and LTT measuring results for Chinese satellite navigation system.     

Spin motion determination of the Envisat satellite through laser ranging measurements from a single pass measured by a single station

The Satellite Laser Ranging (SLR) technology is used to accurately determine the position of space objects equipped with so-called retro-reflectors or retro-reflector arrays (RRA). This type of measurement allows to measure the range to the spacecraft with high precision, which leads to determination of very accurate orbits for these targets. Non-active spacecraft, which are not attitude controlled any longer, tend to start to spin or tumble under influence of the external and internal torques and forces.If the return signal is measured for a non-spherical non-active rotating object, the signal in the range residuals with respect to the reference orbit is more complex. For rotating objects the return signal shows an oscillating pattern or patterns caused by the RRA moving around the satellite’s centre of mass. This behaviour is projected onto the radial component measured by the SLR.In our work, we demonstrate how the SLR ranging technique from one sensor to a satellite equipped with a RRA can be used to precisely determine its spin motion during one passage. Multiple SLR measurements of one target over time allow to accurately monitor spin motion changes which can be further used for attitude predictions. We show our solutions of the spin motion determined for the non-active ESA satellite Envisat obtained from measurements acquired during years 2013–2015 by the Zimmerwald SLR station, Switzerland. All the necessary parameters are defined for our own so-called point-like model which describes the motion of a point in space around the satellite centre of mass.     

10 Years of LAGEOS-1 and 15 years of LAGEOS-2 spin period determination from SLR data

Satellite Laser Ranging (SLR) stations measure distance to the satellites equipped with Corner Cube Reflectors (CCRs). These range measurements contain information about spin parameters of the spacecraft. In this paper we present results of spin period determination of two passive satellites from SLR data only: 10 years of LAGEOS-1 (10426 values), and 15 years of LAGEOS-2 (15580 values). The measurements have been made by standard 10 Hz SLR systems and the first 2 kHz SLR system from Graz (Austria). The obtained data allowed calculation of the initial spin period of the satellites: 0.61 s for LAGEOS-1 and 0.906 s for LAGEOS-2. Long time series of the spin period values show that the satellite’s slowing down rate is not constant but is oscillating with a period of 846 days for LAGEOS-1 and 578 days for LAGEOS-2. The results presented here definitely prove that the SLR is a very efficient technique able to measure spin period of the geodetic satellites.     

22 Years of AJISAI spin period determination from standard SLR and kHz SLR data

Satellite Laser Ranging (SLR) is a powerful and efficient technique to measure spin parameters of satellites equipped with corner cube reflectors. We obtained spin period determination of the satellite AJISAI from SLR data only: 17246 pass-by-pass estimates from standard 1–15 Hz SLR data (14/Aug/1986–30/Dec/2008) and 1444 pass-by-pass estimates (9/Oct/2003–30/Dec/2008) from data of the first 2 kHz SLR system from Graz, Austria. A continuous history of the slowing down of AJISAI spin is derived from frequency analysis, and corrected for the apparent effects. The apparent corrections, elaborated here, allowed very accurate determination of AJISAI initial spin period: 1.4855 ± 0.0007 [s]. The paper identifies also non-gravitational effects as a source of the periodical changes in the rate of slowing down of the satellite.     

New results on spin determination of nanosatellite BLITS from High Repetition Rate SLR data

The nanosatellite BLITS (Ball Lens In The Space) demonstrates a successful design of the new spherical lens type satellite for Satellite Laser Ranging (SLR). The spin parameters of the satellite were calculated from more than 1000 days of SLR data collected from 6 High Repetition Rate (HRR) systems: Beijing, Changchun, Graz, Herstmonceux, Potsdam, Shanghai.     

