First Space-VLBI Observations of Sagittarius A*

We report results from the first Earth-space VLBI observations of the Galactic Center supermassive black hole, Sgr A*. These observations used the space telescope Spektr-R of the RadioAstron project together with a global network of 20 ground telescopes, observing at a wavelength of 1.35 cm. Spektr-R provided baselines up to 3.9 times the diameter of the Earth, corresponding to an angular resolution of approximately 55 μas and a spatial resolution of 5.5R Sch at the source, where R Sch ≡ 2GM/c 2 is the Schwarzschild radius of Sgr A*. Our short ground baseline measurements ( ≲ 80 Mλ) are consistent with an anisotropic Gaussian image, while our intermediate ground baseline measurements (100–250 Mλ) confirm the presence of persistent image substructure in Sgr A*. Both features are consistent with theoretical expectations for strong scattering in the ionized interstellar medium, which produces Gaussian scatter-broadening on short baselines and refractive substructure on long baselines. We do not detect interferometric fringes on any of the longer ground baselines or on any ground–space baselines. While space-VLBI offers a promising pathway to sharper angular resolution and the measurement of key gravitational signatures in black holes, such as their photon rings, our results demonstrate that space-VLBI studies of Sgr A* will require sensitive observations at submillimeter wavelengths.

Precision-Aided Partial Ambiguity Resolution Scheme for Instantaneous RTK Positioning

The use of carrier phase data is the main driver for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). However, carrier phase observations are ambiguous by an unknown number of cycles, and their use in RTK relies on the process of mapping real-valued ambiguities to integer ones, so-called Integer Ambiguity Resolution (IAR). The main goal of IAR is to enhance the position solution by virtue of its correlation with the estimated integer ambiguities. With the deployment of new GNSS constellations and frequencies, a large number of observations is available. While this is generally positive, positioning in medium and long baselines is challenging due to the atmospheric residuals. In this context, the process of solving the complete set of ambiguities, so-called Full Ambiguity Resolution (FAR), is limiting and may lead to a decreased availability of precise positioning. Alternatively, Partial Ambiguity Resolution (PAR) relaxes the condition of estimating the complete vector of ambiguities and, instead, finds a subset of them to maximize the availability. This article reviews the state-of-the-art PAR schemes, addresses the analytical performance of a PAR estimator following a generalization of the Cramér–Rao Bound (CRB) for the RTK problem, and introduces Precision-Driven PAR (PD-PAR). The latter constitutes a new PAR scheme which employs the formal precision of the (potentially fixed) positioning solution as selection criteria for the subset of ambiguities to fix. Numerical simulations are used to showcase the performance of conventional FAR and FAR approaches, and the proposed PD-PAR against the generalized CRB associated with PAR problems. Real-data experimental analysis for a medium baseline complements the synthetic scenario. The results demonstrate that (i) the generalization for the RTK CRB constitutes a valid lower bound to assess the asymptotic behavior of PAR estimators, and (ii) the proposed PD-PAR technique outperforms existing FAR and PAR solutions as a non-recursive estimator for medium and long baselines.

Comment on “Study of Systematic Bias in Measuring Surface Deformation With SAR Interferometry” by Ansari et al. (2021)

<p>In a recent publication Ansari et al. (2021) [1] claim (see, in particular, the Discussion and Recommendation Section in their article) that the advanced differential SAR interferometry (InSAR) algorithms for surface deformation retrieval, based on the small baseline approach, are affected by systematic biases in the generated InSAR products. Therefore, to avoid such biases, they recommend a strategy primarily focused on excluding “the short temporal baseline interferograms and using long baselines to decrease the overall phase errors”. In particular, among various techniques, Ansari et al. (2021) [1] identify the solution presented by Manunta et al. (2019) [2] as a small baseline advanced InSAR processing approach where the presence of the above-mentioned biases (referred to as a fading signal) compromises the accuracy of the retrieved InSAR deformation products. We show that the claim of Ansari et al. (2021) [1] is not correct (at least) for what concerns the mentioned approach discussed by Manunta et al. (2019) [2]. In particular, by processing the Sentinel-1 dataset relevant to the same area in Sicily (southern Italy) investigated by Ansari et al. (2021) [1], we demonstrate that the generated InSAR products do not show any significant bias.</p>

