**1. Introduction**

The use of Global Navigation Satellite Systems (GNSS) data is well established for a range of professional and scientific applications, including atmospheric research. Precipitable Water Vapor (PWV) can be derived from radiosonde measurements, but also estimated with GNSS phase measurements processing techniques [1]. Zenith Tropospheric Delays (ZTDs) are estimated along with other parameters, such as the station position and receiver clock offset. The estimated ZTD is related to the refractive index of air, it can be used directly in atmospheric models, or ZTD can be used to estimate PWV. These values are of essential interest for accurate short-term weather forecasts.

The use of cost-efficient GNSS equipment is of great scientific interest to meteorology and atmospheric research. Traditionally, atmospheric research and meteorology made use of already existing GNSS infrastructures which were set-up for surveying and geodetic applications. Therefore, low-cost GNSS equipment can be a good solution for regions where (commercial) high grade equipment is not readily available.

Analysing ZTDs or PWV from GNSS receivers has proven to be a valuable tool for analysing and forecasting extreme rainfall events [2]. Nowadays Numerical Weather Prediction (NWP) models exist that use these parameters in their data assimilation schemes to improve their rainfall predictions [3]. To estimate ZTD at existing GNSS receivers on the ground, numerous Analysis Centers (ACs) apply techniques such as Double-Differenced (DD) processing of large GNSS networks, or, the stand-alone Precise Point Positioning (PPP) technique [4]. In contrast to network or relative positioning strategies in general, PPP uses undifferenced GNSS observations and relies on precise satellite clock and positions to be available from the International GNSS Service (IGS). Dual-frequency observations are used to form the ionosphere-free linear combination, which removes the majority of the error associated with the delay in the ionosphere layer, but increases the noise by a factor of 3 [5]. In the past, estimating ZTD for meteorological purposes using cost-efficient equipment was only possible with single-frequency receivers, which required interpolation of the ionospheric delay from a network of dual-frequency receivers (e.g., References [6,7]). Recently, also low-cost dual-frequency receivers became available, which in combination with low-priced antennas, inspired the experiment in this paper. This experiment aims to investigate the potential use of low-cost dual-frequency receivers for ZTD estimation, something that was formerly only possible using expensive receiver equipment, or relied on existing geodetic networks to perform corrections. For this experiment different quality antennas, ranging from geodetic to mass-market, are deployed consecutively on a short-baseline. The new low-cost design of the receiver supplemented by a low-cost antenna may enable the cost-efficient estimation of high-quality tropospheric delays.

For high-precision applications, both satellite and receiver antenna corrections need to be applied [8]. These corrections are not only frequency dependent, but they also depend on the azimuth and elevation of the transmitting satellite. The delay caused by the antenna and the near field environment is not the same in every direction. Neither is it possible to find, for a specific frequency, a single point in the antenna for which the delay is the same for every direction. Therefore, a geometric center is something that does not really exists, and concepts like Antenna Phase Center (APC) are only approximate. These variations in antenna delay cause errors in the horizontal and vertical position, but also in the ZTD estimation. In order to correct the carrier phase signals for this effect, antenna calibrations are performed. The result of an antenna calibration is represented by a Phase Center Offset (PCO) with respect to a chosen Antenna Reference Point (ARP), and azimuth- and elevation dependent Phase Center Variations (PCV) with respect to the PCO. PCV and PCO corrections are provided per frequency. They are not independent, and should always be used together in high-precision positioning applications. Applications that require less precision can use only PCO values. On the other hand, for ZTD estimation, the PCO values are not important, and only the PCV values matter.

To obtain PCO and PCV corrections, relative and absolute antenna calibrations can be used. Absolute calibrations are typically expensive and involve sending the antenna to a calibration facility, while a relative calibration can be performed more easily by yourself. The relative calibration is performed over a short baseline, with on one side the antenna to be calibrated, and on the other side a reference antenna that has already been calibrated before (see e.g., Reference [9]). Double-differenced carrier phase residuals are used to compute the relative pattern between the antenna's. It uses the fact that over short baselines for DD observations most errors (e.g., satellite clock and atmospheric delays) are eliminated. The drawback of this calibration method is that it is a relative calibration. Since 2006 [10] it has been common for geodetic applications to use absolute antenna calibrations. Therefore, to obtain an absolute calibration for our antenna, we must add the absolute calibration for the reference antenna to the relative calibration. Absolute calibrations are typically obtained from measurements in an anechoic chamber (see e.g., Reference [11] or Reference [12]) or robotic field calibrations (see Reference [13]). Robotic calibrations have the advantage that they are not affected by multipath effects as in a relative correction.

While high quality geodetic antennas are typically manufactured with highest precision to enable the repetition of phase patterns on the receiving phase center, this is only partially the case for low-cost antennas. Companies specialized in antenna calibrations, such as Geo++ [14] in Germany, generate individual absolute antenna calibrations for geodetic antennas. Absolute antenna calibrations are typically supplied in an Antenna Exchange Format (ANTEX) file [15] that contains PCO as well as azimuth- and elevation dependent PCV for different frequencies and satellite systems. Various individual calibrations of the same antenna type are averaged to type mean calibrations and distributed, such as by the IGS. Using these antenna patterns is a standard practice in geodesy and essential for high precision positioning and also for tropospheric delay estimations. Several studies were performed that compare the differences between type mean and individual antenna phase center calibrations for example, by Araszkiewicz and Völksen (2016) [16], Schmid et al. 2005 [17] and Sidorov and Teferle 2016 [18]. They found a typical difference of only 2 mm horizontal and up to 4 mm vertical between type mean and individual antenna calibrations. For one antenna an offset of up to 17 mm in the vertical and 10 mm in the horizontal direction was observed. The vertical positioning performance gives an indication about the accuracy of the troposphere estimations since both parameters are correlated [19]. Only few studies were performed that analyze the impact of the antenna PCV on tropospheric parameter estimations. Ejigu et al. 2018 [20] investigated the impact of individual and type mean calibrations on Zenith Wet Delays (ZWDs) and tropospheric gradients [21]. They report a mean ZWD bias of 1.8 mm. A study by Pacione et al. 2017 [22] demonstrate similar results with ZTD errors in the mm range between utilizing individual and type mean calibrations.

The low-cost GNSS chips, being affordable and produced for the mass-market, are also of interest for scientific applications, but this only makes sense if also a low-cost antenna can be used. Geodetic antennas are generally characterized by special manufactured designs (e.g., choke ring) to suppress multipath induced effects. With low-cost antennas this is typically not the case. An analysis of low-cost antennas is especially important since they are expected to be particularly prone to multipath effects that are reflected in the antenna phase patterns.

In this paper we investigate the PPP ZTD performance of a recently introduced low-cost dual-frequency receiver connected to antennas of ranging quality (geodetic to mass-market) with and without applying relative antenna calibrations. Additionally, using L1-only data we investigate how well the (un-)corrected single-frequency data from the dual-frequency receiver can be used for meteorological applications. This is achieved by trimming the original data to L1-only datasets and generating a second frequency observation with the Satellite-specific Epoch-differenced Ionospheric Delay (SEID) model which is adjusted to the ionospheric delay based on a surrounding dual-frequency network. The paper is structured as follows—Section 2 describes the methodology, experimental setup and data analysis, Section 3 illustrates the PPP-derived ZTD results, Section 4 the discussion and Section 5 the conclusion.
