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Journal of Geodesy

, Volume 93, Issue 11, pp 2389–2404 | Cite as

Time and laser ranging: a window of opportunity for geodesy, navigation, and metrology

  • P. ExertierEmail author
  • A. Belli
  • E. Samain
  • W. Meng
  • H. Zhang
  • K. Tang
  • A. Schlicht
  • U. Schreiber
  • U. Hugentobler
  • I. Prochàzka
  • X. Sun
  • J. F. McGarry
  • D. Mao
  • A. Neumann
Original Article

Abstract

Recent progress in the domain of time and frequency (T/F) standards requires important improvements in existing time distribution links, in term of accuracy in particular. Satellite Laser Ranging (SLR) has proven to be a fundamental tool, offering a straightforward, conceptually simple, highly accurate, and unambiguous observable. Several time transfers by laser link projects have been carried out over the past 10 years with numerous scientific and metrological objectives. Depending on the mission, SLR is used to transmit time over two-way or one-way distances from 500 to several millions of kilometer. The following missions and their objectives employed this technique: European Laser Timing (ELT, expected in 2020) at 450 km, Time Transfer by Laser Link (T2L2) at 1336 km, Laser Time Transfer at 36,000 km, Lunar Reconnaissance Orbiter at 350,000 km, and MErcury Surface, Space ENvironment, GEochemistry, and Ranging at tens of million km. This article describes the synergy between SLR and T/F technologies developed on the ground and in space and as well as the state of the art of their exploitation. The performance and sources of limitation of such space missions are analyzed. It shows that current and future challenges lie in the improvement in the time accuracy and stability of the time for ground geodetic observatories. The role of the next generation of SLR systems is emphasized both in space and at ground level, from the point of view of Global Geodetic Observing System and valuable exploitation of the synergy between time synchronization, ranging, and data transfer.

Keywords

Time transfer Laser ranging Geodesy Navigation Space and ground reference frames 

1 Introduction

Early ideas about the time transfer by laser ranging technique gave opportunities to enhance the synergy between both laser ranging and time and frequency technologies (Samain et al. 2015; Schreiber and Kodet 2017). The optical time transfer as a specific space technique is motivated primarily by challenges such as fundamental physics (e.g., equivalence principle and isotropy of the speed of light) and interplanetary navigation, e.g., (Cacciapuoti and Salomon 2009; Smith and Zuber 2017). The time transfer technique further provides insights into the time and frequency metrology and space geodesy such as the calibration and validation of microwave systems (Exertier et al. 2016), the understanding of the clock behavior, the comparison of clocks in remote observatories (Mao et al. 2014; Exertier et al. 2017), the monitoring of high-quality space oscillators (Belli et al. 2016), the transfer of Earth time to planetary spacecrafts (Dirkx et al. 2016), the precise orbit determination (POD) (Bauer et al. 2016).
Table 1

List of the space missions (planetary [with a laser altimeter*] and Earth observation) that used the time transfer by laser ranging technique, and their space oscillators (see the list of acronyms in “Appendix”)

Mission

Period

References

Oscillator

Stability at \(\tau \)

MGS

1996–2006

(Albee et al. 1998)

USO (Norton and Cloeren 1996)

 

MOLA*

 

(Abshire et al. 2000)

OCXO (Bloch et al. 2008)

 

MESSENGER

2004–2015

(Solomon et al. 2007)

OCXO

 

MLA*

 

(Cavanaugh et al. 2007)

  

LRO

2009–2014

(Tooley et al. 2010)

OCXO (Weaver et al. 2004)

\(7\times 10^{-14}\) at 40s

LOLA*

 

(Smith et al. 2010)

 

\(2\times 10^{-13}\) at 10,000 s

ICESat

2003–2010

(Schutz et al. 2005)

OCXO monitored by onboard GPS

 

T2L2 /Jason-2

2008–2018

(Samain 2008)

OCXO (Auriol and Tourain 2010)

\(2\times 10^{-13}\) at 10–100 s

LTT /Beidou

2007–2014

(Meng et al. 2013a)

Rubidium

\(3\times 10^{-13}\)at 100 s

ELT /ISS

2020–

(Prochazka et al. 2016)

ACES/Pharao (Laurent et al. 2015)

\(3\times 10^{-16}\) at 1 day

   

ACES/H-maser

\(1\times 5 10^{-15}\) at 10,000 s

Some of these topics have been recently tested and studied by several space missions, where two-way and/or one-way laser ranging measurements were obtained. First, some time transfer experiments used, in addition to the one-way link, the two-way laser ranging from a laser retroreflector array (LRA) placed onboard: the Laser Time Transfer (LTT) project on Beidou at 36,000 km (Meng et al. 2013a), the Time Transfer by Laser Link (T2L2) experiment on Jason-2 at 1336 km (Samain 2008) and the European Laser Timing (ELT) instrument at 450 km to be launched in 2020 on the international space station (Hess et al. 2011). Second, the one-way laser ranging experiment to the Lunar Reconnaissance Orbiter (LRO) spacecraft at lunar distance proved to be an essential tool to improve the orbit determination, despite the issues that have been raised by the instability of the onboard quartz crystal oscillator (Bauer et al. 2016; Buccino et al. 2016; Mao et al. 2017). Finally, an original two-way experiment has been performed to the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) planetary mission, as an asynchronous laser transponder technique using the proper laser altimeter of the mission instead of LRA due to the huge distance (Degnan 2002; Zuber 2006). See on Table 1 the list of the missions, periods and corresponding references in addition to the space oscillators used.

The need for laser ranging station development and adaptation is an enduring challenge in view of achieving a time transfer by laser at 1-nanosecond (ns) of accuracy and less. In all of the above-mentioned missions, a given laser ranging station has been chosen as a primary station to conduct tests, campaigns and routine operations; in each case, a number of technological time and frequency developments have been carried out. As a result, the time transfer technique has achieved a few picosecond (ps) stability at 1000 s and tens of ps accuracy (Samain et al. 2015; Schreiber and Kodet 2017). But the long-term stability and accuracy of the local time with respect to Coordinated Universal Time (UTC) is something to be improved along the international laser ranging network (Pearlman et al. 2009), as it was demonstrated recently from the T2L2 experiment (Exertier et al. 2017).

In addition to the time and frequency technologies developed at ground stations, highly stable oscillators are flown in space for a variety of different science and programmatic missions; e.g., the cesium, rubidium, and passive H-maser oscillators onboard the global navigation satellite systems (GNSS), or the ultra-stable-oscillators (USO) used primarily as time generators in planetary (Dehant et al. 2017) and Earth space missions (Bloch et al. 2008). The onboard oscillators are selected by taking into account some criteria related to the required quality and durability in space conditions depending on the mission objectives, cost and the typical timespan for which they are used (Cash et al. 2008). Among these objectives, it is essential to maintain a short-term frequency (f) stability \({\delta f /f} <10^{-13}\) between 1 and 100 s to ensure precise Doppler measurements from Earth facilities (Auriol and Tourain 2010); it is also important to reduce the systematic change in frequency with time of such free-running oscillators as much as possible, i.e., \({\delta f /f} < 10^{-11}\) day\(^{-1}\) in order to keep time accuracy onboard (Cooper et al. 2012).

