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ETH Zurich developed an absolute GNSS antenna calibration system based on measurements taken in the field. An industrial robot is used to rotate and tilt the antenna to be calibrated. This procedure ensures good coverage of the antenna hemisphere and reduces systematic errors. The calibration system at ETH Zurich is validated by a direct comparison of the obtained calibrations with calibrations from the anechoic chamber method (University of Bonn) and from another absolute field calibration method (Geo++® GmbH). Calibrations by ETH Zurich agree on the sub-millimeter level with both reference calibrations. A second validation was conducted using real measurements on short baselines. Data were acquired on four stations in direct vicinity and processed using different phase center correction models. The experiment shows that individual corrections of ETH Zurich reduce the residuals in the coordinate domain when compared to type-mean calibrations of the International GNSS Service (IGS). However, residual biases between GPS and Galileo coordinates remain. These biases are efficiently reduced when using the new type-mean calibrations from the IGS that include calibration values for all GNSS, including Galileo. The ETH Zurich calibration system is proven to deliver meaningful calibrations that agree with other calibrations on the millimeter level in the azimuth and elevation domain. The field validation shows evidence that the consistency of the Galileo and GPS calibration should be further enhanced by performing a combined GPS and Galileo analysis, which is not yet implemented.

In 2016, an application programming interface was added to the Android operating systems, which enables the access of GNSS raw observations. Since then, an in-depth evaluation of the performance of smartphone GNSS chips is very much simplified. We analyzed the quality of the GNSS observations, especially the carrier phase observations, of the dual-frequency GNSS chip Kirin 980 built into Huawei P30 and other smartphones. More than 80 h of static observations were collected at several locations. The code and carrier phase observations were processed in baseline mode with reference to observations of geodetic-grade equipment. We were able to fix carrier phase ambiguities for GPS L1 observations. Furthermore, we performed an antenna calibration for this frequency, which revealed that the horizontal phase center offsets from the central vertical axis of the smartphone and also the phase center variations do not exceed 1–2 cm. After successful ambiguity fixing, the 3D position errors (standard deviations) are smaller 4 cm after 5 min of static observation session and 2 cm for long observation session.

The access to Android-based Global Navigation Satellite Systems (GNSS) raw measurements has become a strong motivation to investigate the feasibility of smartphone-based positioning. Since the beginning of this research, the smartphone GNSS antenna has been recognized as one of the main limitations. Besides multipath (MP), the radiation pattern of the antenna is the main site-dependent error source of GNSS observations. An absolute antenna calibration has been performed for the dual-frequency Huawei Mate20X. Antenna phase center offset (PCO) and variations (PCV) have been estimated to correct for antenna impact on the L1 and L5 phase observations. Accordingly, we show the relevance of considering the individual PCO and PCV for the two frequencies. The PCV patterns indicate absolute values up to 2 cm and 4 cm for L1 and L5, respectively. The impact of antenna corrections has been assessed in different multipath environments using a high-accuracy positioning algorithm employing an undifferenced observation model and applying ambiguity resolution. Successful ambiguity resolution is shown for a smartphone placed in a low multipath environment on the ground of a soccer field. For a rooftop open-sky test case with large multipath, ambiguity resolution was successful in 19 out of 35 data sets. Overall, the antenna calibration is demonstrated being an asset for smartphone-based positioning with ambiguity resolution, showing cm-level 2D root mean square error (RMSE).