Spin parameters of High Earth Orbiting satellites Etalon-1 and Etalon-2 determined from kHz Satellite Laser Ranging data

The high repetition rate Satellite Laser Ranging (SLR) system developed in Graz, Austria, measures ranges to the High Earth Orbiting satellites Etalon-1 and Etalon-2 with the millimeter accuracy. The 2 kHz repetition rate of the laser and the relatively high return rates allow to use the SLR data to calculate the spin parameters of the Etalon satellites. The analysis of the 10 years (October 2003–September 2013) of the SLR data gives trends of the spin axes orientation (J2000 Inertial Reference Frame):     

Determination of station positions and velocities from laser ranging observations to Ajisai,Starlette and Stella satellites

The positions and velocities of the four Satellite Laser Ranging (SLR) stations: Yarragadee (7090), Greenbelt (7105), Graz (7839) and Herstmonceux (7840) from 5-year (2001–2005) SLR data of low orbiting satellites (LEO): Ajisai, Starlette and Stella were determined. The orbits of these satellites were computed from the data provided by 20 SLR stations. All orbital computations were performed by means of NASA Goddard’s GEODYN-II program. The geocentric coordinates were transformed to the topocentric North–South, East–West and Vertical components in reference to ITRF2005. The influence of the number of normal points per orbital arc and the empirical acceleration coefficients on the quality of station coordinates was studied. To get standard deviation of the coordinates determination lower than 1 cm, the number of the normal points per site had to be greater than 50. The computed positions and velocities were compared to those derived from LAGEOS-1/LAGEOS-2 data. Three parameters were used for this comparison: station coordinates stability, differences from ITRF2005 positions and velocities. The stability of coordinates of LEO satellites is significantly worse (17.8 mm) than those of LAGEOS (7.6 mm), the better results are for Ajisai (15.4 mm) than for Starlette/Stella (20.4 mm). The difference in positions between the computed values and ITRF2005 were little bit worse for Starlette/Stella (6.6 mm) than for LAGEOS (4.6 mm), the results for Ajisai were five times worse (29.7 mm) probably due to center of mass correction of this satellite. The station velocities with some exceptions were on the same level (≈1 mm/year) for all satellites. The results presented in this work show that results from Starlette/Stella are better than those from Ajisai for station coordinates determination. We can applied the data from LEO satellites, especially Starlette and Stella for determination of the SLR station coordinates but with two times lower accuracy than when using LAGEOS data.     

Estimation of the Love and Shida numbers: h2, l2 using SLR data for the low satellites

In this paper we present results for the global elastic parameters: Love number h₂ and Shida number l₂ derived from the analysis of Satellite Laser Ranging (SLR) data. SLR data for the two low satellites STELLA (H = 800 km) and STARLETTE (H = 810 km) observed during 2.5 years from January 3, 2005 until July 1, 2007 with 18 globally distributed ground stations were analyzed. The analysis was done separately for the two satellites. We do a sequential analysis and study the stability and convergence of the estimates as a function of length of the data set used.     

Optical response of nanosatellite BLITS measured by the Graz 2 kHz SLR system

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The optical response of BLITS has been measured by the Graz 2 kHz SLR station and compared with the response of the classical retroreflector arrays (RRA) of the Low Earth Orbiting satellites such as ERS-2 and Stella. This work demonstrates that the optical response of BLITS is flat and featureless, comparable with the signature of a point-source or a flat target, and suggests that this innovative design will deliver a higher normal point (NP) accuracy (2.55 mm) than any other SLR target currently in orbit. The high reflectivity of the glassy BLITS (about 60% of the return rate from the multi-reflector Stella) is found to be decreasing by about 30% per year, probably due to the solar irradiation. Detailed analysis of the reflective half-shell demonstrates that a high return rate of SLR measurements can be achieved regardless of the incident angle of the laser beam, thus making the spherical lens a perfect successor of the classical RRA panels mounted on active satellites such as CHAMP, GOCE and GRACE.     

