# Geodetic VLBI with an artificial radio source on the Moon: a simulation study

## Abstract

We perform extensive simulations in order to assess the accuracy with which the position of a radio transmitter on the surface of the Moon can be determined by geodetic VLBI. We study how the quality and quantity of geodetic VLBI observations influence these position estimates and investigate how observations of such near-field objects affect classical geodetic parameters like VLBI station coordinates and Earth rotation parameters. Our studies are based on today’s global geodetic VLBI schedules as well as on those designed for the next-generation geodetic VLBI system. We use Monte Carlo simulations including realistic stochastic models of troposphere, station clocks, and observational noise. Our results indicate that it is possible to position a radio transmitter on the Moon using today’s geodetic VLBI with a two-dimensional horizontal accuracy of better than one meter. Moreover, we show that the next-generation geodetic VLBI has the potential to improve the two-dimensional accuracy to better than 5 cm. Thus, our results lay the base for novel observing concepts to improve both lunar research and geodetic VLBI.

## Keywords

Geodetic VLBI VGOS Moon Monte Carlo simulations c5++## 1 Introduction

Very Long Baseline Interferometry (VLBI) has a long tradition of serving the astronomical, astrometric and geodetic communities. For the latter two, not only station coordinates and Earth orientation are of interest, but also the realization of the celestial reference frame (CRF), defined by positions of radio sources. VLBI has also been used to observe spacecrafts (e.g., Lebreton et al. 2005; Duev et al. 2012). Moreover, there are efforts to use the technique for the determination of planetary orbits (Jones et al. 2015) and relating those to the International Celestial Reference Frame (ICRF; Fey et al. 2015). Usually, differential VLBI (\(\Delta \)VLBI) is used in order to cancel common error sources and achieve highly precise angular coordinates. Several experiments have been carried out with the purpose to determine the relative and absolute position of radio transmitters on the lunar surface as well as lunar satellites. The goal of these experiments was to obtain a better understanding of the physical properties of the Moon. Examples of recent lunar programs include LADEE (Lunar Atmosphere and Dust Environment Explorer; Elphic et al. 2014), CLEP (Chinese Lunar Exploration Program; Li et al. 2015) and GRAIL (Gravity Recovery and Interior Laboratory; Konopliv et al. 2013). The VLBI technique was also used for the spacecraft orbit determination during the SELENE (SELenological and ENgineering Explorer) mission (Kato et al. 2008) by using phase delays from same-beam differential VLBI (Kikuchi et al. 2009). The Chang’E-3 (CE-3) mission used the same-beam phase-referencing to obtain horizontal position estimates of the lunar rover w.r.t. the lander with a meter-level accuracy (Zhou et al. 2015). Another technique used in the course of this mission was the X-band two-way Doppler tracking, characterized by the measurement precision of about 0.2 mm/s (Wenlin et al. 2017). In terms of a surface position uncertainty, this can be translated to an accuracy on the level of about 10 m (Williams et al. 2006).

The first \(\Delta \)VLBI observations of artificial radio sources on the Moon were carried out in 1970s using Apollo Lunar Surface Experiment Packages (ALSEP), deployed on the Moon during the Apollo program. Combination of S-band \(\Delta \)VLBI with range observations to laser retroreflectors allowed to determine the relative coordinates of the ALSEP transmitters, in the two transverse components, with an uncertainty of about 5 mas, which corresponds to about 10 m on the lunar surface (King et al. 1976). In the case of data obtained only through Lunar Laser Ranging (LLR), the retroreflectors’ coordinates are known to a meter level, as stated by Williams et al. (2006).

## 2 Geodetic VLBI

Compared to Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR) or Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), geodetic VLBI is the only space-geodetic technique which allows to simultaneously determine all Earth Orientation Parameters (EOP; Sovers et al. 1998) and uniquely provides the Earth rotational phase (UT1-UTC). Geodetic VLBI is also important for the realization and the maintenance of the International Terrestrial Reference Frame (ITRF; Altamimi et al. 2016; Bachmann et al. 2016).

VLBI relies on pairs of telescopes which are separated by hundreds or thousands of kilometers and observe the same radio source simultaneously. The difference in signal arrival time (delay) and its time derivative (delay rate) are the main observables of geodetic VLBI and determined in a correlation process. By observing several different radio sources, one can estimate geodetic target parameters, i.e., station coordinates, EOP and source positions as well as auxiliary parameters (clock behavior, wet part of the troposphere; Haas and Schuh 1996; Behrend et al. 2000; Nothnagel et al. 2016). In today’s geodetic VLBI, observations are carried out at two different frequency bands (X and S). This allows to compensate for ionospheric effects by forming a ionosphere-free linear combination. As the precision of the group delay measurements in geodetic VLBI is currently limited to several tens of picoseconds, there are efforts to improve it by developing the next-generation VLBI system called VLBI Global Observing System (VGOS; Petrachenko et al. 2009; Niell et al. 2006, 2014; Cappallo 2014).

### 2.1 VLBI networks used in the study

### 2.2 Inclusion of lunar observations into geodetic VLBI schedules

For this study, lunar observations were added into geodetic VLBI schedules by modifying so-called VLBI experiment (VEX) files (Whitney et al. 2002). Those files are available for IVS-R1 sessions and can be downloaded via one of the IVS servers.^{1} In the case of VGOS, we used a single VEX file converted from a SKD file^{2} (Gipson 2010), which was created during the early design phase of VGOS. It originally consisted of 173,831 observations, which is about 40 times more than the average number of observations in a regular IVS-R1 session in 2014.

