## 1 Introduction
The antenna, but also the utilized ground plane, can influence the  
Figure 1: Schematic illustration of Antenna Reference Point (ARP, black star symbol), Antenna Phase Center (APC, filled circles), lines of constant phase (solid colored lines), and spheres around APC points (dashed lines) on \(L_{1}\) (blue) and \(L_{2}\) (red). The Phase Center Variations (PCVs, thick colored lines between the spheres around APC and line of constant phase) are shown as functions of the elevation f(el) on the respective frequency. phase characteristics. Tests with different ground planes were conducted, e.g., by [9] or [10]. By combining multiple individual calibrations of the same antenna model, type-mean calibrations can be generated. These calibrations are publicly available for an increasing number of geodetic antennas, e.g., by the International GNSS Service (IGS; [11]). With the advent of low-cost receiver and antenna setups for positioning or tropospheric delay analysis, there is a need for the calibration of low-cost antennas. A recent study by [12] found high PCVs of up to 2 cm on L1 and 4 cm on L5 after performing an absolute antenna calibration with a robotic arm using a Huawei Mate20X dual-frequency smartphone. The study by [13] designed a 3D displacement detection test with a u-blox ZED F9P receiver with ANN-MB-00 low-cost antennas and found minimum detectable displacements of 10 mm upwards. Calibrating low-cost antennas is essential to improve their performance, yet individual calibrations are not available for free for such antennas and the calibration, e.g., by a robot, is costly and contradicts the idea of low-cost solutions. A low-cost solution is needed to fully exploit the potential of high-precision positioning applications using low-cost receiver and antenna setups for users of different disciplines (surveying, mapping of rivers, ground control points, or atmosphere monitoring). This study uses a low-cost dual-frequency receiver (u-blox ZED F9P) together with antennas of different quality in the price range of 50 to 1000+ Euros. A relative antenna calibration [4] is performed. The assumption is that if two antennas with the same antenna phase pattern are used, these effects cancel out over a short baseline. Using different antennas for base and rover results in differences that are reflected in the estimated residuals. The obtained relative calibrations are converted to absolute ones by using a base station antenna with known antenna calibration. The presented antenna calibration tool is made available online under [[https://gnss-antcal.citig.tudelft.nl](https://gnss-antcal.citig.tudelft.nl)]([https://gnss-antcal.citig.tudelft.nl](https://gnss-antcal.citig.tudelft.nl)) (accessed on 9 February 2022). It allows users to calibrate their own antenna in the field, provided that a base antenna with known calibration is utilized. The presented method is relying fully on low-cost solutions. It does not require costly software, uses low-cost equipment (about 500 Euros), and provides an inexpensive solution for calibration. The only necessity is access to an antenna for which the antenna calibration parameters are known (e.g., type-mean calibrations from the IGS ANTEX file), or an already individually calibrated antenna for the base station. This can be achieved either by performing the calibration near an already established base station, e.g., a Continuously Operating Reference Station (CORS), or by renting, borrowing, or purchasing a high-grade calibrated antenna for a few days. This opens a wide range of new application domains, especially since this can be done with little or no expertise because complex processing steps are taken into the cloud. Performance of in-field calibrated low-cost receiver and antenna setups is demonstrated using static Precise Point Positioning (PPP) and Post Processed Kinematic (PPK) processing. The presented solution can be particularly interesting for areas where high-precision positioning is not available or application remains limited due to high costs.