Comparison of GPS S/C orbits determined from GPS and SLR tracking data

The last two Global Positioning System (GPS) spacecraft launched on August 30, 1993 and March 10, 1994 carried identical laser retroreflector arrays that allow laser ranging from ground stations. Tracking of these targets is a low priority for most of the ground stations due to the present mandatory support of missions with no alternative tracking. The available data is sparse and concentrated primarily on the first of the two spacecraft, GPS-35 (PRN 5). Despite this, analysis of this data set indicates that there is great potential for engineering and scientific experiments in a synergistic application of Satellite Laser Ranging (SLR) and radiometric GPS techniques.     

Time Transfer by Laser Link: Data analysis and validation to the ps level

The Time Transfer by Laser Link (T2L2) is a very high resolution time transfer technique based on the recording of arrival times of laser pulses at the satellite. T2L2 was designed to achieve time stability in the range of 1 ps over 1000 s and an accuracy better than 100 ps. The project is in operation onboard the Jason-2 satellite since June 2008. The principle is based on the Satellite Laser Ranging (SLR) technology; it uses the input of 20–25 SLR stations of the international laser network which participate in the tracking. This paper focuses on the data reduction process which was developed specifically to transform the raw information given by both space instrument and ground network: first to identify the triplets (ground and onboard epochs and time of flight of the laser pulse), second to estimate a usable product in terms of ground-to-space time transfer (including instrumental corrections), and thirdly to produce synchronization between any pair of remote ground clocks. In describing the validation of time synchronizations, the paper opens a way for monitoring the time difference between ultra-stable clocks thanks to a laser link at a few ps level for Common View passes. It highlights however that without accurately characterizing the onboard oscillator of Jason-2 and knowing the unavailability of time calibrations of SLR stations generally, time transfer over intercontinental distances remain difficult to be accurately estimated.     

First laser measurements to space debris in Poland

The Borowiec Satellite Laser Ranging station (BORL 7811, Borowiec) being a part of the Space Research Centre of the Polish Academy of Sciences (SRC PAS) went through modernization in 2014–2015. One of the main tasks of the modernization was the installation of a high-energy laser module dedicated to space debris tracking. Surelite III by Continuum is a Nd:YAG pulse laser with 10?Hz repetition rate, a pulse width of 3–5?ns and a pulse energy of 450?mJ for green (532?nm). This new laser unit was integrated with the SLR system at Borowiec performing standard satellite tracking. In 2016 BORL 7811 participated actively to the observational campaigns related to the space debris targets from LEO region managed by the Space Debris Study Group (SDSG) of the International Laser Ranging Service (ILRS).Currently, Borowiec station regularly tracks 36 space debris from the LEO regime, including typical rocket bodies (Russian/Chinese) and cooperative targets like the inactive TOPEX/Poseidon, ENVISAT, OICETS and others. In this paper the first results of space debris laser measurements obtained by the Borowiec station in period August 2016 – January 2017 are presented. The results gained by the SRC PAS Borowiec station confirm the rotation of the defunct TOPEX/Poseidon satellite which spins with a period of approximately 10?s. The novelty of this work is the presentation of the sample results of the Chinese CZ-2C R/B target (NORAD catalogue number 31114) which is equipped (probably) with retroreflectors. Laser measurements to space debris is a very desirable topic for the next years, especially in the context of the Space Surveillance and Tracking (SST) activity. Some targets are very easy to track like defunct ENVISAT or TOPEX/Poseidon. On the other hand, there is a big population of different LEO targets with different orbital and physical parameters, which are challenging for laser ranging like small irregular debris and rocket boosters.     