*n*-th quasar scan with one to a radio transmitter on the Moon, regardless whether there was more than one scan at the same time. However, since such a target might not be visible from all stations that were scheduled in that particular scan, those stations at which the lunar target was not visible, i.e., below the local horizon, continued with their originally planned source. This concept was pursued for each IVS-R1 session as well as the chosen VGOS-type session. The study was carried out using different replacement strategies, by substituting every 2nd, 3rd, 4th, 6th and 8th scan in the original schedule (Table 1). Such modified schedules formed then the base for the actual Monte Carlo simulations, which allowed us to assess the impact of observing a transmitter on the Moon together with quasars. It has to be noted that there was a slight decrease in the total number of observations in schedules containing lunar observations, compared to the average number of 4,600 observations in the original IVS-R1 schedules. This decrease can be attributed to the replacement strategy used here where some baselines are no longer part of a scan since only a few sites can see the Moon, whereas other follow the originally scheduled quasar. In the case of IVS-R1 schedules from the whole year 2014, the median number of baselines per scan was equal to three, both for lunar and quasar observations. For the VGOS schedule used in this study, the same statistics, for lunar observations as well as for all substitution strategies, amounted to ten. The incorporation of lunar observations for the VGOS schedule decreased the median number of quasar observations per scan from twenty-one to fifteen, only in the case of the substitution strategies S-2 and S-3.

The number and percentage (in brackets) of lunar observations per single IVS-R1 (average) and VGOS-type session for each group of the modified schedules

Group | Replacement | Frac. of lunar obs. | |
---|---|---|---|

name | strategy | IVS-R1 | VGOS |

S-2 | Every 2nd scan | 684 (14%) | 15,975 (10%) |

S-3 | Every 3rd scan | 456 (9%) | 10,851 (6%) |

S-4 | Every 4th scan | 339 (7%) | 7889 (4%) |

S-6 | Every 6th scan | 227 (4%) | 5377 (3%) |

S-8 | Every 8th scan | 168 (3%) | 4073 (2%) |

The fact that even a faint radio transmitter on the Moon will have a higher flux density than any of the natural radio sources considered in geodetic VLBI implies that the Signal-To-Noise-Ratio (SNR) targets ,which are implicitly set in each observing schedule, will not be violated when replacing a quasar with a lunar observation. This means that even if the slewing times would take longer to point the antenna toward the radio transmitter on the Moon, the scan itself would be shorter as the SNR targets are reached after a shorter integration time. Thus, it can be stated that this relatively simple replacement approach will lead to a feasible observation plan that allows to include a lunar target in a regular geodetic VLBI schedule. Moreover, in order to simulate a realistic location for a lunar-based radio transmitter, the source was assumed to be at 44.12\(^{\circ }\)N, 19.51\(^{\circ }\)W in the Moon’s body-fixed reference frame. This position is close to the coordinates of a lunar lander and a rover which both were delivered to the surface of the Moon in late 2013 during the Chang’E-3 project (Li et al. 2015).

### 2.3 VLBI delay models

Theoretical delays are obtained in the barycentric dynamical time (TDB) due to the fact that the motion of a spacecraft and VLBI telescopes are defined in the Barycentric Celestial Reference System (BCRS). Since the observed VLBI delays are referred the Terrestrial Time (TT), one needs to apply the Lorentz transformation in order to express the computed delay in the proper time scale (Sekido and Fukushima 2006). The total theoretical VLBI delay is then obtained by considering contributions from the atmosphere and technique-specific effects such as the antenna thermal deformation, antenna axis offset and displacement of the telescope reference point (Petit and Luzum 2010).

If one considers near-field VLBI delays for an artificial radio source located on the surface of the Moon, it is necessary to compute its position in the BCRS. This can be achieved by using planetary and lunar ephemerides such as the JPL ephemeris (Folkner et al. 2009). The latter contains also information on lunar librations, which are necessary to obtain the orientation of the principal axis (PA) system relative to the ICRS Earth equator and equinox (Archinal et al. 2011).

### 2.4 Simulation of quasar and lunar observations

The simulated atmosphere and the clock behavior correspond to realistic physical scenarios. The overall precision of the simulated delays is controlled by the standard deviation \(\sigma \) of the Gaussian random number generator, which produces values of \(\tau _\mathrm{rnd}\). The \(\sigma \) values are set station-dependent (e.g., \(\sigma _1\) and \(\sigma _2\)) and error propagation according to \(\sigma =\sqrt{\sigma _1^2 + \sigma _2^2}\) is then used to obtain \(\tau _\mathrm{rnd}\). In the case of equally performing stations, the applied noise level per baseline is therefore \(\sqrt{2} \sigma _j\). Quasar observations were generated from a Gaussian random generator with standard deviation of 14.14 mm (47 ps), which corresponds to a station-specific thermal noise of 10 mm and reflects the average post-fit RMS of today’s geodetic VLBI. For the simulations concerning the VGOS era (cf. Sect. 3.1), the baseline noise was set to 1.41 mm (4.7 ps).

Parametrization of auxiliary parameters, i.e., clock and troposphere models

Parameter | Parametrization | |
---|---|---|

IVS-R1 | VGOS | |

ZWD | 2 h PWL | 0.25 h PWL |

Trop. gradients | 6 h PWL | 2 h PWL |

Station clocks | 1 h PWL | |

Clock reference | WETTZELL |

### 2.5 Processing setup

Concerning the analysis, three different options were studied. Common to all options is the parametrization of the nuisance parameters (Table 2). The first option, where station positions and EOP were assumed to be known and the two-dimensional (2D) lunar coordinates of the lander were estimated, was abbreviated *L*. When considering VGOS, this analysis option was named *VGOS-L* in order to indicate that only lunar lander coordinates were estimated, but using VGOS-type schedules and observations. The second analysis option, called *LE*, considered that the EOP were estimated as well. The third option (referred as *LET*) was with the purpose to study a case where also all station positions are estimated together with the aforementioned parameters.

