Keywords

1 Introduction

Space geodetic observation with Very Long Baseline Interferometry (VLBI), Global Navigation Satellite System (GNSS), Satellite Laser Ranging (SLR), or Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) involves a measurement of travel time of electromagnetic radiation between an emitter and a receiver and/or rates of its change. The position of a ground space geodesy instrument is referred to its own unique reference point. In a similar way, the position of a space-borne emitter or receiver is referred to its own reference point.

Space geodesy techniques have their strengths and weaknesses. VLBI provides a reference to inertial space, SLR provides a reference to the Earth’s center of mass, including the solid earth, oceans, cryosphere and atmosphere, DORIS provides wide spatial coverage, and GNSS is able to sense site deformations with a fine time resolution. It was recognized over 20 years ago that a combination of all space geodesy techniques has the potential to provide the most accurate results by mitigating the weaknesses of each individual technique (see for example, Altamimi et al. 2002). Combination implies that observations necessarily must have something common that ties them together. Ties can be direct in the form of a position vector between either a space-borne or a ground-based reference point that is precisely known, or indirect, for instance in the form of Earth rotation parameters that affect all ground stations.

A number of sites have instruments of more than one technique at distances of 30–500 m. Direct measurement of their positions with respect to each other can establish direct ties. Survey techniques measure angles and distances between markers. These measurements can reach accuracy of 1–3 mm (Matsumoto et al. 2022). However, the ties should provide the positions of technique reference points. Reference points of microwave techniques, such as VLBI and GNSS, cannot be directly pin-pointed by markers. An offset of a reference point with respect to a marker is inferred. In the case of GNSS ground stations, an offset between a marker on the instrument and its phase center can be calibrated, for instance, in an anechoic chamber. In the case of VLBI radiotelescopes, markers are put on the antenna, and the position of a geometric reference point on a fixed axis that is a projection of a moving axis is derived from processing a cloud of points measured with a total station at different antenna azimuths and elevations. Then an assertion is made that the geometric reference point coincides with the reference point estimated in VLBI data analysis. The validity of that assertion cannot be evaluated.

The positions of microwave reference points provided by data analysis of both the GNSS and VLBI techniques may have biases with respect to the geometric reference points. As long as these biases are permanent and do not depend on any other variable parameters, they can remain unnoticed. For a number of applications, for instance for a study of motions caused by plate tectonics or for mean sea level determination, permanent biases are irrelevant. Sarti et al. (2011) showed that antenna gravity deformation caused a 7 mm offset of the microwave reference point of VLBI station medicina, whose position was determined from analysis of VLBI group delay with respect to a geometric refrence point determined from a local survey. Mismodeling antenna gravity deformation will not affect the least square fit and may not be noticed, but biases in local tie measurements comparable or exceeding the internal accuracy of GNSS and VLBI techniques make them close to useless.

The fundamental problem of tie measurements with local surveys is that the optical technique used by a survey instrument, such as a total station, cannot measure the phase center of a microwave technique. While the accuracy of measurements of a vector between markers can be evaluated from a scatter of residuals, the accuracy of a vector between a marker to a phase center is poorly known. That makes tie vectors determined with local surveys unreliable. A typical discrepancy between VLBI positions determined from analysis of group delays and GNSS positions reduced to the VLBI reference point via tie vectors determined with local surveys is 5–20 mm (Ray and Altamimi 2005). Lack of realistic uncertainties of tie vectors does not allow us to interpret these discrepancies because we do not know whether they are due to systematic errors of space geodetic techniques or due to error in tie vectors. That motivated us to seek for alternative measurements of tie vectors.

2 A Microwave Technique for VLBI/GNSS Tie Measurements

We are leveraging the High Rate Tracking Receiver (HRTR) to serve as both an advanced software-defined GNSS receiving system and a general purpose L-band receiver (York et al. 2012, 2014). It directly digitizes voltage from the receiver in a range of 1 to 2 GHz at a rate of 2 gigasamples per second. To access a larger extent of the signal in the 1–2 GHz range, we modified a commercial GNSS antenna. Specifically, we removed the internal amplifier and narrowband bandpass filters that are provided, and we have replaced them with an alternate amplification and filtering stage of our own design. The aggregate RF system including modified components has a passband of approximately [1.10, 1.65] GHz. The antenna elements are not altered in this modification. Therefore, phase center offset/variation corrections of the modified antennas are the same as of the original antenna.

The HRTR performs digital downconversion of the input samples and produces up to nine independently chosen frequency bands 40.912 MHz wide. The HRTR also allows us to configure the bit depth of the received signal. We utilized complex encoding for our work, using one bit for the in-phase and one bit for the quadrature voltage. Datastreams with the baseband signal from each band are recorded to a general purpose RAID of magnetic hard drives.

In addition to recording voltage from the receiver, HRTR simultaneously computes conventional GNSS observables on civil GNSS signals in real time and provides an output convertible to RINEX format. We can recompute conventional GNSS observables by processing digital records of the baseband signal if needed.

