**2. Methods**

Our experiment includes several steps to estimate the impact of different quality antennas on the ZTD performance using a low-cost dual-frequency receiver. The fundamental step upon which our investigation is based is a short-baseline analysis to perform a relative antenna calibration. Thereafter, different relative antenna calibration results are evaluated using the ZTD from two different PPP experiments. The experimental setup and overview of the data analysis procedure are described in Sections 2.1 and 2.2. The antenna calibration procedure is explained in Section 2.3. Section 2.4 describes the evaluation of the ZTD estimations with dual-frequency data in more detail. The antenna calibration impact on single-frequency data is covered in Section 2.5.

#### *2.1. Experimental Setup*

This subsection describes the test site, instrument setup, data handling as well as the receivers and antennas that were used in the experiment.

Our experiment consists of a series of consecutive short-baseline experiments using the International GNSS Service (IGS) station DLF1 as a base station and a U-blox ZED-F9P as rover. The DLF1 station is located on the rooftop of the Nederlands Metrology institute (NMi) in Delft. The station uses a Trimble NetR9 receiver, capable of tracking most GNSS signals, with a Leica AR25.R3 (LEIAR25.R3) chokering antenna with LEIT radome. The antenna has been calibrated by Geo++. The antenna is installed on the permanent marker with DOMES number 13502M009.

The rover receiver is an engineering sample of recently released low-cost dual-frequency receivers, that was obtained from the manufacturer for testing purposes. It covers the following frequencies: GPS L1C/A, L2C, GLONASS L1OF, L2OF, Galileo E1, E5b and BeiDou B1l, B2l and QZSS L1C/A, L2C. Notably missing GNSS signals are GPS L2P/Y, GPS L5 and Galileo E6. However, with the new generation GPS satellites, the L2C signal becomes rapidly available on almost all satellites and enables obtaining dual-frequency measurements from an increasing number of available GPS satellites. With up to 184 channels available, the receiver is capable of tracking two frequencies on each of the described satellite constellations and is still able to receive correction service data from augmented GNSS (e.g., Reference [23]).

The antennas of the rover are placed on a geodetic marker at a horizontal distance of approximately 10 m and 1.5 m height difference from DLF1. Different antenna types have been installed during consecutive periods from 15 February 2019 onwards. The investigated rover antennas cover a range of prices, starting with the lowest cost antennas U-blox ANN-MB-00 and Taoglas AQHA50 between about 50 and 100 euros, the middle price segment antennas Trimble AV28 and Trimble GA530 and antennas with a price of above 1000 euros, LEIAR25.R3 LEIT and TRM55971.00 NONE (also known as Trimble Zephyr 2 Geodetic). For these antennas, the mount point DOMES 13502M003 (GPS Mark 15) is used (Figure 1b). The antennas with hole-mount design (Trimble AV28) and without screw-hole at the bottom (U-blox ANN-MB-00) are mounted on top of a metallic rectangular extension bracket and also with a circular metallic ground plane with 10 cm diameter. For the other tested antennas, a tribrach with an adjustable circular level is used. The receiver itself is placed in a pelican case in the proximity and data logging is performed with a Raspberry Pi Zero on a local SD card (Figure 1a). Depending on weather conditions and observation time, antennas are switched after at least having recorded three full days of raw data. Data is transferred manually from the SD card for post-processing purposes.

The installation environment (regarding near-field effects and multipath) can be regarded as relatively clean. Both antenna positions (DLF1 and GPS Mark 15) are characterized by an unobstructed view over the full horizon. The time frame of antenna placements is depicted in Table 1. All antennas are active and, depending on the type, require different voltage as input. The antennas GA530, LEIAR25.R3 and TRM55971.00 require 12 V input voltage which cannot be supplied by the Raspberry Pi. Instead, the antennas are powered by a Septentrio receiver and the antenna signal is split to the U-blox ZED-F9P. The other antennas are working with voltage at or below 5 V that is supplied via the USB port of the Raspberry Pi and is considered as stable.