The coordinates of the lander were solved for as horizontal 2D components of lunar latitude and longitude (\(\phi _\mathrm{lan},\lambda _\mathrm{lan}\)). This parameterization was chosen since the VLBI observing geometry does not allow for a consistent and reliable decoupling of all three coordinates of the lander. Therefore, the height component was fixed to an arbitrary constant value of 0.00 m. However, results from additional simulations related to the three-dimensional case (3D), i.e., estimating all three coordinates of the lander, are presented in Sect. 3.2.

Earth rotation parameters, i.e., pole coordinates (\(x_p\), \(y_p\)) and UT1-UTC, were estimated session-wise. This applied also to station positions, in the case of the *LET* analysis option. Clock and troposphere parameters are estimated as described in Table 2. For all observations, an elevation cutoff angle of \(3^\circ \) was applied. Since all station coordinates were solved for in the analysis option *LET*, the singularity of the normal-equation matrix had to be dealt with by introducing No-Net-Translation (NNT) and No-Net-Rotation (NNR) conditions w.r.t. the a priori ITRF coordinates (Petit and Luzum 2010).

## 3 Results

Repeatabilitites in the form of Weighted Root-Mean-Square (WRMS) errors were computed from the Monte Carlo results for each of the determined parameters. Since the WRMS refers to the a priori information, we can directly access the accuracy of each obtained parameter.

### 3.1 Position of the lander

We studied how the horizontal accuracy (\(\text {WRMS}_{\text {2D}}\)) of the lander’s position depends on the precision of lunar observations. Figure 3 depicts this behavior for IVS-R1 sessions and substitution strategies S-2, S-3, S-4, S-6 and S-8.

As one would expect, more frequent and precise lunar observations lead to a higher accuracy of the lander’s position. For observational precision worse than 20 mm, a direct relation between the noise of lunar observations and the \(\text {WRMS}_{\text {2D}}\) exists. On the contrary, observations with precision better than 20 mm do not improve the positioning results significantly and the \(\text {WRMS}_{\text {2D}}\) values settle between 270 and 340 mm. This is thought to be attributed to the fact that the tropospheric turbulence is dominating the noise budget and thus is the limiting factor, as discussed later in Sect. 3.5. The scatter plot as well as the corresponding histograms do not indicate any significant systematic effects.

In order to study how the estimation of additional parameters affects the lander’s position, the \(\text {WRMS}_{\text {2D}}\) statistics were also computed for the *LE* and *LET* analysis options. We averaged \(\text {WRMS}_{\text {2D}}\) results from all five groups of modified schedules, i.e., from S-2 to S-8, which allowed us to compare the impact of different analysis options on the lander’s position. Thus, relative changes of the 2D positioning performance can be examined by computing the ratio \(\beta \) between the \(\text {WRMS}_{\text {2D}}\) of extended solutions (*LE* resp. *LET*) and the *L* solution. Values of \(\beta \) larger than one imply degradation, while values smaller than one indicate an improvement w.r.t. the *L* solution. Values of \(\beta \) are shown in Fig. 4 for the *LE* and *LET* analysis options in dependence of the lunar observation precision.

In general, the obtained \(\beta \) factors indicate that the estimation of additional parameters decreases the accuracy of the estimated position of the lander. Depending on the precision of the lunar observations, this degradation is between 8 and 2% w.r.t. the *L* solution and indicates that highly precise lunar observations would be affected more than imprecise observations of the same type. Increasing the parameter space leads also to a larger uncertainty of the estimates. However, in the case of imprecise lunar observations this effect is negligible.

After studying the current VLBI performance in terms of lunar observations, the logical question is how the next-generation VLBI system will perform. VGOS will provide a measurement precision that is at least one order of magnitude better than the current geodetic VLBI technology. Thus, we followed a similar strategy as for the IVS-R1 sessions, but assumed an observation precision of 1.41 mm (4.7 ps) for quasar targets. The \(\text {WRMS}_{\text {2D}}\) values corresponding to VGOS-type schedules are presented in Fig. 5, including also a scatter plot of the lunar position estimates for the substitution strategy S-3 simulated with an assumed lunar observation precision of 15.97 mm. The pattern of the scatter is similar to the one shown in Fig. 3b and also indicates a larger spread in the latitudinal direction. The results show that VGOS-type observations improve the accuracy of the lunar coordinate estimates by a factor of eight compared to the IVS-R1 schedules (cf. Fig. 3). Although the impact of the troposphere is significantly reduced with VGOS, there is still a small contribution from this error source, thus preventing an improvement of the lunar lander’s positions when decreasing the observational noise. This means that, for lunar observations with a precision of up to 10.0 mm, the \(\text {WRMS}_{2D}\) does not change significantly, varying between 20 and 50 mm in dependence of the number of lunar observations. For less precise lunar observations, the accuracy of the lander’s position is still below a meter, which indicates the potential of lunar observations in the VGOS era.

### 3.2 Estimating the 3D position of the lander

*L*and

*VGOS-L*analysis options were applied with this new parameterization. The \(\text {WRMS}\) values of the estimated position components are shown in Table 3 for the lunar observation noise of 15.97 mm and based on the group S-3 of schedules.