The goal of this article is to highlight the different parts of the technological developments that made the success of some recent optical time transfer ranging experiments both in space and on the ground, and to extrapolate the necessary improvements to achieve future scientific goals in terms of fundamental physics, navigation, and chronometric geodesy. First, Sect. 2 answers basic questions on the time transfer by laser ranging as its principle, advantages and prospect. Then, Sect. 3 is dedicated to time and frequency technologies that have been developed for ground laser stations, whereas Sect. 4 describes the characteristics of space oscillators used to time tag the received laser pulses. Sections 5 and 6 describe the time transfer experiments that use both one-way and two-way laser ranging measurements, which are based on retroreflectors or transponders (with onboard laser altimeters), respectively. Finally, we discuss the next generation of optical time transfer techniques and consider the necessary future improvements to reach a better accuracy in Sect. 7, and then we conclude.

2 Time and laser ranging: basics

Improving clock—its frequency accuracy and long-term stability—is a challenge for primary T / F metrology, i.e., the definition of the International Atomic Time (TAI). TAI is the basis of realization of time scales used in dynamics, for modeling the motions of artificial and natural celestial bodies, with applications in the exploration of the solar system, tests of theories, geodesy, geophysics and studies of the environment. But it rests critically on the methods of clock comparison which are still the factor that can act to the detriment of a highly precise time scale; there is a long record of studies and experiments using atomic clocks and comparison techniques, local or remote.

In the early 1990s, a revolutionary step for remote clock comparisons over intercontinental distances was the use of satellite techniques, firstly with the Global Position System (GPS) (Ray and Senior 2005). The use of light link as a time carrier, instead of microwave link, to disseminate ultra-stable references has been studied very early in view of applications such as geodesy and tests of the general relativity (Einstein’s gravitational frequency shift, notably) (Ashby and Allan 1979; Petit and Wolf 2005). The stability and accuracy provided by the laser ranging technology combined with ground and space dedicated timing electronics proved to achieve a time transfer performance better than 10 times the one of operational comparison techniques based on a one-way or even two-way microwave link (Exertier et al. 2016).

From a pulsed laser, the principle of the optical time transfer consists in timing a very short signal (of tens of picoseconds) emitted by a station from an accurate clock toward a space receiving equipment in the form of a lens, detector, event timer and clock; the comparison of both times, given at ground and in space, is the basic of time transfer by laser ranging. It is operated in two modes actually, one-way and/or two-way, depending on the space segment. When the satellite is equipped with LRA, the ground-to-space time transfer is thus accurately determined from the two-way ranging which gives a very precise measure (a few ps at best) of the time of flight of the laser pulse (Exertier et al. 2017). Without LRA, however, it is necessary to solve for both range and/or time simultaneously when comparing the two clocks; this requires independent radio-tracking data in addition to a precise dynamical model to estimate the time-of-flight (range); see, e.g., the LRO experiment (Mao et al. 2011; Bauer et al. 2016).

A laser beam is attenuated as it propagates through the atmosphere to the distance \((d^2)^2\) for the two-way mode (Degnan 1993). In addition, the laser beam is often broadened, defocused, and may even be deflected from its initial propagation direction, effects which have far-reaching consequences for the use of lasers in ranging, remote sensing, and optical communication (Djerroud et al. 2010). The intensity of the arriving pulse depends on the atmosphere, the distance, the initial energy of the beam (from 1 to 300 mJ), the size and number of corner cubes of the embarked LRA (if any). Thus, the detection mode can be multi- or single photon, the latter being the indivisible minimum energy unit of light. Detectors (avalanche photodiodes) with the capability of single-photon detection are the most sensitive instruments and thus provide unambiguous range measurements notably to satellite equipped with a large LRA like the GNSSs (Sosnica et al. 2015).

For these reasons, the two-way laser ranging is currently limited to the lunar distance, obviously in the single-photon detection mode (Buccino et al. 2016). In order to transfer Earth time at the scale of the solar system, the one-way laser ranging technique, being attenuated to the distance \((d^2)\), proved to be a challenging tool for navigation (Dirkx et al. 2016). Because accurate time keeping is not obvious to be achieved onboard a planetary mission, that is on a long period of time—see, e.g., (Cooper et al. 2012), a new generation of embarked atomic clock is under study (JPL-DSAC 2017). On the other hand, the principle of a double one-way time transfer technique—from Earth to space and then from the space equipment (with an embarked laser) to the Earth (Degnan 2002)—has been demonstrated with the MESSENGER at 0.16 Astronomical Unit (AU) (Zuber 2006); it opened the door to deep space exploration (Neumann et al. 2014).

3 Time and frequency on the ground

3.1 Timing electronics

The timing electronics at the ground stations have to time tag the transmitted and the received laser pulses to the resolution and accuracy required by the laser time transfer. They usually consist of a counter or timer clocked by a stable oscillator and a register that records the timer reading when triggered by an external event. The timer reading has to be referenced to a standard time, such as the UTC or the GPS time (Exertier et al. 2017).

The timer can be a time interval analyzer (TIA) which measures the time from a periodic time mark, such as the GPS 1 pulse per second (1 PPS) tick and reset at these time marks. Another type of timer is an event timer (ET) that continuously record the time, also known as continuous time interval analyzer, which records the times of external events as well as standard time marks (Kalisz 2004). The underlining clock to either a TIA or an ET is usually free running to achieve the highest clock stability. The clock frequency can be calibrated by recorded times of the standard time marks such as the GPS 1 PPS ticks (Ray and Senior 2005).

Early TIAs were made of simple counters driven by an oscillator; the timing resolution was equal to its period. Time to digital converters (TDC) were later used to improve the timing resolution to a small fraction of the oscillator period by delaying the signal through a series of logic gates and use digital logics to determine the time of the signal arrival from the previous edge (Paschalidis 2002). The propagation delays of the logic gates are kept constant with respect to the reference clock time with the use of a delay lock loop (Prochazka et al. 2016; Schreiber and Kodet 2017). TDCs achieve fine time interval measurements without the need for a high-speed clock. They use ordinary silicon integrated circuit technology to achieve picosecond timing at the same electrical power consumption as ordinary complementary metal-oxide semiconductor (CMOS) devices. TDC can be implemented in field programmable gate array (FPGA) or application-specific integrated circuit (ASIC). Nowadays, TDC can achieve 1 ps resolution at a standard external clock frequency of 5 or 10 MHz. TDCs have been used in both ground stations and laser timing instruments in space; see, e.g., (Kalisz 2004).

