The library provides staff members and guests of the institute with scientific literature. The library are situated on the same floor of our institute and provides staff members and guests with scientific literature. In exceptional cases other intrested persons may ask for allowance to use the library. Astronomy, time and time systems, VLBI, satellite Geodesy, terrestrial navigation, aircraft navigation, satellite navigation, aerospace. Data processing and computing techniques, information systems, digital terrain models, signal processing. Geodesy, physical geodesy, mathematical geodesy, geodetic differential geometry, geodetic boundary value problem, map projections, gravimetry.
Geophysics, geodynamics, precession, nutation, rotation of the Earth, tides, geology, hydrography. Institute reports, conference reports, proceedings, Festschrift, general higher education, individual journal issues and individual series issues. The final orbit solutions do not contain any predictions and were calculated some weeks after our experiments took place. They were used for the calculation of a priori delays see Section 4. As mentioned above, these final orbits show post-fit residuals of 10—20 m. A comparison of all available predicted and final orbits revealed differences of several m up to 1 km in the along-track and cross-track directions.
In the radial direction, the discrepancies are much lower with values in the range of several meters. Hence, when we assume that the final orbits are accurate on a level of 10—20 m, we can conclude that the predicted orbits used for satellite tracking were only accurate on the level of several hundred meters.
The rather low accuracies of the predicted as well as of the final orbit solutions have consequences on different stages of the observation and data processing schemes discussed in this paper. The starting point of each VLBI experiment is the observation planning, referred to as scheduling. In general, VLBI schedules define which antennas observe which source at what time.
The scheduling task itself is complicated due to the large number of different observation criteria that have to be considered, such as common visibility of the target from remote sites, slew times between consecutive scans, and the determination of required on-source time to reach the target SNR. For planning the discussed experiments, the VieVS satellite scheduling module [ 32 ] was used. It allows for the scheduling of VLBI observations of near-field targets along with observations of natural extragalactic radio sources, which are routinely observed in geodetic VLBI campaigns.
The natural sources are selected automatically by optimizing the sky coverage at all stations as common for geodetic VLBI sessions [ 33 ]. The observation geometry that was determined by continental-wide baselines and the very low orbit of APOD was a major limiting factor for scheduling. On average, the APOD satellite was visible by individual AuScope telescopes four times a day for a couple of minutes only.
The projected fields of view are displayed in terms of shaded red circles in Figure 2.
Only in the intersecting areas was APOD simultaneously visible by two stations. As indicated in Figure 2 , common visibility from all three AuScope telescopes was restricted to very low elevation angles and scan durations as short as a couple of minutes at most. In general, APOD was simultaneously visible by only two of the three antennas, limiting the experiment design to single-baseline scans. Due to these restrictions, it was not possible to observe more than two single-baseline scans shortly after another during a flyover, as exemplarily indicated in Figure 2 for two consecutive scans and in Experiment a The next occasion for an APOD scan only existed about Despite these circumstances, we took every chance from November 11 to 14, , and observed APOD whenever common visibility from two AuScope antennas was given.
All observed experiments are listed in Table 1 , which also provides details on the observation durations.
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During observations, APOD was tracked continuously by the antennas as long as common visibility was given and the signal was recorded continuously. Each of these recorded APOD tracks is referred to as scan in this paper, which must not be mixed up with the term observation. Due to the high SNR, delays could be derived in a 1 s interval, i.
In general, the data analysis becomes more challenging due to the consistently low elevations, as the effects of the neutral atmosphere and the ionosphere on the observed signals increase with decreasing elevation. Furthermore, estimates of station heights, zenith wet delays, and station clocks do not decorrelate properly without observations at varying elevations e.
On the other side, the change rates of the topocentric antenna pointing directions azimuth and elevation rates decrease as the distance between antenna and satellite increases with lower elevation angles. Hence, the demands on the tracking and on the pointing accuracy of the antenna decrease at lower elevation angles. Therefore, the APOD satellite was easier to keep within the field of view via the observing antennas at low elevations than at high elevations.
We were able to assess the received signal live during APOD tracks by a spectrum analyzer connected to the intermediate frequency IF channels at the recorder racks. Our experience was that the signal amplitude became increasingly unstable at higher elevation angles, especially in the X-band due to the narrower field of view.
We think that these tracking issues were mainly caused by the low accuracy of the predicted APOD orbits used for tracking, which show offsets to the final orbits of up to m see Section 2. With a beam-width of about Furthermore, the internal interpolation of the tracking data in the ACU might not be accurate enough to precisely follow such a fast satellite. If there is already a pointing offset caused by the tracking data, additional inaccuracies due to a non-optimal interpolation of the data in the ACU may be enough to cause severe pointing problems in the X-band—even at moderate elevation angles.
For the sake of brevity, we only mention quasars when we talk about natural radio sources, as the most common type of active galactic nucleus AGN observed in the geodetic VLBI. To be precise, we do not exclude the possibility that other types of AGN were observed as well in the described experiments.
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The main reason for the inclusion of quasars in the observation plan was to use them as calibrator sources in order to establish an initial clock model in the correlation process as outlined in Section 4. Experiment a was designed differently: Basically, it is a geodetic 24 h VLBI session consisting of three-station scans to strong quasars with a minimum flux density of 0. For the scheduling we optimized the sky coverage at each site in order to decorrelate estimates of station clocks, station heights, and troposphere delays.
The first two scans and , which are illustrated in Figure 2 , are used as a generic example in this paper. This particular session design with satellite scans being embedded in quasar scans allows for additional analysis options, such as using Zenith Wet Delays ZWDs estimated in a quasar-only solution, to correct the APOD observations a priori for more details, we refer to Section 5.