\(\text {WRMS}\) values of the estimated 3D position components using *L* and *VGOS-L* analysis options based on the group S-3 and a lunar observation noise set to 15.97 mm

| | |
---|---|---|

\(\text {WRMS}_\mathrm{LAT}\) | 14.84 | 1.76 |

\(\text {WRMS}_\mathrm{LON}\) | 7.67 | 0.69 |

\(\text {WRMS}_\mathrm{h}\) | 15.98 | 2.08 |

\(\text {WRMS}_\mathrm{3D}\) | 23.18 | 2.81 |

Correlations between position components of the lander using the *L* option for a single IVS-R1 session (06/01/2014–07/01/2014)

\(\phi _\mathrm{lan}\) | \(\lambda _\mathrm{lan}\) | \(h_\mathrm{lan}\) | |
---|---|---|---|

\(\phi _\mathrm{lan}\) | 1 | − 0.997 | − 0.997 |

\(\lambda _\mathrm{lan}\) | 1 | 0.995 | |

\(h_\mathrm{lan}\) | 1 |

Since all three parameters are strongly correlated with \(| r_{ij} | > 0.995\), it is evident that it is almost impossible to solve for all three parameters unless external information is available or constraints are applied. On the contrary, when the height component is fixed, the correlation between the remaining two parameters \(\phi _\mathrm{lan}\) and \(\lambda _\mathrm{lan}\) is significantly lower and amounts to \(-\,0.685\). Nevertheless, if all three position components need to be estimated from a single monolithic fit, the correlations prevent a meaningful interpretation of the individual coordinates. Individual components become indistinguishable and position solutions scatter within a spheroid that reflects the 3D accuracy of the lander’s coordinates. In order to demonstrate this behavior, dedicated simulations with the IVS-R1 and VGOS-type sessions were carried out. As presented in Table 3, the \(WRMS_{3D}\) value for the VGOS is about three meters, which is about eight times smaller than the same measure obtained from IVS-R1 schedules. Even though the 3D positioning performance is worse than the 2D case for VGOS, as discussed in Sect. 3.1, the results are comparable to the vertical accuracy of present digital elevation models (DEM) of the Moon (Barker et al. 2016).

### 3.3 Earth orientation parameters

*LE*and

*LET*analysis options can act as proxies that give insights into this question. Therefore, the daily estimates of pole coordinates (\(x_p\), \(y_p\)) and the phase of the Earth’s rotation (UT1-UTC) were studied based on the results from the Monte Carlo runs and compared against the performance of simulated IVS-R1 sessions which did not include observations to the Moon. Similar to the case of lunar coordinates, repeatabilities in the form of \(\text {WRMS}\) errors were used as evaluation criteria. Corresponding results are shown in Fig. 6.

The results indicate slightly higher \(\text {WRMS}\) values for the \(x_p\) and \(y_p\) estimates when lunar observations are included in the IVS-R1 schedules. Also for UT1-UTC estimates a small accuracy degradation can be identified when including lunar observations. Although EOP estimates tend to be slightly worse than the results from reference solutions, the identified decrease in accuracy is rather small when comparing against the performance of actual VLBI sessions, especially in the case of UT1-UTC estimates. As stated by Malkin (2009), the precision of the latter parameter and pole coordinates, both derived based on the IVS-R1 sessions, amounts to 3 \(\mu \text {s}\) and 60 \(\mu \text {as}\), respectively.

In general, the slightly worse performance can be explained by two main factors. First, due to the mutual visibility constraints, schedules with lunar observations contain less observations and thus lead to a slightly larger scatter of the EOP. Second, the inclusion of lunar observations, based on the replacement strategy presented before, leads also to less optimal observing geometries. Compared to the original IVS-R1 schedules, which have a varying observing geometry, lunar observations lead to a recurrent observing strategy due to a cyclic revisit of the lunar lander as a radio target. However, observations to artificial radio sources are characterized by short scan lengths. The latter feature paired with dedicated observing schedules could reduce the shortcomings of adding lunar observations to geodetic VLBI sessions. This indicates already how one could improve the concept in the future.

### 3.4 Station positions

*LET*analysis option allowed us to access the necessary statistics related to the station coordinates and their accuracies. Here, the \(\text {WRMS}\) values of position components expressed as topocentric coordinates (north, east, up) can be taken from the Monte Carlo simulations and understood as a measure for station position accuracy. As in the case of the EOP, \(\text {WRMS}\) values were computed for the original as well as the modified IVS-R1 observing schedules. Results for stations participating in more than 60% of the IVS-R1 sessions in 2014 and the substitution strategy S-3 are shown in Fig. 7.

An insignificant increase in average WRMS of about 1 mm is found. Similar to the EOP-related study (cf. Sect. 3.3), this can be attributed to the smaller number of total observations per 24-h session, as compared to the original IVS-R1 schedules. In addition, one needs to take into account the change of the local sky coverage, which negatively impacts the sensitivity to estimate the station positions. These two drawbacks will be overcome when sophisticated scheduling strategies are considered.

### 3.5 Impact of error sources

Refractivity variations in the neutral atmosphere are considered to be the dominant error source which limits the accuracy of obtained VLBI target parameters and thus leads to a degradation of the estimated coordinates of the lander. This is especially pronounced in Figs. 3a and 5a where one can identify a settling of \(\text {WRMS}_{\text {2D}}\) for lunar observations with the precision of better than 10 mm.