Comment on “Study of Systematic Bias in Measuring Surface Deformation With SAR Interferometry” by Ansari et al. (2021)

<p>In a recent publication Ansari et al. (2021) [1] claim (see, in particular, the Discussion and Recommendation Section in their article) that the advanced differential SAR interferometry (InSAR) algorithms for surface deformation retrieval, based on the small baseline approach, are affected by systematic biases in the generated InSAR products. Therefore, to avoid such biases, they recommend a strategy primarily focused on excluding “the short temporal baseline interferograms and using long baselines to decrease the overall phase errors”. In particular, among various techniques, Ansari et al. (2021) [1] identify the solution presented by Manunta et al. (2019) [2] as a small baseline advanced InSAR processing approach where the presence of the above-mentioned biases (referred to as a fading signal) compromises the accuracy of the retrieved InSAR deformation products. We show that the claim of Ansari et al. (2021) [1] is not correct (at least) for what concerns the mentioned approach discussed by Manunta et al. (2019) [2]. In particular, by processing the Sentinel-1 dataset relevant to the same area in Sicily (southern Italy) investigated by Ansari et al. (2021) [1], we demonstrate that the generated InSAR products do not show any significant bias.</p>

Assessment of Quad-Frequency Long-Baseline Positioning with BeiDou-3 and Galileo Observations

Quad-frequency signals have thus far been available for all satellites of BeiDou-3 and Galileo systems. The major benefit of quad-frequency signals is that more extra-wide-lane (EWL) combinations can be formed with quad-frequency than with triple- or dual-frequency, of which the ambiguities can be fixed instantaneously in medium and long baselines. In this paper, the long-baseline positioning algorithm based on optimal triple-frequency EWL/wide-lane (WL) combinations of BeiDou-3 and Galileo is proposed. First, the theoretical precision of multi-frequency combinations of BeiDou-3 and Galileo is studied, and EWL/WL combinations with a small noise amplitude factor and a small ionospheric scalar factor are selected. Then, geometry-free methods are used to estimate the a priori precision of EWL/second EWL/WL signals for different combination schemes. Second, the double-differenced (DD) geometry-based function models of quad-frequency configurations and three different triple-frequency configurations are given, and the DD ionospheric delays are estimated as unknown parameters. In the end, the real BeiDou-3 and Galileo data are used to evaluate the positioning preference. The results show that, when using fixed EWL observations to constrain WL ambiguities, the proposed triple-frequency EWL/WL signals composed of (B1I,B3I,B2a) of BeiDou-3 and (E1,E5a,E6) of Galileo can achieve the same precision as the quad-frequency signals. Therefore, the method proposed in this article can realize long-baseline instantaneous decimeter-level positioning while reducing the dimension of matrix and improving calculation efficiency.

On the geometry of baselines suitable for UT1 estimation with VLBI Intensive sessions

&lt;p&gt;One hour single baseline VLBI sessions, so-called Intensives, are routinely observed to derive UT1-UTC with a short latency.&amp;#160;The selection of baselines for VLBI Intensive sessions and their application for the determination of UT1-UTC is a complex task.&amp;#160;Thus far, it has been understood that long east-west extensions are critical for the accuracy of UT1-UTC.&amp;#160;In this presentation, we show, that the answer is not as simple as that.&amp;#160;&lt;/p&gt;&lt;p&gt;We run Monte-Carlo simulations for a global 10&amp;#176; grid of artificial station locations and discuss the suitability of the individual baselines for UT1-UTC estimation based on the formal error of dUT1.&amp;#160;The antennas are located at latitudes of -80&amp;#176; to 80&amp;#176; and longitudes of 0&amp;#176; to 180&amp;#176; and are assumed to have the same properties than the WETTZ13S telescope.&amp;#160;The nine stations at longitude 0&amp;#176; on the northern hemisphere are defined as reference stations.&amp;#160;In total, 2898 possible baselines between the reference stations and other artificial stations are investigated over one year based on monthly schedules to minimize potential seasonal variations. Thus, with this study, it is possible to derive a complete picture of which baselines are most suitable for dUT1 estimates.&amp;#160;&lt;/p&gt;&lt;p&gt;In general, the findings show optimal global geometries concerning Intensives.&amp;#160;For example, we can confirm that the IVS-INT1 baseline including the stations Kokee and Wettzell is among the best ones available.&amp;#160;Furthermore, we show that north-south baselines are also sensitive to dUT1 as long as their orientations are not parallel to the Earth rotation axis.&amp;#160;Moreover, we highlight that east-west baselines on the equator are not suitable for estimating dUT1 due to the lack of variety in right-ascension of the visible sources.&amp;#160;Additionally, we highlight, that very long baselines are problematic due to the highly restricted mutual visibility.&lt;/p&gt;