Contemporary plate motions from Lageos: A decade later

Reduction of a decade's worth of Lageos Satellite Laser Ranging (SLR) is providing new insights into contemporary plate kinematics. Globally, the SLR results have largely confirmed the plate motion models developed from geologic evidence. Analysis of the data from 12 base stations finds all interstation SLR rates having a linear cross correlation of .91 with the Minster and Jordan geologic model. To within their uncertainties, the time scales of the geologic and SLR models are found to be in agreement indicating that globally, the tectonic rates are linear over time scales of 1 to 10 million years. Regionally, SLR data exclusively has been used to develop a model of the absolute station motions for observing sites within the Western United States. The observed intersite motion of the two stations comprising the San Andreas Fault Experiment appears to be non-linear over the last decade, with the relative motion between these sites changing from −6 to −2 cm/year during the last four years. The results achieved with SLR are complemented and largely confirmed by those achieved with other space technologies. It is clear that Satellite Laser Ranging has reached a new level of maturity. After passing through the threshold of confirming the global nature of plate kinematics, research is now focusing on the development of models for the effective utilization of the constraints provided by space geodesy. These constraints will assist in our understanding of the mechanisms which drive tectonic motions and cause a complex picture of strain accumulation at the plate boundaries.     

Characteristics of GOCE orbits based on Satellite Laser Ranging

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first European Space Agency’s (ESA) Earth Explorer core mission. Through its extremely low, about 260?km above the Earth, circular, sun-synchronous orbit, the satellite gained high spatial resolution and accuracy gravity gradient, and ocean circulation data. Global Positioning System (GPS) receivers, mounted on the spacecraft, allowed the determination of reduced-dynamic and kinematic GOCE orbits, whereas Laser Retroreflector Array (LRA) dedicated to Satellite Laser Ranging (SLR) allowed an independent validation of GPS-derived orbits. In this paper, residuals between different GPS-based orbit types and SLR observations are used to investigate the sensitivity and the influence of solar, geomagnetic, and ionospheric activities on the quality of kinematic and reduced-dynamic GOCE orbits. We also analyze the quality of data provided by individual SLR sites, by detecting time biases using ascending and descending sun-synchronous GOCE orbit passes, and the residual analysis of the measurement characteristics, i.e., the dependency of SLR residuals as a function of nadir and horizontal angles. Results show a substantial vulnerability of kinematic orbit solutions to the solar F10.7 index and the ionospheric activity measured by the variations of the Total Electron Content (TEC) values. The sensitivity of kinematic orbits to the three-hour-range KP index is rather minor. The reduced-dynamic orbits are almost insensitive to indices describing ionospheric, solar, and geomagnetic activities. The investigation of individual SLR sites shows that some of them are affected by time bias errors, whereas other demonstrate systematics, such as a dependency between observation residuals and the satellite nadir angle or the horizontal azimuth angle from the SLR station to the direction of the satellite.     

Spin parameters of Low Earth Orbiting satellites Larets and Stella determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) measurements contain information about the spin parameters of the fully passive, geodetic satellites. In this paper we spectrally analyze the SLR data of 5 geodetic satellites placed on the Low Earth Orbits: GFZ-1, WESTPAC, Larets, Starlette, Stella, and successfully retrieve the frequency signal from Larets and Stella only. The obtained signals indicate an exponential increase of the spin period of Larets: T = 0.860499·exp(0.0197066·D) [s], and Stella: T = 13.5582·exp(0.00431232·D) [s], where D is in days since launch. The initial spin periods calculated from the first month of the SLR observations are: Larets: T_initial = 0.8239 s, Stella: T_initial = 13.2048 s. Analysis of the apparent effects indicates the counter-clockwise spin direction of the satellites. The twice more heavy Stella lost its rotational energy more than four times slower than Larets. Fitting the spin model to the observed spin trends allows determination of the spin axis orientation evolution for Larets and Stella before their rotational period becomes equal to the orbital period.     

Precision orbit determination for TOPEX/Poseidon using TDRSS doppler tracking data