*L*option and S-3 schedules. This is summarized in Fig. 8. The first run considers all error sources and corresponds to the results shown in Fig. 3a. Assuming no contributions from the turbulent troposphere (while still solving for ZWD), as done in the second run, shows an improvement of about 50% in terms of \(\text {WRMS}_{\text {2D}}\) for lunar observation precision of better than 10.0 mm. Neglecting also the clock instability (while still solving for \(\textit{clk}\)), leads to further improvement on the level of about 30%. In order to study almost noise-free observations, a dedicated simulation run assuming no noise contributions from the troposphere and clocks as well as VGOS-type quasar observations (i.e., \(\sigma = 1.41~\text {mm}\)) was carried out. This fourth run confirms that \(\text {WRMS}_{\text {2D}}\) linearly depends on the observation precision, as one would expect. In summary, it can be concluded that an improved handling of the tropospheric turbulence will lead to a better lunar positioning performance. Reducing contributions from the reference clocks and observational noise could lead to a centimeter position accuracy of the lander, as already partly confirmed by the VGOS study (cf. Sect. 3.1).

## 4 Summary and conclusions

We studied how geodetic VLBI can be used to determine the position of an artificial radio source on the Moon and we revealed the impact of this observational concept on classical geodetic parameters. We described the results of our extensive Monte Carlo simulations, based on the IVS-R1 schedules, and it was discussed how the quality and quantity of observations to the Moon affect the determination of EOP, VLBI station coordinates and position accuracy of the lander. We also carried out simulations reflecting the future VGOS performance. In addition, we investigated the capabilities to estimate three-dimensional lunar position components and revealed the limiting factors preventing centimeter-accurate positioning on the lunar surface.

In general, the results based on the IVS-R1 schedules (Sect. 3.1) indicate that a sub-meter position accuracy of an artificial radio source on the Moon could be achieved. Considering that ionospheric delays have to be corrected with the help of external information, such as GIM, a realistic positioning performance of about a meter is anticipated. However, if one would deploy a dual-frequency transmitter on the surface of the Moon, ionosphere-free observations would become available, leading to a horizontal position accuracy of better than 40 cm. Such performance could be already achieved when the lunar target is only observed in every eighth scan (i.e., 3% of total number of observations).

Utilizing VGOS-type schedules provides an improvement in terms of the two-dimensional position precision by a factor of eight. This corresponds to \(\text {WRMS}_{\text {2D}}\) values in the range of 2–5 cm and 10–20 cm for ionosphere-free and externally ionosphere-corrected observations, respectively. Thus, for the VGOS case, the impact of the troposphere is no longer a major issue. Instead, the proper ionospheric delay mitigation for lunar observations is of high importance.

The results presented in Sect. 3.1 for the VGOS case are especially important from the scientific point of view. Positioning of an object in two dimensions with a precision of a few centimeters by geodetic VLBI can be beneficial for the development of lunar dynamical models and ephemerides. Geodetic VLBI could complement Lunar Laser Ranging (LLR) and contribute with sensitivity perpendicular to the line of sight. Moreover, long-term and frequent lunar observations could be provided within the IVS observing programs. Given that suitable lunar radio transmitters are provided, the existing global network of VLBI stations could track those as well as quasars within the same 24-h experiments at no extra cost. As confirmed, inclusion of lunar observations into IVS-R1 schedules did not significantly impact the estimation of EOP and coordinates of the VLBI stations. Furthermore, observing programs, dedicated for both near-field and far-field observations, would allow to access the parameters that have been out of the reach for traditional geodetic VLBI, such as geopotential coefficients, lunar physical librations (Rambaux and Williams 2011) and parameters of general relativity theory.

VGOS-type quasar measurements have already been taken at several stations around the world. Moreover, the first observations of the CE-3 signals with geodetic VLBI were already performed in April 2014 on the Onsala–Wettzell baseline and regular observations of that probe with the global network of VLBI stations were also proposed to the IVS Program Committee which resulted in four OCEL sessions (Observing the Chang’E Lander with VLBI) per year from 2014 to 2016 (Klopotek et al. 2017; Haas et al. 2017). This allowed to broaden the knowledge and gain new experience concerning geodetic VLBI observations of lunar targets. However, geodetic VLBI analysis of the Chang’E-3 data is still ongoing. In general, suitable processing routines for observations of different types of artificial radio sources (co-location satellites, GNSS; Tang et al. 2016; Plank et al. 2017) are still under investigation. Moreover, provision of geodetic VLBI observables suffers from technical difficulties which need to be solved before one can access the full potential of such new observation types (McCallum et al. 2017).

The Chang’E-3 mission can be seen as a pathfinder for subsequent lunar missions with the aim to explore the Moon. A lunar lander equipped with space-geodetic instruments such as LLR reflectors and multi-frequency broadband radio transmitters would be a unique opportunity for comprehensive investigations concerning the structure and motion of the Moon and the dynamics of the Earth–Moon system (King et al. 1976). Geodetic VLBI can provide valuable insights that motivate the scheduling and observation of lunar radio transmitters along with standard quasar sources and therefore is expected to stimulate new observing concepts for geodesy as well as planetary science.

## Footnotes

## Notes

### Acknowledgements

The authors would like to thank Dmitry Duev for his help concerning the VLBI near-field model as well as the reviewers for their constructive comments, which led to a major improvement of the manuscript. The IVS is acknowledged for providing VEX files and the VGOS schedule used in this work.

## Compliance with ethical standards

## Conflict of interest

The authors declared that they have no conflict of interest.

## Authors’ contributions

GK and TH implemented VLBI near-field models and simulation module in c5++ and extended its interface in order to cope with lunar observations. GK performed all the simulations, created the figures and wrote the manuscript. TH and RH supervised GK and helped to improve the manuscript.