We noticed that the HRTR has a striking similarity to a radiotelescope that is an element of a VLBI network. Like a radiotelescope, the HRTR digitizes voltage from the antenna and records the data with time stamps from a precise clock. HRTR data are processed after the experiment in a similar way as VLBI. Extending this analogy further, we came to the idea of using a HRTR itself as an element of a VLBI network. A GNSS antenna with an effective diameter of \(\sim \! 0.08\) m surrounded by 0.38 m wide choke ring is roughly four orders of magnitude less sensitive than a 12–30 m radiotelescope, it operates at a lower frequency, and at a first glance does not look competitive. However, the use of a GNSS antenna as an element of a VLBI network is very promising for local tie measurement. Atmospheric contribution is negligible at short baselines of 30–3000 m. Varenius et al. (2021) demonstrated that baseline length repeatability at a sub-millimeter level has been achieved from processing of phase delays at short baselines. We should stress that the baseline vector between two antennas evaluated from VLBI observations is between the microwave reference points of the radiotelescopes. Therefore, by processing GNSS/radiotelescope data, we can eliminate the weakest link in the measurement chain of a tie vector with the use of conventional local surveys: the offset between a marker and a microwave reference point.

The measurement concept is presented in Fig. 1. The voltage of the emission received by the GNSS antenna in a range of 1.0 to 2.0 GHz is transferred via a coaxial cable to an analog-to-digital converter and recorded. The digital records are re-sampled and re-coded to VDIF format that is commonly accepted in radio astronomy. Emission received by a VLBI antenna is processed the same way, but with different hardware. The output of both the GNSS and VLBI antennas is recorded in the same format. Further processing is performed exactly the same way as processing of any other VLBI data: the data are correlated, the fringe fitting procedure finds group delays and phase delay rates that maximize the fringe amplitude coherently averaged over time and frequency, and finally, group and phase delays are used for determination of the baseline vector. Therefore, we expect that a position vector of a GNSS antenna/radiotelescope baseline will be determined with the same sub-millimeter accuracy as position vectors of other short baselines.

Fig. 1
figure 1

Measurement concept of VLBI/GNSS ties with a microwave technique

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3 Early Results

Implementation of VLBI with a GNSS antenna requires overcoming a number of difficulties (Skeens et al. 2023). It is essential that the HRTR does not perform any analog signal transformation. It simply digitizes signal as is, performs digital filtering into several bands, and writes the digital signal. This early digitization approach shifts the burden of signal processing to programming. This facilitates the tuning of the processing pipeline since digital recordings can be re-processed as many times as needed.

We performed three 3 hr observing sessions in 2022 between two transportable HRTRs and a 25 m radiotelescope fd-vlba. That radiotelescope is a part of the Very Long Baseline Array dedicated for VLBI and has been operating since 1991. It is equipped with an H-maser clock. The antenna has a number of very sensitive receivers, including the one that operates at L-band. We put the first HRTR within 90 m of the fd-vlba. That HRTR was stabilized by a Rubidium clock. We put the second HRTR within 9000 m of fd-vlba near the NASA VLBI station macgo12m. This HRTR was stabilized by the H maser clock used by macgo12m. Since macgo12m does not have the technical capability to observe below 2 GHz, we performed observations at only the two HRTRs and fd-vlba.

The observing schedule included observations of seven of the brightest radiogalaxies and a number of GNSS satellites. We have detected all but one radiogalaxy at the short baseline with fd-vlba and some sources at the 9 km long baseline. As expected, no detection was found between the two HRTR stations. Figure 2 shows fringe phases and normalized fringe amplitudes of radiogalaxy Cyg-A located at a distance of \(7.2 \cdot 10^{21}\) m. This goes well beyond (fourteen orders of magnitude!!) the intended use of the GNSS equipment. The interferometric fringes of radiogalaxies were stable over time, and integration could be extended up to 20 min without a noticeable degradation of fringe amplitude.

Fig. 2
figure 2

Fringe phase (upper) and normalized fringe amplitude of Cyg-A at a 90 m long baseline hrtr/fd-vlba. Signal to noise ratio (SNR) 387 was achieved for 60 s of integration time. Left plot shows fringe phase and amplitude versus frequency and right plot shows fringe phase and amplitude versus time

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Figure 3 shows fringe plots of a GPS satellite over 10 s integration time. We processed GPS signal as a random noise (Skeens et al. 2023). The fringe amplitude has a peak at the carrier frequency of 1575.42 MHz, emission near 1 MHz of the peak due to the C/A signal, and a broad emission due the binary offset carrier modulation of the M-code that has a detectable power within \(\pm 15\) MHz of the carrier. This allows us to compute group delay over the total bandwidth of \(\sim \! 30\) MHz with a precision of 60–90 ps over 10 s. This should be sufficient for resolving phase delay ambiguities with spacings of 635 ps and then use it for data anlysis. Interferometric responses have been detected at the 9 km long baselines as well. At this stage of the project we did not yet attempt to perform geodetic analysis.