If current event timers are able to achieve precision and resolution at the 1 ps level, however, the overall time distribution system of a given station at ground level, which includes ground cables, electronic devices, etc., and a necessary link to the standard UTC or GPS time, can be shifted by several nanoseconds (Exertier et al. 2017).

3.2 Compensation of local delays

Optical time transfer from ground to space and from ground via space to ground requires a continuous control over all acting system delays between the respective clocks (Samain et al. 2015; Schreiber and Kodet 2017). Unlike for laser ranging applications, where the estimation of the epoch of the laser fire event does not require a resolution higher than 1 ns, accurate time transfer demands a resolution of a few ps. The same stringent requirements apply for the local system delays.

Time on an observatory in practice is defined as a fast rising leading edge 1 PPS signal at a specific output port of a high quality local clock, for example a hydrogen maser (H-maser), which ideally is referenced to UTC (Sun et al. 2013). In order to compare this clock to an orbiting clock in space, one has to establish the time it takes for this 1 PPS signal to propagate from the reference clock to the laser ranging system timer. In addition to that the actual laser pulses used for the time transfer have to be accurately related to the reference point of the laser ranging system with respect to their time delay. Therefore, a meaningful measurement resolution of about 1 ps is desirable in order to make the local clock error small compared to the time transfer error.

Unlike the transfer of reference frequencies operating a clock, the transfer of time requires a very accurate time-tagging process. Temperature-related variations of the transfer time of the 1 PPS signal through electronic circuitry, thermal expansion in electrical transmission lines and variations in the electric ground potential may cause fluctuations of the time delay in the order of roughly 30 ps. In the case of serious problems, the experienced delay changes may exceed 100 ps (Exertier et al. 2016).
Fig. 1

Block diagram of the delay compensation circuit. Over several hundred meters the coherence of the time could be stabilized to within 1 ps

Table 2

Ground laser (532 nm) ranging stations used as primary station; (Sun et al. 2013)\(^{(1)}\), (Samain et al. 2015)\(^{(2)}\), (Samain et al. 2018)\(^{(3)}\), (Schreiber and Kodet 2017)\(^{(4)}\). These SLR stations use a H-maser clock and picosecond resolution and precision event timer. For the GGAO site, we separated the different experiments that were conducted since 2005 on MLA (MESSENGER), MOLA (MGS) and LRO equipped with a one-way uplink

Station

Laser (Hz/mJ/ps)

Calib. (ns)

Link to Std time

Std time/Accur. (ns)

GGAO, NASA\(^{(1)}\)

 

1

All-in-View GPS

USNO/1

MLA

240/14/–

  

MET/1

MOLA

49/11/–

1

 

MET/130

LRO

28/50/5500

  

MET/10–20

Grasse, France\(^{(2)}\)

10/100/10–200

\(<\,0.100\)

CV GPS

UTC (OP)/1–2

SHAO, China\(^{(3)}\)

20/150/250

\(<\,1\)

id.

GPS time/1–2

Wettzell, Germany\(^{(4)}\)

20/200/10

0.025

id.

UTC (GOW)/1

One possible way of controlling the local system delay sufficiently, is the application mode-locked fs-pulse (femto) lasers. They have ultra-low noise properties in the optical as well as in the microwave regime. When the time markers are carried from the clock to the ranging facility by the ultra-short laser pulses in a two-way approach, temperature- or strain-induced length variations of the connecting optical fiber can be compensated. For this purpose, the reference frequency from the local clock is used to determine and fix the repetition rate of the mode-locked pulse laser. The pulses are then traveling through the fiber. A combination of two types of fibers, of which one is the conjugate of the other, compensates the effects of dispersion and ensures that the laser pulses remain short. At the end of the fiber near the timer of the laser ranging facility, the pulses are reflected by a semi-transparent mirror and traveling back to the source. At the source the outgoing laser pulses are correlated with the returning signal, and a variable delay line at the beginning of the transmission line is adjusted in a closed loop configuration to a constant path delay. Figure 1 illustrates this procedure in a simplified block diagram.

A prototype of this time distribution system has been set up at the Geodetic Observatory in Wettzell (Germany) in preparation of the optical time transfer for the Atomic Clock Ensemble in Space (ACES) (Schlicht et al. 2012). Currently, it achieves a stability for the phase of the transferred time of 1 ps over several days; when the time distribution system is fully integrated to the laser ranging facility, it should be possible to relate the ground clock to the ACES clock with an accuracy smaller than 25 ps for a single-shot measurement (Schreiber and Kodet 2017).

On the other hand, the Grasse laser ranging station has time calibrated its laser system, in the context of T2L2, achieving an accuracy better than 100 ps of the ground link between the laser system and the T/F laboratory (equipped with a H-maser) (Samain et al. 2015). The calibration procedure based on a mobile equipment (event timer, fiber, etc.) has been applied several times during T2L2 time transfer campaigns conducted from 2013 to 2016 at different locations in Europe and China; see (Exertier et al. 2016) and (Samain et al. 2018), respectively.

3.3 Accuracy of the ground station clocks

Since the oscillator frequencies drift over time, ground station timing accuracy degrade over time and links to the standard time— i.e. UTC, GPS time or TAI (Temps Atomique International)—have to be performed periodically. In order to maintain a uniform time frame on the long term, this issue is of particular importance especially when a network of stations is needed. We learned from both the LRO and T2L2 time transfer experiments that some ground station clocks may have time offsets \(\delta t\) of hundreds of ns and even more (Exertier et al. 2017), despite the International Laser Ranging Service (ILRS) recommendations of \(\delta t < 100\) ns (Pearlman et al. 2009).

The easiest method to maintain a ground station time to within a 1–2 ns to the standard time is to reference it to the GPS time from a nearby receiver; see, e.g., (Ray and Senior 2005). However, the GPS time from a generic GPS receiver is affected by some delays, as internal (including receiver and ground cables) and external (atmosphere), of the microwave signal (Lombardi 2008). It is thus necessary to carry out a time calibration of the equipment (Rovera et al. 2014). The performance of carrier-phase-based GPS precision time transfer has been investigated by several authors. The Common-View (CV) and All-in-View (AV) techniques have been examined in terms of time transfer; the RMS differences computed by these two typical techniques agreed with Circular-T (distributed by BIPM) at the level of 0.3–0.65 ns (Lee et al. 2008).

The NASA Goddard Space Flight Center (GSFC) has calibrated its H-maser to the master clock and hence TAI at the nearby United State Naval Observatory (USNO). An All-in-View GPS receiver (DiCOM GTR50) was used to monitor the time offset between the 1 PPS signal of the H-maser to the GPS time over a 20-month period thus achieving a long-term accuracy of 1 ns (Sun et al. 2013). In the same way, the Grasse H-maser has been calibrated against the UTC(”Observatoire de Paris“) via the GPS-CV technique, achieving an accuracy of 1–2 ns (Rovera et al. 2014). See details per primary station on Table 2.