## References

- Altamimi Z, Rebischung P, Métivier L, Collilieux X (2016) ITRF2014: a new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J Geophys Res Solid Earth. https://doi.org/10.1002/2016JB013098 Google Scholar
- Archinal BA, A’Hearn MF, Bowell E, Conrad A, Consolmagno GJ, Courtin R, Fukushima T, Hestroffer D, Hilton JL, Krasinsky GA, Neumann G, Oberst J, Seidelmann PK, Stooke P, Tholen DJ, Thomas PC, Williams IP (2011) Report of the IAU working group on cartographic coordinates and rotational elements: 2009. Celest Mech Dyn Astron 109(2):101–135. https://doi.org/10.1007/s10569-010-9320-4 CrossRefGoogle Scholar
- Bachmann S, Thaller D, Roggenbuck O, Lösler M, Messerschmitt L (2016) IVS contribution to ITRF2014. J Geod 90(7):631–654. https://doi.org/10.1007/s00190-016-0899-4 CrossRefGoogle Scholar
- Barker MK, Mazarico E, Neumann GA, Zuber MT, Haruyama J, Smith DE (2016) A new lunar digital elevation model from the Lunar Orbiter Laser Altimeter and SELENE Terrain Camera. Icarus 273:346–355. https://doi.org/10.1016/j.icarus.2015.07.039 CrossRefGoogle Scholar
- Behrend D, Cucurull L, Vilà J, Haas R (2000) An inter-comparison study to estimate zenith wet delays using VLBI, GPS, and NWP models. Earth Planets Space 52(10):691–694. https://doi.org/10.1186/BF03352265 CrossRefGoogle Scholar
- Behrend D, Böhm J, Charlot P, Clark T, Corey B, Gipson J, Haas R, Koyama Y, MacMillan D, Malkin Z, Niell A, Nilsson T, Petrachenko B, Rogers AEE, Tuccari G, Wresnik J (2009) Recent progress in the VLBI2010 development. Springer, Berlin, pp 833–840. https://doi.org/10.1007/978-3-540-85426-5_96 Google Scholar
- Cappallo R (2014) Correlating and fringe-fitting broadband VGOS data. In: Behrend D, Baver KD, Armstrong KL (eds) IVS 2014 general meeting proceedings, international VLBI service for geodesy and astrometry, pp 91–96Google Scholar
- Duev DA, Calves MG, Pogrebenko SV, Gurvits LI, Cimo G, Bahamon TB (2012) Spacecraft VLBI and doppler tracking: Algorithms and implementation. Astrono Astrophys 541:A43. https://doi.org/10.1051/0004-6361/201218885 CrossRefGoogle Scholar
- Elphic RC, Delory GT, Hine BP, Mahaffy PR, Horanyi M, Colaprete A, Benna M, Noble SK (2014) The lunar atmosphere and dust environment explorer mission. Space Sci Rev 185(1):3–25. https://doi.org/10.1007/s11214-014-0113-z CrossRefGoogle Scholar
- Fey AL, Gordon D, Jacobs CS, Ma C, Gaume RA, Arias EF, Bianco G, Boboltz DA, Böckmann S, Bolotin S, Charlot P, Collioud A, Engelhardt G, Gipson J, Gontier AM, Heinkelmann R, Kurdubov S, Lambert S, Lytvyn S, MacMillan DS, Malkin Z, Nothnagel A, Ojha R, Skurikhina E, Sokolova J, Souchay J, Sovers OJ, Tesmer V, Titov O, Wang G, Zharov V (2015) The second realization of the international celestial reference frame by very long baseline interferometry. Astron J 150(2):58. https://doi.org/10.1088/0004-6256/150/2/58 CrossRefGoogle Scholar
- Folkner WM, Williams JG, Boggs DH (2009) The planetary and lunar ephemeris DE 421. IPN Prog Rep 178:42–178Google Scholar
- Gipson J (2010) An introduction to Sked. In: Behrend D, Baver KD (eds) IVS 2010 general meeting proceedings, international VLBI service for geodesy and astrometry, pp 77–84Google Scholar
- Haas R, Schuh H (1996) Determination of frequency dependent Love and Shida numbers from VLBI data. Geophys Res Lett 23(12):1509–1512. https://doi.org/10.1029/96GL00903 CrossRefGoogle Scholar
- Haas R, Halsig S, Han S, Iddink A, Jaron F, La Porta L, Lovell J, Neidhardt A, Nothnagel A, Plötz C, Tang G, Zhang Z (2017) Observing the Chang’E-3 lander with VLBI (OCEL): technical setups and first results. In: Nothnagel A, Jaron F (eds) Proceedings of the first international workshop on VLBI observations of near-field targets, October 5–6, 2016, Schriftenreihe des Inst. f. Geodäsie u. Geoinformation, Vol. 54, ISSN 1864-1113, Bonn, vol 54, pp 41–64Google Scholar
- Herring TA, Davis JL, Shapiro II (1990) Geodesy by radio interferometry: the application of Kalman Filtering to the analysis of very long baseline interferometry data. J Geophys Res Solid Earth 95(B8):12561–12581. https://doi.org/10.1029/JB095iB08p12561 CrossRefGoogle Scholar
- Hobiger T, Otsubo T (2014) Combination of GPS and VLBI on the observation level during CONT11—common parameters, ties and inter-technique biases. J Geod 88(11):1017–1028. https://doi.org/10.1007/s00190-014-0740-x CrossRefGoogle Scholar
- Hobiger T, Kondo T, Schuh H (2006) Very long baseline interferometry as a tool to probe the ionosphere. Radio Sci. https://doi.org/10.1029/2005RS003297 Google Scholar