Fig. 3
figure 3

Fringe phase (upper) and normalized fringe amplitude of a GPS satellite at a 90 m long baseline hrtr/fd-vlba. SNR 138 was achieved for 10 s of integration time. Left plot shows fringe phase and amplitude versus frequency and right plot shows fringe phase and amplitude versus time

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4 Discussion

A vector tie can be determined from both observations of natural sources, such as radiogalaxies, and from observations of navigational satellites. The broadband GPS signal due to the modulation of the M-code has flux density around \(-\)200 dBW/m\({ }^2\)/Hz (Thoelert 2019) within 30 MHz, i.e. \(\sim \! 1\) MJy, while there are only 10 natural radio sources brighter that 0.02 MJy at 1.5 GHz, i.e. a factor of 50 fainter. The scarcity of very strong radiogalaxies makes preparation of a VLBI schedule optimized for geodesy difficult.

Detection of a radio source requires observations with a sensitive VLBI antenna. fd-vlba is dedicated for astronomy and its L-band receiver has a system equivalent flux density (SEFD) of 289 Jy. Compare with SEFD 2500 Jy at the 2–3 GHz band at 12 m geodetic VLBI antennas. Since sensitivity of an interferometer is proportional to the square root of the product of SEFD of individual antennas, VLBI observations of a GPS satellite between a HRTR and a radiotelescope requires \(50^2=2500\) times less sensitive radiotelescope than observations of radiogalaxies. Figures 2, 3 seem to contradict that statement. It turned out fd-vlba receiver worked in a saturated regime when observing a megajansky source, and fringe amplitude was strongly underestimated. Applying an additional attenuation is required to mitigate the problem. But in general, it is much easier to reduce the sensitivity than to increase it.

The primary observable that will be used for determination of the tie vector will be phase delay. Phase delay ambiguities can be resolved if group delay can be determined with an accuracy 1/4 of the phase ambiguity spacing or better and short-term systematic differences between phase and group delays have a scatter not exceeding that number. Since precision of group delay is reciprocal to the bandwidth of a detected signal, observations of navigational satellites with a relatively broad spectrum, such as GPS and Galileo, is preferable.

Determination of a tie vector between a HRTR and a geodetic VLBI antenna is interesting, but not exactly what is needed. We need to determine a tie vector between a VLBI antenna and a permanent GNSS antenna. There are two possible solutions. First, one can make HRTR a permanent GNSS site. It is expected that in 2023–2024, permanent HRTRs will be installed within a hundred meters of each of the ten VLBA antennas. Second, one can install a HRTR on a temporary monument and determine a tie vector HRTR/radiotelescope using VLBI and subsequently a tie vector between the HRTR and the existing GNSS antenna by processing double-differenced GNSS carrier phase measurements. Processing differential GNSS data at baselines of \(\sim \!\! 100\) m long provides a millimeter level accuracy owing to cancellation of the atmospheric contribution. Then combining the VLBI/HRTR and HRTR/GNSS tie vectors, we get a VLBI/GNSS tie.

Radiotelescopes used for radio astronomy often have receivers in 1.2–1.8 GHz ranges, although very few instruments have the ability to simultaneously record within a band of 1.15–1.65 GHz that covers navigation signals L1, L2, and L5. Radiotelescopes dedicated for geodesy usually cannot receive emission below 2 GHz because of strong high-pass filters installed to mitigate the impact of radio interference. Some new generation broad-band VLBI Geodetic Observing System (VGOS) radiotelescopes have a low cutoff frequency as high as 3.0 GHz because broadband receivers are much more susceptible to radio interference. A solution is to equip existing geodetic radio telescopes with auxiliary receivers operating in the 1–2 GHz range dedicated to VLBI observations of navigational satellites. Since the GNSS signal is so strong, such receivers do not require cooling. The navigational receiver can be installed alongside the main receiver, and the signal can be directed to it either with a deployable mirror or with a dichroic plate.

5 Summary

We propose a novel concept of GNSS/VLBI tie measurements based on a microwave technique. We essentially transform a GNSS antenna into an element of the VLBI network. This method will allow us to estimate the tie vector between the VLBI and GNSS reference points directly using the microwave technique without the need to determine the position offsets of the microwave reference points with respect to markers accessible to local surveys.

We expect that the application of this method will have a profound impact because we expect this method will be bias-free. As a result, vector tie repeatability could be used as a measure of the accuracy of tie vector determination. Knowing errors of tie vectors will enable us to close the budget of the differences of the VLBI reference points reduced to the GNSS reference points and make an inference about whether these differences are statistically significant or not.

We ran three 3 h long observing sessions between the fd-vlba radiotelescope and a high rate GNSS receiver co-located within 90 m. We have detected fringes from both natural extragalactic radio sources and GPS satellites with the SNR well above 100. Thus, we have demonstrated that technical problems related to GNSS/radiotelescope VLBI can be solved. Future work will be focused on the determination of vector ties using this technique.