4 Oscillators in Space

Most spacecrafts carry quartz crystal oscillators as clock references for time keeping. The oscillator and clock are reset shortly before launch. A counter is used to count the clock cycles and uses it to define the mission elapse time (MET). The onboard clock time is periodically compared against a common time standard, such as UTC, via a special time-keeping procedure between a ground station and the spacecraft. The onboard clock frequency and drift rate are estimated by comparing the MET and UTC over a given period of time. Therefore, the time-keeping procedure between the ground station and the spacecraft has to be performed frequently enough to guarantee that the clock frequency of the onboard free-running oscillator (USO) can be modeled and predicted to the required precision; see, e.g., (Belli et al. 2016).

For precision geodetic instruments such as a laser altimeter, a very stable and precise clock oscillator is needed. The clock oscillator has to have a short-time stability of \(< 10^{-13}\) over a few seconds so that the clock frequency drift during the time of flight of the laser is negligible. A temperature-compensated crystal oscillator (TCXO) or an oven-controlled crystal oscillator (OCXO) have to be used to meet these requirements (Weaver et al. 2004). For precision radio frequency tracking and Doppler shift measurement of a spacecraft, a USO with even more stringent requirements must be used (only in the case of a one-way system), as it is the case with the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) tracking technique (Auriol and Tourain 2010).

The planetary and Earth Observation missions, which are described in Sects. 4 and 5, generally use a highly stable OCXO oscillator with a short-term stability of a few \(10^{-14}\) to \(3{-}5 \times 10^{-13}\) between 10 and 100 s (see Table 1). LRO has a one-way laser ranging system that requires the OCXO to be stable to a few ns over the 2-hour LRO orbit period (Cash et al. 2008). NASA Jet Propulsion Laboratory will soon launch its Deep Space Atomic Clock (DSAC) in space as a technology demonstration which will greatly enhances the performance of current space clock designs and virtually decrease spacecraft clock errors to benefit future navigation and radio science (JPL-DSAC 2017). Over long time periods (important, e.g., Solar system ephemerides), however, the results from two-way tracking will continue to be superior to the one-way due to the inevitable noise and/or drift of the space clock.

5 Time transfer experiments with laser retroreflectors

5.1 LTT

Laser Time Transfer is the first ground and satellite time synchronization system by laser ranging to navigation satellites (Meng et al. 2013a). The whole system including the onboard instruments and ground SLR station was designed by the Shanghai Astronomical Observatory (SHAO); see the block diagram on Fig. 2. On board the MEO satellites, the LRA includes 42 corner cubes, instead of 90 for the GEO/IGSO ones (See the list of acronyms in “Appendix”). Because of the limited geographical area of the ground network of stations, high-precision time synchronization is required between BeiDou Satellites (BDS) and ground stations; see, e.g., (Urschl et al. 2007; Sosnica et al. 2015). The mainly time synchronization of BDS is using a microwave system, but LTT was installed as a test experiment of the whole laser link, and for better time measurement precision and accuracy.
Fig. 2

Block diagram of LTT experiment, from ground to space clocks

Table 3

Time transfer by laser ranging; characteristics of onboard instruments

Instrument

Accuracy

Detector (photon, ps)

Timer (ps)

Stability

Link

1-shot (ps)

NP (ps)

MLA

1 ns

 

200

500

 

1-way downlink

LRO

\(<\,1\) ns

 

200

360

165 / 5 s

1-way uplink

T2L2

\(<\,100\) ps

Multiple, 70

3

45–50

3–4 / 30 s

2-way (LRA)

LTT

 

Single, \(<\,150\)

\(<\,100\)

260

20 /500 s

id.

ELT

25 ps

Single, 10

<1

10

3 /300 s

id.

GPS (CV)

1–2 ns

  

5 ns (15’)

1 ns /1 day

1-way

The ground station includes the normal laser ranging instruments, an additional timer and a laser emitting control system. The characteristics of the ground laser station and onboard equipment are given in Tables 2 and 3, respectively. The onboard laser detector adopts a 25 \(\upmu \)m in diameter active area (Si); a single-photon avalanched diode (SPAD) produced by Czech Technical University with a quantum efficiency of about 20%. This type of device has been passed through the radiation resistance test made by CNES (the French space agency) and proved to be sunlight resistant. The detector is doubled for backup. When the very weak laser signal arrives at the detector, it must run at single-photon mode (Meng et al. 2013b). To reduce the noise from Earth, there is alternatively a big field of view for elevation \(>30^{\circ }\) (\(23^{\circ }\) for MEO, \(15^{\circ }\) for IGSO) and a small one for elevation \(> 50^{\circ }\) (\(17^{\circ }\) for MEO, and \(11^{\circ }\) for IGSO). Additional solar optics and narrower band width filters are also adopted in order to reduce noise photons. Another consideration for single-photon detector is a gate signal like the one for laser ranging systems, which is synchronized with onboard 1 PPS. This also leads to a clock prediction requirement and a ground laser emitting time control system. The onboard timer receives the 1 PPS and 10 MHz from the satellite, generates 20 PPS gate signals. Because of the limited capability of the navigation channel, one value is selected over twenty per second. The onboard timer achieves 100-ps single-shot precision.
Fig. 3

Timing stability of LTT time transfer on MEO satellite

Fig. 4

Block diagram of the T2L2 space segment

The LTT payloads were installed on Beidou MEO/IGSO satellites and launched on April 2007, August 2010, April 2011, and April 2012. All four LTT experiments were carried out successfully, and the ground and satellite time difference results have the same trend compared to microwave method, but with different precision and system delay (Meng et al. 2013a), the performance of Beidou satellite clock is approximately \(5 \times 10^{-12} \, \tau ^{-1/2}\) for \(\tau < 10^4\) s, whereas LTT is able to reach a stability of a few \(10^{-14}\). All the measurement of LTT experiments have a single-shot precision of around 300 ps and a time stability of 20 ps over a single session of 500 s duration (Fig. 3, Table 3) (Meng et al. 2013b). The gate-mode LTT payload and field of view contribute to the noise resistance. The detector can only work within the gate; thus, a lot of noise outside the gate time can be removed. The smaller field of view makes less noise from the Earth going into the detector. These two aspects showed much better noise resistance advantage when the satellite goes outside the Earth’s shadow.
Fig. 5

Ground-to-ground time transfer via T2L2/Jason-2 between Herstmonceux (UK) and Grasse (F) SLR stations (with H-masers); September 16, 2013

After modifying the rate of the ground laser ranging system to 1 kHz, a new Chinese Laser Timing (CLT) project is under development which will be based on a similar structure to the LTT system.