- Jones DL, Folkner WM, Jacobson RA, Jacobs CS, Dhawan V, Romney J, Fomalont E (2015) Astrometry of Cassini With the VLBA to improve the Saturn ephemeris. Astron J 149:28. https://doi.org/10.1088/0004-6256/149/1/28 CrossRefGoogle Scholar
- Kareinen N, Klopotek G, Hobiger T, Haas R (2017) Identifying optimal tag-along station locations for improving VLBI Intensive sessions. Earth Planets Space 69(16):1–9. https://doi.org/10.1186/s40623-017-0601-y Google Scholar
- Kato M, Sasaki S, Tanaka K, Iijima Y, Takizawa Y (2008) The Japanese lunar mission SELENE: science goals and present status. Adv Space Res 42(2):294–300. https://doi.org/10.1016/j.asr.2007.03.049 CrossRefGoogle Scholar
- Kikuchi F, Liu Q, Hanada H, Kawano N, Matsumoto K, Iwata T, Goossens SJ, Asari K, Ishihara Y, Tsuruta S, Ishikawa T, Noda H, Namiki N, Petrova N, Harada Y, Ping J, Sasaki S (2009) Picosecond accuracy VLBI of the two subsatellites of SELENE (KAGUYA) using multifrequency and same beam methods. Radio Sci. https://doi.org/10.1029/2008RS003997 Google Scholar
- King RW, Counselman CC, Shapiro II (1976) Lunar dynamics and selenodesy: results from analysis of VLBI and laser data. J Geophys Res 81(35):6251–6256. https://doi.org/10.1029/JB081i035p06251 CrossRefGoogle Scholar
- Klioner SA (2003) A practical relativistic model for microarcsecond astrometry in space. Astron J 125(3):1580. https://doi.org/10.1086/367593 CrossRefGoogle Scholar
- Klopotek G, Hobiger T, Haas R (2017) Implementation of VLBI near-field delay models in the c5++ analysis software. In: Nothnagel A, Jaron F (eds) Proceedings of the first international workshop on VLBI observations of near-field targets, October 5–6, 2016, Schriftenreihe des Inst. f. Geodäsie u. Geoinformation, Vol. 54, ISSN 1864-1113, Bonn, vol 54, pp 29–33Google Scholar
- Konopliv AS, Park RS, Yuan DN, Asmar SW, Watkins MM, Williams JG, Fahnestock E, Kruizinga G, Paik M, Strekalov D, Harvey N, Smith DE, Zuber MT (2013) The JPL lunar gravity field to spherical harmonic degree 660 from the grail primary mission. J Geophys Res Planets 118(7):1415–1434. https://doi.org/10.1002/jgre.20097 CrossRefGoogle Scholar
- Lagler K, Schindelegger M, Böhm J, Krásná H, Nilsson T (2013) GPT2: empirical slant delay model for radio space geodetic techniques. Geophys Res Lett 40(6):1069–1073. https://doi.org/10.1002/grl.50288 CrossRefGoogle Scholar
- Lebreton JP, Witasse O, Sollazzo C, Blancquaert T, Couzin P, Schipper AM, Jones JB, Matson DL, Gurvits LI, Atkinson DH, Kazeminejad B, Perez-Ayucar M (2005) An overview of the descent and landing of the Huygens probe on Titan. Nature 438:758–764. https://doi.org/10.1038/nature04347 CrossRefGoogle Scholar
- Li P, Hu X, Huang Y, Wang G, Jiang D, Zhang X, Cao J, Xin N (2012) Orbit determination for Chang’E-2 lunar probe and evaluation of lunar gravity models. Sci China PhysMech Astron 55(3):514–522. https://doi.org/10.1007/s11433-011-4596-2 CrossRefGoogle Scholar
- Li C, Liu J, Ren X, Zuo W, Tan X, Wen W, Li H, Mu L, Su Y, Zhang H, Yan J, Ouyang Z (2015) The Chang’e 3 mission overview. Space Sci Rev 190(1):85–101. https://doi.org/10.1007/s11214-014-0134-7.
- Malkin Z (2009) On comparison of the Earth orientation parameters obtained from different VLBI networks and observing programs. J Geod 83(6):547–556. https://doi.org/10.1007/s00190-008-0265-2 CrossRefGoogle Scholar
- McCallum J, Plank L, Hellerschmied A, Böhm J, Lovell J (2017) Technical challenges in VLBI observations of GNSS sources. In: Nothnagel A, Jaron F (eds) Proceedings of the first international workshop on VLBI observations of near-field targets, October 5–6, 2016, Schriftenreihe des Inst. f. Geodäsie u. Geoinformation, Vol. 54, ISSN 1864-1113, Bonn, vol 54, pp 7–10Google Scholar
- Moyer TD (2000) Formulation for observed and computed values of deep space network data types for navigation. Monograph 2. The deep-space communications and navigation systems series. JPL Publication 00-7, Jet Propulsion Laboratory, California Institute of Technology, PasadenaGoogle Scholar
- Niell A, Whitney A, Petrachenko B, Schlüter W, Vandenberg N, Hase H, Koyama Y, Ma C, Schuh H, Tuccari G (2006) VLBI2010: Current and future requirements for geodetic VLBI systems. In: Behrend D, Baver K (eds) International VLBI service for geodesy and astrometry 2005 annual report, IVS coordinating center, NASA/TP-2006-214136Google Scholar
- Niell AE, Beaudoin CJ, Bolotin S, Cappallo RJ, Corey BE, Gipson J, Gordon D, McWhirter R, Ruszczyk CA, SooHoo J (2014) VGOS operations and geodetic results. In: Behrend D, Baver KD, Armstrong KL (eds) IVS 2014 general meeting proceedings, international VLBI service for geodesy and astrometry, pp 97–101Google Scholar