The recent release of consumer-grade dual-frequency receivers sparked scientific interest into use of these cost-efficient devices for high precision positioning and tropospheric delay estimations. Previous analyses with low-cost single-frequency receivers showed promising results for the estimation of Zenith Tropospheric Delays (ZTDs). However, their application is limited by the need to account for the ionospheric delay. In this paper we investigate the potential of a low-cost dual-frequency receiver (U-blox ZED-F9P) in combination with a range of different quality antennas. We show that the receiver itself is very well capable of achieving high-quality ZTD estimations. The limiting factor is the quality of the receiving antenna. To improve the applicability of mass-market antennas, a relative antenna calibration is performed, and new absolute Antenna Exchange Format (ANTEX) entries are created using a geodetic antenna as base. The performance of ZTD estimation with the tested antennas is evaluated, with and without antenna Phase Center Variation (PCV) corrections, using Precise Point Positioning (PPP). Without applying PCVs for the low-cost antennas, the Root Mean Square Errors (RMSE) of the estimated ZTDs are between 15 mm and 24 mm. Using the newly generated PCVs, the RMSE is reduced significantly to about 4 mm, a level that is excellent for meteorological applications. The standard U-blox ANN-MB-00 patch antenna, with a circular ground plane, after correcting the phase pattern yields comparable results (0.47 mm bias and 4.02 mm RMSE) to those from geodetic quality antennas, providing an all-round low-cost solution. The relative antenna calibration method presented in this paper opens the way for wide-spread application of low-cost receiver and antennas.

In 2019, the University of Warmia and Mazury in Olsztyn, in cooperation with Astri Polska, started a European Space Agency (ESA) project. The purpose of the project is the development and implementation of a field calibration procedure for a multi-frequency and multi-system global navigation satellite system (GNSS). The methodology and algorithms proposed in the project are inspired by the “Hannover” concept of absolute field receiver antenna calibration; however, some innovations are introduced. In our approach, the antenna rotation point is close to the nominal mean phase center (MPC) of the antenna, although it does not coincide with it. Additionally, a National Marine Electronics Association local time zone (NMEA ZDA) message is used to synchronize the robot with the GNSS time. We also propose some modifications in robot arm movement scenarios. Our first test results demonstrate consistent performance for the calibration strategy and calibration procedure. For the global positioning system (GPS) L1 frequency, the calibration results show good agreement with the IGS-type mean values. For high satellite elevations (20°–90°), the differences do not exceed 1.5 mm. For low elevation angles (0°–20°), the consistency of the results is worse and the differences exceed a 3 mm level in some cases.

Low-cost dual-frequency receivers and antennas have created opportunities for a wide range of new applications, in regions and disciplines where traditional GNSS equipment is unaffordable. However, the major drawback of using low-cost antenna equipment is that antenna phase patterns are typically poorly defined. Therefore, the noise in tropospheric zenith delay and coordinate time series is increased and systematic errors may occur. Here, we present a field calibration method that fully relies on low-cost solutions. It does not require costly software, uses low-cost equipment (~500 Euros), requires limited specialist expertise, and takes complex processing steps into the cloud. The application is more than just a relative antenna calibration: it is also a means to assess the quality and performance of the antenna, whether this is at a calibration site or directly in the field. We cover PCV calibrations, important for deformation monitoring, GNSS meteorology and positioning, and the computation of PCOs when the absolute position is of interest. The method is made available as an online web service. The performance of the calibration method is presented for a range of antennas of different quality and price in combination with a low-cost dual-frequency receiver. Carrier phase residuals of the low-cost antennas are reduced by 11–34% on L1 and 19–39% on L2, depending on the antenna type and ground plane used. For the cheapest antenna, when using a circular ground plane, the L1 residual is reduced from 3.85 mm before to 3.41 mm after calibration, and for L2 from 5.34 mm to 4.3 mm. The calibration reduces the Median Absolute Deviations (MADs) of the low-cost antennas in the vertical direction using Post Processed Kinematic (PPK) by 20–24%. For the cheapest antenna, the MAD is reduced from 5.6 to 3.8 mm, comparable to a geodetic-grade antenna (3.5 mm MAD). The calibration also has a positive impact on the Precise Point Positioning (PPP) results, delivering more precise results and reducing height biases.