Impact of the precise ephemeris on accuracy of GNSS baseline in relative positioning technique

For advanced geodesy tasks that require high-accuracy, such as tectonics, surveying services usually use not only long-baselines but also the duration of tracking GNSS satellites in a long (e.g., 24/7). The accuracy of these baselines in baseline analysis is dominated by inaccuracy satellite positioning and orbit, leading to specified accuracy may not be adequate. One way to overcome this problem is to use the final precise ephemeris, provided by IGS. The objective of this study is to investigate the impact of precise ephemeris on the accuracy of GNSS baselines in relative positioning techniques in two aspects: baseline length and duration of tracking GNSS satellites. To this end, 197 baselines were generated from a total of 88 CORS stations in South Korea, and then thirteen testing cases were constructed by grouping baseline lengths from under 10 km to over 150 km. Besides, data for one day of each CORS was divided into the different duration, such as 1, 2, 3, 6, and 24 hours. The GNSS measurements have been processed by TBC software with an application of the broadcast and precise ephemerides. The precision of the baseline processing from two types of ephemeris was analyzed about baseline lengths and time of data. The obtained results showed that using precise ephemeris significantly improved the accuracy of baseline solutions when the length of the baseline larger than 50km. In addition, this accuracy is independent of the length of baselines in the case of the precise ephemeris. Finally, the result of the testing baselines was enhanced when the duration of tracking data increases.

A Multi-GNSS Differential Phase Kinematic Post-Processing Method

We propose a multiple global navigation satellite system (multi-GNSS) differential phase kinematic post-processing method, expand the current Track ability, and finely tune processing parameters to achieve the best results for research purposes. The double-difference (DD) phase formulas of GLONASS are especially formulated, and the method of arc ambiguity resolution (AR) in post-processing is developed. To verify the feasibility of this AR method, a group of static baselines with ranges from 8 m to 100 km and two kinematic tests were used. The results imply that 100% of ambiguities in short baselines and over 90% in long baselines can be fixed with the proposed ambiguity resolution method. Better than a 10-mm positioning precision was achieved for all the horizonal components of those selected baselines and the vertical components of the short baselines, and the vertical precision for long baselines is around 20 to 40 mm. In the posterior residual analysis, the means of the residual root-mean-squares (RMSs) of different systems are better than 10 mm for short baselines and at the range of 10–20 mm for baselines longer than 80 km. Mostly, the residuals satisfy the standard normal distribution. It proves that the new method could be applied in bridge displacement and vibration monitoring and for UAV photogrammetry.

A New Method of Real-Time Kinematic Positioning Suitable for Baselines of Different Lengths

This study introduces a new real-time kinematic (RTK) positioning method which is suitable for baselines of different lengths. The method merges carrier-phase wide-lane, and ionosphere-free observation combinations (LWLC) instead of using pseudo-range, and carrier-phase ionosphere-free combination (PCLC), or single-frequency pseudo-range and phase combination (P1L1). In a first step, the double-differenced wide-lane ambiguities were calculated and fixed using the pseudo-range and carrier-phase wide-lane combination observations. Once the double-differenced wide-lane integer ambiguities were known, the wide-lane combined observations were regarded as accurate pseudo-range observations. Subsequently, the carrier-phase wide-lane, and ionosphere-free combined observations were used to fix the double-differenced carrier-phase integer ambiguities, achieving the final RTK positioning. The RTK positioning analysis was performed for short, medium, and long baselines, using the P1L1, PCLC, and LWLC methods, respectively. For a short baseline, the LWLC method demonstrated positioning accuracy similar to the P1L1 method, and performed better than the PCLC method. For medium and long baselines, the positioning accuracy of the LWLC method was slightly higher than those of the PCLC and P1L1 methods. In conclusion, the LWLC method provided high-precision RTK positioning results for baselines with different lengths, as it used high-precision carrier-phase observations with fixed ambiguities instead of low-precision pseudo-range observations.