**Figure 1.** Waterproof pelican box rover equipment on the ground next to the marker (**a**). The pelican box contains the U-blox ZED-F9P, a Raspberry Pi Zero for data logging, power and a Septentrio receiver. The Septentrio receiver is used to provide power, through an antenna splitter, to the antennas: LEIAR25.R3 (**b**), Zephyr2 (**c**) and GA530 (**d**). No data collection or processing is performed with the Septentrio receiver. The verification setup is depicted in (**b**). It shows the baseline setup with two LEIAR25.R3 LEIT antennas. The antenna in the foreground is at the marker that is used for the investigation. In the background the radome and antenna of the base station DLF1 is visible. Both antennas are oriented North. The subfigures (**b**–**f**) illustrate the marker used for the investigation with different installed antennas. The antennas AV28 (**e**) and ANN-MB-00 (**f**) are depicted with a circular plane.

**Table 1.** Time frame and antenna descriptions of the antenna placements on GPS Mark 15 for the short-baseline experiments.


The GA530 lost satellite tracking on L1 on 15 March 2019 17.23 UTC and one day later also L2 data was lost, presumably due to moisture in the antenna connector. Data from 15 March 2019 onwards is therefore discarded from the GA530 observations. The AQHA50 data was not processed due to very low Signal-to-Noise (SNR) ratio, despite free-sky conditions, which we were unable to resolve. After quick and uncomplicated communication with the manufacturer the antenna could be returned and a replacement was provided. It was, however, not examined further in this experiment because of time limitations and practical considerations. A power outage in the Delft region, in the morning of Monday 25 March 2019, ended the data tracking for the LEIAR25.R3 antenna. Except for the AQHA50 antenna, sufficient data have been recorded for the remaining antennas for the analysis. Details about the data logging and conversion can be found in Appendix A.

The data is analysed in post-processing, with DLF1 as base station, and the antennas under investigation as rover. The rover data is available as 1-s daily RINEX 3 observation files. For the base station data, high-rate (1 Hz) RINEX3 data from the IGS station DLF1 were downloaded. High-rate 15-min RINEX 3 DLF1 observations were merged into daily files. Broadcast navigation data from the satellites were collected from the Crustal Dynamics Data Information System (CDDIS) [24]. For simplicity reasons and driven by the fact that most antenna calibrations are available for GPS, we used GPS-only data for our analysis.

### *2.2. Antenna Calibration and ZTD Evaluation Procedure*

This subsection aims to provide a general overview of the antenna calibration and ZTD evaluation procedure. The experiment basically follows the steps illustrated in Figure 2. First, the antenna calibration is performed by retrieving residuals in a short baseline experiment, for which errors caused by the troposphere and ionosphere delays can be safely neglected. The original L1 + L2 RINEX data of base and rover were processed in RTKLIB, in static mode, to obtain the carrier phase residuals for each frequency, as well as azimuth (az) and elevation (el) angles of the corresponding satellites. The residuals, that can be considered as relative PCVs, together with IGS ANTEX type mean PCVs of the base station antenna (LEIAR25.R3 LEIT), were processed to create absolute PCVs which are saved in new ANTEX entries for each rover antenna. Details on the antenna types used in the experiment are provided in Table 1.

**Figure 2.** Steps in the Zenith Tropospheric Delay (ZTD) evaluation procedure. The top central box illustrates the short baseline with base station (DLF1) on the left and rover on the right. The base station DLF1 uses a Trimble NetR9 receiver and LEIAR25.R3 LEIT antenna, which did not change during the time frame of our experiment. The rover is illustrated on the right, with an U-blox ZED-F9P receiver and five antenna types applied consecutively.

Subsequently, the L1 + L2 RINEX data from the rover antennas, with the new ANTEX entries, were processed in goGPS (PPP-mode) to obtain absolute ZTD estimations. The obtained set of ZTD estimations for the low-cost receiver and different antennas was compared against the IGS final ZTD estimations by the US Naval Observatory (USNO) based on Bernese 5.2 in PPP mode from the IGS station DLF1. Further details on the antenna calibration and ZTD estimation procedures can be found in the following subsections.