Performing the high-precision Global Navigation Satellite System (GNSS) applications with low-cost antennas is an up-and-coming research field. However, the antenna-induced phase biases, i.e., phase center corrections (PCCs), of the low-cost antennas can be up to centimeters and need to be calibrated in advance. The relative field antenna calibration method is easy to conduct, but the classical procedure entails integer ambiguity resolution, which may face the problem of low success rate under the centimeter-level PCCs. In this contribution, we designed a relative field calibration method suitable for the low-cost GNSS antennas. The triple-differencing operations were utilized to eliminate the carrier-phase ambiguities and then construct PCC measurements; the time-differencing interval was set to a relatively long time span, such as one hour, and the reference satellite was selected according to the angular distance it passed over during a time-differencing interval. To reduce the effect of significant triple-differencing noise, a weight setting method based on the area of a spherical quadrilateral was proposed for the spherical harmonics fitting process. The duration of the data collection with respect to GPS and BDS was discussed. The performance of the proposed method was assessed with real GPS and BDS observations and a variety of simulated phase patterns, showing that calibration results could be obtained with millimeter-level accuracy. The impact of cycle slip and elevation mask angle on the calibration results was also analyzed.

The Sentinel-6 Michael Freilich altimetry mission flies two GNSS receivers: a primary multi-GNSS (GPS plus Galileo) PODRIX receiver and a GPS-only TriG receiver. Each of these receivers is independently capable of supporting the precise orbit determination (POD) requirement for < 1.5 cm radial rms error. In this study, we characterize the performance of single-receiver solutions and evaluate the benefits of a combined TriG and PODRIX orbit solution. The availability of both sets of receiver observations revealed a 10 mm in-track difference between orbit solutions derived independently from TriG and PODRIX tracking data. Based on satellite laser ranging (SLR) residuals, this bias has been isolated to an apparent inconsistency between the estimated TriG receiver clock and observation time-tags of approximately 1.3  μ s , which is equivalent to a common range error of roughly 400 m in the TriG observations. After applying this calibration, the TriG and PODRIX displayed similar performance in terms of orbit overlap precision. PODRIX-Galileo observations showed lower code and phase tracking residual rms values compared to the GPS observations. Overall, processing the calibrated TriG and PODRIX observations separately results in highly accurate orbit solutions with radial orbit accuracies better than 1 cm rms as indicated by one-way SLR residual rms of 7.2 mm or better for each solution. Orbit solution accuracy is slightly improved by processing both TriG and PODRIX observations together, resulting in one-way SLR residual rms of 7.0 mm.

Information about satellite antenna phase center offsets (PCOs) is indispensable for high-precision applications of global navigation satellite systems. Pre-flight manufacturer calibrations of the PCOs are available for all individual Galileo satellites and each frequency. So far, geodetic usage of Galileo is focused on the ionosphere-free linear combination of the E1 and E5a signals. In view of the growing number of E5b- and E6-capable receivers and upcoming multi-frequency applications, the consistency of the PCO values for different frequencies becomes a topic of increasing importance. Galileo satellite antenna PCOs have been estimated from the ionosphere-free linear combinations of E1/E5a, E1/E5b, and E1/E6. The mean horizontal PCOs of the different frequencies agree on the few millimeter level. The X-PCOs show a bias of about 1 cm compared to the manufacturer calibrations, whereas the Y-PCOs are free of such a bias. The Z-PCOs have a systematic offset of - 11 to - 15 cm w.r.t. the manufacturer calibrations due to scale inconsistencies of the current version of the International Terrestrial Reference Frame (ITRF2020) and the manufacturer calibrations. The maximum Z-PCO difference between the various linear combinations amounts to 4 cm and provides a measure of the presently achieved consistency of ground and space antenna calibrations across different frequencies. This inconsistency would translate into height differences of about 1.6 mm and associated scale differences of the terrestrial reference frame of 0.25 ppb, when adjusting station coordinates with manufacturer calibrated Galileo PCOs for different frequency pairs.