5.2 T2L2

T2L2 is based on a ground segment materialized by a ground station network issued from the ILRS network of stations (Pearlman et al. 2009), and a dedicated space instrument which was launched as a passenger experiment on the Jason 2 satellite in June 2008 (Samain 2008); see Fig. 4. The elementary time transfer which benefits from both one-way (ground-to-space) and two-way (range from the Jason-2 LRA) links is provided by a ground laser station firing the space segment over a typical pass of 1000 s; the resulting observable is called a “triplet”: the start and return times at the ground station plus the onboard time. The time transfer between two remote ground clocks is calculated from several independent elementary links, the space segment being a relay; in the common view (CV) mode (the onboard field of view is of \(55^\circ \)) ground stations are firing T2L2 together, whereas in the non common view mode (over intercontinental distances > 4000 km) the ground-to-space passes are separated by the time of flight of the satellite between the SLR stations.

The T2L2 experiment was designed to realize time transfers with a stability better than 1 ps over 1000 s and an accuracy better than 100 ps (Samain et al. 2014); see Table 3. The objectives are essentially of metrological nature, especially with the common view ground-to-ground time transfer, where the deviations of the onboard clock can be reduced almost entirely. This clock is based on the reference oscillator of the DORIS tracking technique which contributes, in addition to the LRA, to the precise orbit determination of the Jason-2 satellite (Table 1). Supplementary objectives of the mission are dedicated to space geodesy and fundamental physics. For example, the stability of the T2L2 ground-to-space time transfer has been used to accurately determine the frequency bias of the DORIS USO during the satellite pass over laser stations equipped with an highly stable atomic clock (e.g., a H-maser) (Belli et al. 2017).

Several field campaigns were carried out between 2012 and 2016 from the primary laser station of T2L2 (Grasse, France) and at the international level. First, the ground-to-ground time transfer between remote H-masers in common view (in Europe) demonstrated a very good stability over days (of tens of ps, see Fig. 5) in addition to an accuracy of 150 ps which was confirmed by GPS(CV) links (Exertier et al. 2016). Additionally, the stability of ground-to-ground links is going to be tested now using GPS(iPPP) solutions against T2L2 over three baselines (between three SLR stations) in Europe; early results show a standard deviation below 100 ps (Leute et al. 2018). Second, concerning space geodesy, the ability of the T2L2 ground-to-space time transfer to directly “read” the frequency bias of the DORIS USO at a few parts in \(10^{-13}\) has permitted to develop a frequency model of physical nature (Belli et al. 2016). As a result, the integration of this model allowed calculation of an onboard time scale between 1200 and 15,000 seconds regularly. This integration was applied to determine the ground-to-ground time transfer from the Grasse laser ranging station (as primary station permanently linked to GPS time with 1–2 ns accuracy) to almost all clocks of the ILRS stations during 8 years (Exertier et al. 2017).

Due to its presence in space since almost 10 years, T2L2 being accessible to many SLR stations has permitted to monitor each clock from a unique time standard. As a result, it has appeared that most of the SLR station reference clocks have a UTC shift higher than 100 ns, and some times hundreds of ns and even of a few \(\upmu \)seconds (Belli et al. 2017).

5.3 ELT/ACES

The European Laser Timing experiment will perform optical time transfer to the Atomic Clock Ensemble in Space (ACES). ACES is an ESA mission in fundamental physics which will bring atomic clocks of unprecedented stability into space (Cacciapuoti and Salomon 2009). Mounted on the International Space Station (ISS) at the nadir pointing platform of the Columbus module, it will establish a time scale built upon an active hydrogen maser for short time stability and a laser-cooled Cs clock, called PHARAO (Laurent et al. 2015), for long time accuracy (Table 1). The onboard timescale will have a stability of \(10^{-16}\).

The hardware in space consists of a retroreflector of CHAMP type, a SPAD detector for the conversion of photons into an electrical signal, and a timer time tagging the events in the ACES timescale. To allow one-way and two-way laser ranging at the same time, an attenuation of the incoming laser pulse at the ISS by a factor of \(\sim \) 100 depending on the angle of incidence has to be guaranteed. This attenuation is achieved by a diffuser plate in combination with a field stop in the shape of a snowflake (Prochazka et al. 2016). The large field of view will allow a tracking from a ground laser station from elevation of \(30^{\circ }\). Near zenith the field stop will limit the tracking to \(85^{\circ }\) elevation. The experiment will use the single-photon mode for the detection. Due to the high stability of the onboard timescale, not only common view time transfer between ground stations is possible, but also non-common view. The targeted accuracy (in CV) is 25 ps and stability of 3 ps at 300 s of integration time (see Table 3).

The time transfer in single-photon mode is the difference to T2L2 and is in common with LTT. It prevents many systematic effects coming, e.g., from varying laser pulse lengths and energies. The complexity of the measurement is transferred to the station operation and keeps the space segment simple. The greatest improvement is the stability of the space clock. With T2L2, the non-common view time transfer is limited by the onboard oscillator (USO), whereas with ELT time transfer will be limited by the method itself but not by the clock.

In addition to the optical time transfer, clock comparison can be performed on a frequency basis by GNSS when the onboard GNSS receiver is connected to the ACES frequency. The main clock comparison method is a microwave link (MWL) which will be operated at time laboratories in Europe, the USA and Japan. This instrument uses modulated frequencies in the Ku- and S-band with a modulation frequency in Ku of 100 MHz. MWL and ELT will share a common timer, tightly connecting these two methods. So in total two time comparison and one frequency comparison methods are available and can be compared at the collocation site Wettzell (GOW, Germany) operating both techniques.
Fig. 6

Difference between true and predicted clock behavior

The advantage of the MWL is due to the high modulation frequency which will allow a time comparison space to ground of 0.3 ps precision in 300 s integration time with an accuracy of 100 ps. In contrast the optical link with a laser repetition rate of 1 kHz and a pulse length of 10 ps will reach a precision of 3 ps in 300 s. Optical links can be calibrated in the near field with high accuracy, so the accuracy of the calibrated time transfer can be as good as 25 ps space to ground. The objectives of ELT are to show the capability of single-photon time transfer in the discussed accuracy and precision, to exploit the capability to calibrate the MWL, and to study the tropospheric delays in the microwave regime.

Many aspects make the ELT experiment very challenging. Some of them are related to the single-photon method in combination with the low orbit of the ISS, others come along with the fact that the ISS is a manned space station. SLR stations participating in ELT have to meet safety requirements, like hardware control of laser power and handling a go/nogo flag controlled by the mission operators (Schreiber et al. 2014; Schlicht et al. 2012). Concerning the orbit, predictions every 90 min have to be handled. The laser power has to be controlled to measure in the single-photon mode. The detector onboard will open the gate every 1–10 ms (station dependent) in ACES time. The offset of ACES time to UTC will be known to better than 50 ns and will be communicated by the ELT data center (Marz et al. 2016) via the prediction file. The biggest challenge for the station will be the fact that at daytime the detector has to be hit by the laser pulse within 100 ns after gate opening, making a strict time keeping to UTC and controlling laser fire time within some nanoseconds necessary. A real-time determination of time bias and correction of the predictions to this value will help to get along with this challenge.