The observing mode used for all described experiments was designed pursuing two purposes: 1 to record the full APOD S- and X-band signals and 2 to derive reasonable geodetic results from standard observations of quasars at the same time. Changing the observation mode when switching between quasars and APOD was not an option as it might have introduced unknown systematic biases. Data was recorded in 16 channels with 16 MHz bandwidth each, 10 in the X-band and 6 in the S-band, applying 2-bit sampling, which results in a recording rate of 64 Mbps per channel.
The frequency allocation is illustrated in Figure 3. Only 4 of 16 channels were dedicated to record the APOD tones. The purpose of the others was to increase the frequency coverage for quasar observations to enable the calculation of reasonable multi-band delays.
Estimation and analysis of Galileo differential code biases
APOD signal and recording channel allocation in the frequency domain. The 16 MHz recording channels are illustrated by red X-band, upper side band , blue X-band, lower side band , and cyan S-band, upper side band boxes. The X-band signals span over The S-band tones are covered by one 16 MHz channel centered at the carrier bottom panel. Publicly available two-line element TLE data sets e. However, a final schedule iteration is recommended shortly before a session, as the observation times may slightly change with updated orbit elements. The data points for the tracking files were determined in a 1 s interval with the calculations being based on the latest APOD orbit predictions provided by BACC about 12 h before an experiment.
They contain a full description of the experiments, including all receiver and recorder settings for the whole antenna network, and the observation time schedule. The participating stations extract all relevant information from the VEX file using the Field System program drudg.
Drudg creates station-specific control files which contain all required commands to run the experiment fully automated by the Field System, including antenna motion control, calibration routines, and the setup of the signal chain. Only one major modification from this standard procedure was required to enable satellite tracking: Prior to satellite scans, the tracking mode of the ACUs had to be manually switched over from the star tracking mode, which is used per default for astronomical sources, to the AZEL tracking mode described in Section 2.
These setup changes had to be done individually for all observing antennas. Manually changing the tracking mode only affected the antenna motion control, while the signal chain was still controlled by the Field System based on the setup parameters defined in the VEX file. To incorporate these additional steps, about 5 min of idling time was defined in the observation schedules prior and after APOD tracking.
Our goal was to stay as close as possible to the processing scheme that is operationally applied for geodetic VLBI sessions. As a result, standard VLBI delay models e. In our study, we need modeled near-field delays for APOD at two stages: 1 for the correlation a priori delays—the so-called correlator input model—and 2 for the data analysis, which is discussed in Section 5.
For the delay computation, we used VieVS 3. The implemented formalism is described in [ 37 ]. Near-field delays are calculated in the geocentric celestial reference system GCRS , taking into account gravitational effects of bodies within our solar system. The initial ITRF station positions were corrected for various tidal and non-tidal effects, as is common in VLBI processing, to obtain the most accurate values for the actual observation epochs.
As described earlier Section 2. The orbit data were provided as position and velocity time series in 1 s intervals in the WGS84 system, which were then interpolated in VieVS by 9th-order Lagrange polynomials. Fifth-order polynomials valid over 30 s were fitted to the time series of geocentric delays calculated in VieVS. For more details on the practical implementation in VieVS, we refer to [ 22 ]. The data were first correlated using the DiFX 2. A first correlation of the quasar signals was made to establish the clock model using a standard approach with the HOPS package. This initial correlation used a 1 s integration time and a spectral resolution of Yarragadee was chosen as the reference station and the a priori clock model of Hobart and Katherine were established from strong detections selected from quasar scans across the duration of the experiment.
These scans were correlated at a fine spectral resolution of 1 kHz and a 0. Detailed investigations give us confidence on the consistency between quasar and APOD data. There are no intrinsic differences between the data. All data follows identical observing configuration with no changes to the analog pathway. Zoom-bands as implemented in DiFX do not cause any systematic differences. Figure 4 and Figure 5 show the magnitudes of the auto-spectra of Scans and in Experiment a for all zoom-band channels in the S- and X-bands, respectively. The signal magnitudes in the S-band are much smoother and more constant over time compared to the X-band.
Presumably, these perturbations are caused by tracking inaccuracies caused by the low quality of the predicted APOD orbits, which were used to calculate the tracking data, and potential deficiencies of the AZEL tracking mode of the ACU see Section 3. Auto-spectrum magnitudes of the S-band zoom-bands of Scans upper panels and lower panels of Experiment a The frequency axes horizontal axes depict the five 32 kHz wide DiFX zoom-bands described in Table 3 next to one another.
The time axes indicate seconds since the start of Scan UTC. Auto-spectrum magnitudes of the X-band zoom-bands of Scans upper panels and lower panels of Experiment a The cross correlation spectra depicted in Figure 6 S-band and Figure 7 X-band show a similar pattern in the magnitude: again, magnitudes in the S-band are more stable over time compared to the X-band. Cross-spectrum magnitudes left column and phases right column of the S-band zoom-bands of Scans upper panels and lower panels of Experiment a The frequency axes horizontal axes depict the five 32 kHz wide DiFX zoom-band described in Table 3 next to one another.
Cross-spectrum magnitudes left column and phases right column of the X-band zoom-bands of Scans upper panels and lower panels of Experiment a The a priori delay model used for correlation was not accurate enough to stop phase wrapping due to residual delay rate, as evident from the phase plots in Figure 6 , Figure 7 and Figure 8. Due to the smaller wavelength, the phases wrap about four times faster in the X-band, limiting the integration time to 0. Cross-spectrum magnitudes left column and phases right column of the S-band Carr S , upper panels and X-band Carr X , lower panels carrier tones of Scan of Experiment a The time axes horizontal indicate seconds since the start of Scan UTC.
All fringe fittings of the APOD data used the zoom-bands as an input.