Precision orbit determination on the TOPEX/Poseidon (T/P) altimeter satellite is now being routinely achieved with sub-5cm radial and sub-15 cm total positioning accuracy using state-of-the-art modeling with precision tracking provided by a combination of: (a) global Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), or (b) the Global Positioning System (GPS) Constellation which provides pseudo-range and carrier phase observations. The geostationary Tracking and Data Relay Satellite System (TDRSS) satellites are providing the operational tracking and communication support for this mission. The TDRSS Doppler data are of high precision (0.3 mm/s nominal noise levels). Unlike other satellite missions supported operationally by TDRSS, T/P has high quality independent tracking which enables absolute orbit accuracy assessments. In addition, the T/P satellite provides extensive geometry for positioning a satellite at geostationary altitude, and thus the TDRSS-T/P data provides an excellent means for determining the TDRS orbits. Arc lengths of 7 and 10 days with varying degrees of T/P spacecraft attitude complexity are studied. Sub-meter T/P total positioning error is achieved when using the TDRSS range-rate data, with radial orbit errors of 10.6 cm and 15.5 cm RMS for the two arcs studied. Current limitations in the TDRSS precision orbit determination capability include mismodeling of numerous TDRSS satellite-specific dynamic and electronic effects, and in the inadequate treatment of the propagation delay and bending arising from the wet troposphere and ionosphere.     

Analysis of laser ranges and angular measurements data fusion for space debris orbit determination

In the framework of space debris, the orbit determination process is a fundamental step, both, for researchers and for satellite operators. The accurate knowledge of the orbit of space debris objects is needed to allow space debris characterization studies and to avoid unnecessary collision avoidance maneuvers.The accuracy of the results of an orbit determination process depends on several factors as the number, the accuracy, the kind of processed measurements, their distribution along the orbit, and the object-observer relative geometry. When the observation coverage of the target orbit is not homogeneous, the accuracy of the orbit determination can be improved processing different kind of observables. Recent studies showed that the satellite laser ranging technique can be successfully applied to space debris.In this paper, we will investigate the benefits of using laser ranges and angular measurements for the orbit determination process. We will analyze the influence of the number of used observations, of the covered arc of orbit, of each observable, and of the observation geometry on the estimated parameters. Finally, using data acquired on short observation arcs, we analyze the achievable accuracies for the orbital regimes with the highest space debris density, and to the consequences of the data fusion on catalog maintenance operations. The results shown are obtained using only real data (both angular and laser measurements) provided by sensors of the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald owned by the Astronomical Institute of the University of Bern (AIUB) and for some studies also using ranges provided from other stations of the International Laser Ranging Service (ILRS).     

Estimation of the elastic Earth parameters (h2, l2) using SLR data

We present results for the global elastic parameters h₂ and l₂ derived from the analysis of Satellite Laser Ranging (SLR) data. SLR data for the two satellites LAGEOS 1 and LAGEOS 2 observed during 2.5 years from January 3, 2005 until July 1, 2007 with 18 globally distributed ground stations were analysed using different approaches. The analysis was done separately for the two satellites and approaches to estimate the two elastic parameters independently and together were performed. We do a sequential analysis and study the stability of the estimates as a function of length of the data set used. The adjusted final values for h₂ equal to 0.6151 ± 0.0008 and 0.6152 ± 0.0008, and those for l₂ equal to 0.0886 ± 0.0003 and 0.0881 ± 0.0003 for LAGEOS 1 and LAGEOS 2 tracking data are compared to other independently derived estimates. These parameters and their errors achieve stability at about the 24 and 27 month time interval for h₂ and l₂, respectively.     

Spin parameters of nanosatellite BLITS determined from Graz 2 kHz SLR data

The nanosatellite BLITS (Ball Lens In The Space) is the first object designed as a passive, spherical retroreflector of the Luneburg type, dedicated for Satellite Laser Ranging (SLR). The 2 kHz SLR station Graz measures spin parameters of this satellite, providing information about the rotational dynamics of the body. The measurements obtained during the period from September 26, 2009 to November 24, 2010 show a significant change of the spin configuration. The spin axis was dynamically precessing since the launch and currently is sinus-like behaving between coordinates RA 120°…150°, Dec 30°…60° (J2000 inertial reference frame). The angle between the symmetry axis and the spin axis of BLITS is not constant, but is decreasing since the launch, while its spin period is rather stable with a mean value of 5.613 s (clockwise rotation). The satellite was dynamically changing its attitude during the first three months after deployment; after this time the spin parameters are relatively stable.