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 nextgeneration 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.

Position determination of the Chang’e 3 lander with geodetic VLBI

“…Apart from real observations, a set of Monte Carlo simulations with the same parameterization and observing geometry as in the analysis of OCEL08 and OCEL09 was also carried out in order to validate the uncertainty of the obtained position estimates and quantify the impact of potential systematic effects. In Monte Carlo simulations, a geodetic VLBI observable comprises the calculated VLBI delay and contributions from three major error sources, i.e., tropospheric turbulence, reference clocks and thermal noise (Klopotek et al 2018). The precision of simulated VLBI observations of the lander can be controlled with a baseline (Gaussian) noise, generated in our case with the standard deviation of the Gaussian random number generator set to 0.20 m and 0.24 m in order to obtain the post-fit WRMS of residuals derived from the analysis of OCEL08 and OCEL09.…”

“…OCEL sessions provided first insights concerning global geodetic VLBI observations of artificial lunar radio sources. Based upon the gained knowledge and encountered technical difficulties, organization of similar programs in the future would be valuable to better understand this new observing concept and fully benefit from its true potential (Klopotek et al 2018). Further steps concern an improvement of the lunar-based parameter determination via an automated and optimized scheduling as well as an enhancement of the postcorrelation analysis of lunar observations.…”

“…It is expected that the introduction of dual-frequency observations could improve the positioning performance as ionosphere errors would be further reduced and estimation of VTEC biases as well as additional clock offsets could be avoided. Moreover, observations of such targets in the next-generation VLBI system (Niell et al 2018) would benefit from an improved observation density of both quasar and lunar sources, better handling of tropospheric turbulence as well as significantly decreased observation noise at VLBI stations (Klopotek et al 2018).…”

“…Step IV covered the target parameter estimation using c5++ (Hobiger et al 2010), whose VLBI module has been recently extended with the possibility to utilize both quasar and lunar observations (Klopotek et al 2018). Weighted least-squares adjustment in c5++ includes variance component estimation (Hobiger and Otsubo 2017) resulting in χ 2 /ν close to Fig.…”

“…a reference sphere with a radius Table 1 Characteristics of OCEL sessions and problems encountered during the analysis, shown for the selected experiments Folkner et al 2009) for calculating the barycentric coordinates of the CE-3 lander and it includes periodic changes of the lunar lander's position caused by the solid Moon tides. Due to the nature of VLBI observations, i.e., poor sensitivity in the line-of-sight direction, H lan needs to be constrained to a well known a priori value (with σ = ± 10 m) as VLBIonly observations do not allow for a reliable decoupling of all position components of the lander (Klopotek et al 2018). However, range (or range-rate) observations could be used in the future to avoid an incorrect a priori height of the lander biasing the horizontal estimates by introducing an additional position shift.…”