- Nilsson T, Haas R (2010) Impact of atmospheric turbulence on geodetic very long baseline interferometry. J Geophys Res Solid Earth. https://doi.org/10.1029/2009JB006579 Google Scholar
- Nothnagel A, Artz T, Behrend D, Malkin Z (2016) International VLBI service for geodesy and astrometry–delivering high-quality products and embarking on observations of the next generation. J Geod. https://doi.org/10.1007/s00190-016-0950-5 Google Scholar
- Petit G, Luzum B (eds) (2010) IERS conventions (2010). IERS Technical Note 36, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am MainGoogle Scholar
- Petrachenko B, Böhm J, MacMillan D, Niell A, Pany A, Searle A, Wresnik J (2008) VLBI2010 antenna slew rate study. In: Finkelstein A, Behrend D (eds) IVS 2008 general meeting proceedings, international VLBI service for geodesy and astrometry, pp 410–415Google Scholar
- Petrachenko B, Niell A, Behrend D, Corey B, Böhm J, Charlot P, Collioud A, Gipson J, Haas R, Hobiger T, Koyama Y, MacMillan D, Malkin Z, Nilsson T, Pany A, Tuccari G, Whitney A, Wresnik J (2009) Design aspects of the VLBI2010 system. Technical Report NASA/TM-2009-214180Google Scholar
- Plank L, Hellerschmied A, McCallum J, Böhm J, Lovell J (2017) VLBI observations of GNSS-satellites: from scheduling to analysis. J Geod 91(7):867–880. https://doi.org/10.1007/s00190-016-0992-8 CrossRefGoogle Scholar
- Rambaux N, Williams JG (2011) The Moon’s physical librations and determination of their free modes. Celest Mech Dyn Astron 109(1):85–100. https://doi.org/10.1007/s10569-010-9314-2 CrossRefGoogle Scholar
- Reid MJ, Honma M (2014) Microarcsecond radio astrometry. Annu Rev Astron Astrophys 52:339–372. https://doi.org/10.1146/annurev-astro-081913-040006 CrossRefGoogle Scholar
- Schaer S, Beutler G, Rothacher M, Springer TA (1996) Daily global ionosphere maps based on GPS carrier phase data routinely produced by the CODE. In: Neilan RE, Van Scoy PA, Zumberge JF (eds) Proceedings of the IGS analysis center workshop, international GNSS service, pp 181–192Google Scholar
- Sekido M, Fukushima T (2006) A VLBI delay model for radio sources at a finite distance. J Geod 80(3):137–149. https://doi.org/10.1007/s00190-006-0035-y CrossRefGoogle Scholar
- Sekido M, Kondo T, Kawai E, Imae M (2003) Evaluation of GPS-based ionospheric TEC map by comparing with VLBI data. Radio Sci. https://doi.org/10.1029/2000RS002620 Google Scholar
- Sovers OJ, Fanselow JL, Jacobs CS (1998) Astrometry and geodesy with radio interferometry: experiments, models, results. Rev Mod Phys 70(4):1393–1454. https://doi.org/10.1103/RevModPhys.70.1393 CrossRefGoogle Scholar
- Tang G, Sun J, Li X, Liu S, Chen G, Ren T, Wang G (2016) APOD mission status and observations by VLBI. In: Behrend D, Baver KD, Armstrong KL (eds) IVS 2016 general meeting proceedings, international VLBI service for geodesy and astrometry, pp 363–367Google Scholar
- Treuhaft RN, Lanyi GE (1987) The effect of the dynamic wet troposphere on radio interferometric measurements. Radio Sci 22(2):251–265. https://doi.org/10.1029/RS022i002p00251 CrossRefGoogle Scholar
- Wenlin T, Peng X, Songjie H, Jianfeng C, Peng D, Yanlong B, Lue C, Songtao H, Xuefei G, Wenxiao L, Jinsong P, Yun-Kau L, Geshi T (2017) Chang’e 3 lunar mission and upper limit on stochastic background of gravitational wave around the 0.01 Hz band. Adv Space Res 60(6):1315–1326. https://doi.org/10.1016/j.asr.2017.06.008
- Whitney A, Lonsdale C, Himwich E, Vandenberg N, van Langevelde H, Mujunen A, Walker C (2002) VEX File definition/example. http://www.vlbi.org/vex/docs/vex%20definition%2015b1.pdf, Technical Report 1.5b1
- Williams JG, Turyshev SG, Boggs DH, Ratcliff JT (2006) Lunar laser ranging science: gravitational physics and lunar interior and geodesy. Adv Space Res 37(1):67–71. https://doi.org/10.1016/j.asr.2005.05.013 CrossRefGoogle Scholar
- Zheng W, Huang Y, Chen Z, Wang GW, Liu Q, Tong F, Li P (2014) Realtime and high-accuracy VLBI in the CE-3 mission. In: Behrend D, Baver KD, Armstrong KL (eds) IVS 2014 general meeting proceedings, international VLBI service for geodesy and astrometry, pp 466–472Google Scholar
- Zhou H, Li H, Dong G (2015) Relative position determination between Chang’E-3 lander and rover using in-beam phase referencing. Sci China Inf Sci 58(9):1–10. https://doi.org/10.1007/s11432-015-5363-1 Google Scholar

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