The accuracy of the trajectory of the clock is the biggest uncertainty contribution in the transformation of proper time to coordinate time. The clock prediction is therefore limited by the accuracy of the orbit and altitude prediction of the ISS. In order to analyze the prediction procedure, a comparison between the time transformation of a hypothetical clock based on predicted orbits and the one based on real orbits was performed. For this analysis, orbits together with their predictions were calculated by DLR on the basis of a Space Integrated GPS/Intertial Navigation System (SIGI) data receiver mounted on the ISS. Each file contains 12 h of the calculated orbit and 12 h of prediction. Every 3 h a new file was generated. Based on these orbits, the difference between the predicted clock and the true clock is shown in Fig. 6. The maximum difference observed for 18 orbits was 14 picoseconds for a 12-hour prediction.

To permit synchronization of the laser ranging stations to the ACES clock at 100 ns, only the linear drifting part of the ACES time scale is communicated. So, additional to the error due to predicted orbit, the variability of the clock along the orbit is neglected. The calculated clock correction without drift is of 2 ns peak-to-peak over 24 h; the linear drift is accurate within 1.5 ns.

6 Time transfer experiments with laser altimeters in space

NASA GSFC has built several space-borne laser altimeters over the past 25 years which provided a unique opportunity to demonstrate laser time transfer from ground stations to the spacecrafts at interplanetary distance. In-orbit calibrations were conducted in which the spacecraft points the laser altimeter at Earth and scans the instrument bore sight about the ground station in a raster pattern. Laser pulses were transmitted simultaneously between the laser altimeter in space and ground station. The times of the transmitted and the received laser pulses were recorded at both terminals. The laser pulse arrival times and spacecraft pointing data were used to estimate the laser pointing angle with respect to the spacecraft coordinate system, the receiver bore sight, and co-alignment with the camera. The relative clock offset and drift rate with respect to ground time were estimated as well.

6.1 Time transfer to MESSENGER via two-way laser ranging

In May 2005, a two-way laser ranging test was conducted between the 1.2-m telescope facility at the Goddard Geophysical and Astronomical Observatory (GGAO) and the Mercury Laser Altimeter (MLA) following its second Earth flyby, at a distance of nearly 24 million km (Smith et al. 2006; Zuber 2006; Neumann et al. 2014). The primary objective of the test was to calibrate the MLA ranging function and instrument bore sight. It also demonstrated a precision laser time transfer over the longest distance in space to date. The test setup was that of an asynchronous laser transponder (Degnan 2002). The one-way light time from the ground to the laser pulse arrivals at MLA was captured as well as the downlink light times of MLA laser pulses to the ground station, over a span of half an hour. The unknown variables included the motion of the spacecraft during the time of the laser pulse arrivals from Earth, and the USO-driven MET clock used to time the laser pulses received and emitted by MLA. The spacecraft trajectory was also estimated independently to a high precision from radio-frequency tracking, and the clock parameters were adjusted daily by the MESSENGER project, allowing an overall comparison.

The MLA timing electronics not only measured the time interval of its laser time of flight to the Mercury surface, and it could also be configured as an event timer to record the times of the laser emission and detection on a common time base at about 0.2 ns resolution for the nearly 3-min round-trip light time. The laser time transfer precision was only limited by the MLA timing electronics and the receiver signal-to-noise ratios (SNR), to 10–20 cm rms. Finally, MLA shared the clock signal from the MESSENGER spacecraft and was synchronous with MET to within a fraction of 1 ns.

Laser ranging tests between MLA and GGAO were successfully conducted on May 25 and 31, 2005. Uplink and downlink are detailed in Tables 2 and 3. The ground station detected 14 and 24 laser pulses from MLA over periods spanning 2 and 3 s on the first and second occasions, respectively, chiefly limited by the brief time period when MLA and the ground station formed direct line of sight during the raster scan. MLA detected more than 100 laser pulses from GGAO over a 30 minutes period on both occasions. The precision achieved from a total of 90 uplink and 15 downlink pulses was 0.2 m in range and 0.66 ns in time, in spite of a very weak uplink detection (Smith et al. 2006).

The MESSENGER spacecraft USO stability during the test period was comparable to the resolution of the MLA timing electronics, with an unknown system offset of a few microseconds between MLA and the radio subsystem time. Since the tests were conducted during solar system cruise and the Earth’s motion is known, the instantaneous one-way light time from GGAO to MESSENGER and the frequency offset of the onboard clock oscillator could be solved via simple regression to the observations. The range measured by the laser pulses was 23,964,675,408.4 ± 0.2 m, after accounting for a 486.6 m additional range due to the relativistic effect. The difference between the laser measurement and the predicted spacecraft ephemeris was 27.1 m, which is well within the error bounds of the orbit determination from radio data plus an uncertainty in the ground station time delay in various subsystems. Finally, the time differences between the laser measurement and the spacecraft MET estimated from the radio-frequency tracking data were 0.35 and 0.14 ms on the two successful days, which was well within the accuracy and resolution of the MET model for navigation and science operation.

6.2 One-way uplink time transfer experiment to MOLA in Mars orbit

A one-way laser transmission experiment was successfully conducted from GGAO to MOLA on the MGS spacecraft in Mars orbit over 81 million km on September 28, 2005 (Abshire et al. 2007). It was near the end of the MGS mission and the MOLA clock oscillator had ceased to operate (see Tables 2 and 3). The timing resolution of MOLA was degraded to the 0.125 s intervals during which the spacecraft acquired data from MOLA. The major uncertainty of the epoch time on MOLA was the delay from the MGS MET to MOLA through the software. The MET on MGS spacecraft was assumed accurate for this test.

The MOLA laser on the MGS spacecraft scanned the GGAO telescope/detector two times during a 40-min period. The laser pulses rate was set to 49 Hz to avoid being a multiple and consequently synchronous with the MOLA 8 Hz measurement window. For the second raster scan, the laser pulses were shuttered on and off at 1.22 s interval (6 pulses of the 49 Hz laser). There were several hundreds of laser pulses detected at MGS/MOLA during both the scans. By correlating the transmitted and the received laser pulse train patterns from the second raster scan, the time delay from the spacecraft clock time to the MOLA clock time was solved to be 137 ms at the maximum correlation. This was consistent with the time delay solved from radio frequency tracking of the spacecraft and the MOLA ground track matching, 114 ms (Rowlands et al. 1999), considering the tolerance of the epoch time in orbit determination. Despite the coarse timing resolution, this GGAO to MGS/MOLA test remained to be the longest distance and truly interplanetary laser link experiment to date.

