**1. Introduction**

The correct calibration of global navigation satellite system (GNSS) antennas is the basis for precise satellite positioning and plays a key role in many aspects of positioning and navigation [1,2]. In general, GNSS antennas have a well-defined antenna phase centre (APC, Figure 1) and should be described by the azimuth (α) and elevation (β) functions [3]. The APC determined by phase centre variation (PCV) is a shift in position depending on the observed elevation angle and azimuth with regards to the satellite [4]. The antenna reference point (ARP) is a physical point where the antenna height above the physical point is measured [5]. The antenna phase centre offset (PCO) is the difference between the ARP and the mean electrical APC defined by the intersection of the vertical antenna axis of symmetry with the bottom of the antenna [6]. The combination of PCO and PCV is called phase centre corrections (PCC).

**Citation:** Borowski, L.; Kudrys, J.; Kubicki, B.; Slámová, M.; Maciuk, K. Phase Centre Corrections of GNSS Antennas and Their Consistency with ATX Catalogues. *Remote Sens.* **2022**, *14*, 3226. https://doi.org/10.3390/ rs14133226

Academic Editors: José Fernández, Juan F. Prieto and Serdjo Kos

Received: 6 June 2022 Accepted: 2 July 2022 Published: 5 July 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Figure 1.** A phase shift due to antenna model change.

Depending on the accuracy and quality of solutions needed to be achieved, absolute and relative antenna calibration models are used. For many years, relative phase centre corrections were made based on measurements on a short baseline referred to as a reference antenna (The Dorne Margolin T of Allen Osborne Associates antenna—AOAD/M\_T), with the arbitrary assumption that the PCV of the reference antenna is zero [7,8]. Absolute correction for an antenna can be obtained either by measurement in an anechoic chamber [9] or by field measurements on a short baseline using a robot mount [10].

As the research shows, the problem of the antenna calibrations is not new, but it still experiences issues with proper assumptions regarding calibrations and the correctness of calculations. Different antenna calibration models impact, among other things, estimated station positions. Some empirical research tests show a relative vertical offset exists with the same model of antennas of up to 1 mm, while horizontal offsets are negligible [11]. The research conducted by Baire et al. showed agreement to the level of 2 mm in the case of horizontal offsets and 5 mm in the case of the height component based on daily static Precise Point Positioning (PPP) sessions [3]. A variety of studies have been conducted for the establishment of new calibration methods, e.g., [11–14]. The differences in model calibrations between the robot and anechoic chamber have an impact on the coordinates: up to +/− 2 mm for the horizontal and +/− 10 mm for the height component [15]. Over 10 mm of the height component difference occurs when individual antenna corrections by GEO++ are comparable to igs08.atx [16]. Moreover, in specific conditions, it is worth considering the impact of other environmental phenomena, such as multipath interference [17,18], antenna mounting [19,20], the near-field effect, or seasonal snow cover [21]. Analyses performed for EUREF permanent network (EPN) stations show that the change to the new catalogue of absolute calibration models (from IGS08.ATX to IGS14.ATX) might have an impact on stations' coordinates. Phase centre corrections (PCC) are an integral part of high accuracy GNSS applications [22]. The research showed on more than 40 PCC models that the magnitudes of the PCO shifts among different versions of the antenna files (Antex) were above 1 mm [23]. The differences between the antenna model (mean) and the individual PCC may cause a discrepancy of 10 mm for the horizontal and vertical components, but this does not usually exceed 2 mm for the horizontal and 4 mm for the vertical ones [24].

Based on this knowledge, an analysis of the selected antenna models, TRM57971.00 NONE and ASH70195C\_M SNOW, was performed. These antennas are used on EPN's KRA1 (TRM57971.00 NONE) and KRAW (ASH70195C\_M SNOW) stations (Kraków, Poland). The stations are located close to each other (3.5 m), which is a convenient situation for the verification of their individual characteristics by comparison to the catalogue ones. The study consisted of several analyses. The first was focused on differences of the studied models in the igs08.atx and igs14.atx catalogues. The second was the difference in height between the antenna ARP, as calculated by different satellite methods. Additionally, height differences were referenced to the auxiliary stations (KR01 and KR02) and to precise spirit levelling. The third analysis gathered archival material based on several experiments that have been conducted since 2011.