6.3 One-way downlink time transfer from GLAS/ICESat to GSFC

A one-way laser downlink time transfer experiment was successfully conducted on November 3, 2006, from the Geoscience Laser Altimeter System (GLAS) on the ICESat spacecraft to NASA GSFC during a routine ICESat-GSFC overpass operations (Schutz et al. 2005). The primary purpose of the overpass was to compare the atmospheric backscatter profile measurement from GLAS in nadir direction and those from ground based lidar at GSFC in zenith direction. It also provided a unique opportunity to demonstrate laser time transfer from an orbiting laser altimeter. A GLAS flight spare detector was placed along the ground track of ICESat overpass. An oscilloscope and an event timer were used to record the waveforms and the time of the received laser pulses with respect to UTC (Abshire et al. 2005).

A total of 28 laser pulses from GLAS were recorded over a 1.1 second time period, including pulses before and after the direct line of sight during the overpass. The GLAS laser pulses forward scattered by atmosphere were strong enough to be detected by the ground detector located a few km from the actual laser footprint. Since GLAS measured the laser time of flight (i.e., light time) during the overpass, one could solve for the time offset of GLAS by pairing up the transmitted and the received laser pulses and calculate the differences. The measured and predicted times differed by 3.43 \(\upmu \)s. The time offset obtained from the special GLAS timing calibration operation at the White Sand was \(3\pm 1\) \(\upmu \)s (Magruder et al. 2005). The measurement precision and accuracy were limited by the GPS receiver time accuracy, uncertainty in the system delay, and pulse waveform saturation, which could all be improved.

6.4 Laser time transfer with the one-way laser ranging receiver on LRO

The LRO mission carries a one-way laser ranging system to complement the radio-frequency tracking for precision orbit determination (Zuber et al. 2010). It has a small telescope co-bore-sighted with the high-gain antenna (HGA), which can receive laser pulses from Earth while LRO is in view from the ground station. The laser ranging receiver field of view is wide enough to cover the entire Earth so that laser ranging stations at different parts of the world can range to LRO simultaneously as long as the moon is in view. The signals detected by LRO are transmitted to one of the receiver channel of the Lunar Orbiter Laser Altimeter (LOLA) over an optical fiber bundle. The laser pulse emission and detection times are recorded by both LOLA with respect to the spacecraft MET and the ground station with respect to UTC. The time bases at LRO are sufficiently stable that the relative time drift were only a few ns over a laser ranging pass of around 1-h duration. The ground station clock at the primary ground station at NASA GSFC was based on a Cesium frequency standard from 2009 to 2011 and later switched to a H-maser clock source. As mentioned earlier, the frequency and the epoch time of the clock was monitored against the USNO master clock to within 1-ns rms using an All-In-View GPS receiver. The difference between the laser pulse event times at LRO and the ground station gave an so one-way time-of-flight measurement, which includes the spacecraft orbit movement plus a nearly constant offset. The offset was a slow varying variable comparing to the periodic orbit error; from an improvement in the dynamical model, it has been possible to solve for this offset.

The LRO laser ranging system operated continuously from LRO launch in June 2009 to the end of the first extended science mission in September 2014. Several groups independently worked on this mission, providing new insights in term or orbit determination notably (Bauer et al. 2016). The laser ranging measurements also provided a direct monitor of the spacecraft time to tens of nanoseconds, and the LRO clock time predicted to within a few \(\upmu \)s for months (Mao et al. 2017).

Since LRO system could detect and record laser pulses from multiple ground stations simultaneously (Mao et al. 2011), the results of these simultaneous laser ranging measurements could be used to compare the ground station clocks, or transfer times using the light times from radio-frequency tracking. The accuracy of the time transfer depended only on the difference of the light times from the ground stations to a large tolerate in light time measurement accuracy. For an LRO orbit position uncertainty of 100 m (10 m typical) in radial direction, the time transfer accuracy limited by the light time accuracy was \(<\,0.1\) ns. A detailed analysis of the clock monitoring is given in (Sun et al. 2013).

The concept of LRO time transfer was first verified on ground between NGSLR and the nearby MOBile LAser System (MOBLAS-7) at NASA GSFC by ranging to a corner cube target at 50 m. The laser pulse arrival times at the target from both laser stations were recorded during 1 hour; the time offsets solved from these one-way laser ranging tests differed by 0.3 ns. Laser time transfer between NGSLR and MOBLAS-7 to LRO was then conducted a number of times over a 20-month period from 2013 to 2014. The results show a time transfer accuracy of about 1 ns over many months (Mao et al. 2014). Laser time transfer tests were also conducted between NGSLR at Greenbelt, Maryland and the McDonald Laser Ranging System (MLRS) at Fort Davis, Texas over a 6-month period. However, MLRS did not have access to a nearby master clock site that published All-In-View GPD data. Instead, the All-In-View GPD data from USNO at Washington DC were used. As a result, the timing accuracy at MLRS was not as accurate as NGSLR and MOBLAS-7. There were some systematic trends in the time between stations, up to 45 ns peak to peak and 10–20 ns on average.

7 Next generation and future requirements

7.1 Laser ranging and planetary navigation

Several space missions have been and will be proposed with a laser link. Some of them use a coherent laser link, which is well suited for frequency transfer or measurements of position variation (Djerroud et al. 2010). Others use a propagation of laser pulses, which are most suited to meet the needs of absolute localization or time transfer (Schreiber and Kodet 2017; Exertier et al. 2016).

For space missions which are at the scale of the Solar System, the distances are thus in the range of several billion kilometers. Such distances cannot be measured through a classical passive two-way laser ranging scheme (Degnan 2002). The Earth–Moon distance is now considered as a maximum with a link budget in the ratio of 1/\(10^{20}\); that means \(10^{20}\) emitted photons (i.e., a laser pulse of 0.5 J and 0.3 ns duration) for one returned photon statistically, due to the beam attenuation along the distance in \(d^4\) (Degnan 1993). To go further, it is necessary to use a one-way technique (uplink or up- and downlink); see (Abshire et al. 2007) for an uplink to Mars. With a payload instrument based on optics having an aperture of 100 mm, a beacon divergence of 5 arc seconds, 300 mJ per pulse and a distance of 400 million km, we might have a link budget (downlink) of around 1 photoelectron. The MESSENGER and MGS experiments opened the door to future laser to be used for deep space exploration, may be at around 1 AU (Neumann et al. 2014).

For planetary missions unable to provide such an onboard equipment (laser), however, progress into the onboard oscillator in terms of long-term stability and reduced sensitivities to temperature and radiation might be very fruitful. The future NASA/JPL’s Deep Space Atomic Clock (DSAC) represents an enormous advance toward improving deep space navigation through more accurate time transfer data. The mission is developing a small mercury ion atomic clock with Allan deviation of less than \(10^{-14}\) at 1 day (current estimates \(\sim \,3 \times 10^{-15}\)) for a yearlong space demonstration in 2018 (JPL-DSAC 2017). But on the long term, the continuous improvement in radiometric tracking data (e.g., Ka/X band system) is strictly necessary (Dehant et al. 2017).

7.2 Laser ranging, time transfer, and metrology

What is the perspective of time transfer? The recent experiments of time transfer by laser ranging around the Earth, such as LTT (Beidou), T2L2 (Jason-2), and ELT (ISS) between 36,000 and 500 km, proved the possibility to establish time links into space or ground links via a space equipment with an unprecedented stability (1 to a few ps over thousands of seconds) and accuracy (100 ps, currently and 25 ps expected at GOW, Germany with ELT/ACES), even on a operational basis. To achieve this performance, the primary stations behind these experiments have played on important role in maintaining a high stability of the 1 PPS distribution signals on the long term and in accurately calibrating most of the equipment, as geodetic and time and frequency.
Fig. 7

Constellation for a common ranging and time transfer in optical two-way (laser ranging) and GNSS tracking, to separate the contribution of troposphere, clock and station height in a common parameter estimation

Currently, there is a significant effort in process toward linking major National Metrology Institutions together by optical clocks over compensated fiber networks (Lisdat et al. 2016). This allows accurate frequency comparisons over long distances, already achieving around \(10^{-18}\) over 1000 km in Europe (Germany, France and United Kingdom), which level corresponds to around 1 cm high on the geoid (Lion et al. 2017). Adding space optical time transfer, especially on intercontinental distances, would be an important step toward using time as an observable in space geodesy and cutting edge metrology. This gives way of what we call “chronometric” geodesy, that is a new (relativistic) era of geodesy.

7.3 Laser ranging and GNSS

Communication links between GNSS satellites are available on GPS since a long time (Rajan et al. 2003), but only recently such links are also used for ranging and time transfer on GLONASS satellites (Shargorodsky et al. 2013). Some studies about using inter-satellite links on Galileo in the future were also published (Wolf 2000; Sanchez et al. 2008; Fernandez et al. 2010; Fernandez 2011). These links will make use of the whole synergy provided by the exchange of electromagnetic signals between two satellites, namely data transfer, the capability to synchronize clocks, and the measurement of distances. This will increase the autonomy of the space segment, reduce the time to alert, and lead to better orbits and synchronization of the space clocks.

Doing a combined optical time transfer and ranging together with GNSS is the best technology for decoupling both orbit and clock parameters (see Fig. 7). The troposphere is decorrelated as the optical wavelength do not suffer much from a highly variable wet delay. The clock is decoupled due to time transfer with a system that can be calibrated to a high extent. The capability of calibrating optical links with high accuracy is the reason why the collocation of GNSS receivers with SLR will allow the calibration of the collocated receiver as well as evaluating its systematic errors, like multipath. At the same time, it requires not only local survey to determine the local ties, but also the calibration of timing links. Although optical links can be calibrated to a high extent-ELT aims at 25 ps—it is not enough for a GNSS phase measurement, where about 3 ps are necessary. Therefore, the parameters have to be extracted by a common estimation for periods during which the phase coherence between clock and SLR timer can be kept. Kinematic positioning would benefit the most by clock synchronization. As SLR cannot be easily transported a reference station would be required with the capability of locally distributing the clock information.

There are two major applications of GNSS tracking in geodesy: The determination of station positions using precise point positioning (PPP) and the realization of reference frames. In both cases not all three components of the position can be determined with the same accuracy. Whereas horizontal position in a weekly IGS solution has an accuracy of about 4 mm, the height is with 8 mm less accurately determined (Kouba 2015). This fact is caused by the high correlation between three parameters, namely station height, station clock, and atmospheric delays. In addition, systematic errors, like multipath and phase center offset and its variations contribute to the error budget of the station height component. For PPP, it is already known that additional information helps to decorrelate these parameters. It was, e.g., shown by (Weinbach and Schön 2011) and (Wang and Rothacher 2013) that modeling of ground clocks can improve the kinematic precise point positioning height solution by a factor of 2–3. Surely the PPP solution will also benefit from better reference frames. The important parameters in this task are the modeling of satellite clocks and orbits in the present of the already mentioned systematic errors. With inter-satellite links, we will have very precise relative orbits with degrees of freedom in rotation and translation. These degrees of freedom can be fixed by a combination of SLR and GNSS (Sosnica et al. 2015; Thaller et al. 2011; Urschl et al. 2007). The difficulties the combination has to face lies in the systematic errors of both systems.

Sosnica et al. (2015) have pointed out that SLR observations to GNSS satellites provide an non-equivalent data source to improve the orbit modeling at that altitude and/or to allow assessment of the orbit quality. Nevertheless, the current knowledge of the exact distance between both the LRA and microwave antenna onboard GNSS satellites is not precisely determined and thus does not allow the computation of a consistent international terrestrial reference frame (ITRF) at 1-mm accuracy. (See the GGOS requirements.)

For tying the orbit system to Earth not many stations are needed, but the ones used should be equipped with highly stable clocks. A subset of SLR stations with collocated GNSS receivers and a precise timing system synchronized to the GNSS space segment would fulfill this task perfectly as their systematic behavior can be studied, as elucidated already in the discussion of PPP. In such a system biases can be estimated and monitored and systematic effects detected. Common view analyses will help separating modeling errors from other systematics. In order to overcome the weather dependence of the optical link the ground station clocks should be synchronized by fiber links. In this case the synchronization of the ground time scale and the GNSS time scale can be performed by any station without clouds, at least for periods during which phase coherence can be kept. Non-collocated ITRF sites will benefit from fixed orbits and monitored biases. They may be calibrated and their multipath analyzed by transportable SLR stations.

8 Conclusion

The present space experiments which use both time transfer and laser ranging demonstrated the need for:
1.

Better ground time equipment in current laser ranging stations generally, in order to make available a worldwide network of stations being able to transmit time accurately (at the 1-ns level).

2.

New space detector and timing systems onboard future GNSS satellites to help solving for unknown clock parameters from time transfer and laser ranging.

3.

Better long-term stability of clock on space missions, especially for planetary investigations to improve the determination of distance from clock comparisons.

Notes

Acknowledgements

The authors want to thank SLR stations of the ILRS network for providing ranging data to numerous space missions including GNSS satellites. They want to thank the Labex FIRST-TF for its support in 2017, and DLR for the orbit prediction and analysis data of the ISS to perform the relativistic correction tests. Finally, the authors want to thank the reviewers for helpful and very constructive remarks

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • P. Exertier
    • 1
    Email author
  • A. Belli
    • 1
    • 4
  • E. Samain
    • 1
  • W. Meng
    • 2
  • H. Zhang
    • 2
  • K. Tang
    • 2
  • A. Schlicht
    • 3
  • U. Schreiber
    • 3
  • U. Hugentobler
    • 3
  • I. Prochàzka
    • 3
  • X. Sun
    • 4
  • J. F. McGarry
    • 4
  • D. Mao
    • 4
  • A. Neumann
    • 4
  1. 1.CNRS-OCA-UNSGeoazurValbonneFrance
  2. 2.Shanghai Astronomical Observatory, CASShanghaiChina
  3. 3.TUMMunichGermany
  4. 4.NASA Goddard Space Flight CenterGreenbeltUSA

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