## 1 Introduction  
Global Navigation Satellite Systems (GNSS) allow the determination of the 3D position of a point on the Earth's surface (constituted by its geodetic coordinates, i.e., longitude, latitude and altitude), by using the signal code and/or carrier phase and, therefore, measuring the distance (pseudorange) from the receiver antenna to the orbital position of at last four satellites within a certain time [1; 2; 3]. The main satellite constellations from which the antenna of the different GNSS receivers can receive the signals are GPS (Global Positioning System), operated by US Department of Defence and using 31 satellites; GLONASS (GLObal NAvigation Satellite System), operated by the Russian Federation and using 23 satellites; BeiDou, operated by China and using 49 satellites; EGNOS (European Geostationary Navigation Overlay Service), SBAS (Satellite-Based Augmentation System) developed by the European Space Agency (ESA) under the Galileo project and using 22 satellites; QZSS (Quasi-Zenith Satellite System) or MSAS (Multi-functional Satellite Augmentation System), SBAS operated by Japan and using 4 satellites. A GNSS to be used must be economically viable and, depending on the crop and on the cultivated area, achieve high values of precision and accuracy. The accuracy is the difference between the measured value of a quantity and the real one, so the positioning accuracy of a GNSS is the distance between the position of a point on the Earth's surface determined by this system and the real one [4]. The precision is, however, the statistical dispersion degree of computed data with reference to their mean, i.e., their standard deviation with reference to the mean of the sample [5]. GNSS can often determine the position of a point with a positioning accuracy which is better than 1 m, even if this accuracy can be improved through the reception of differential correction signals, in real time or in post-processing [4]. The process for achieving positioning accuracy up to one centimetre in GNSS involves a complex algorithm known as Real-Time Kinematic (RTK) or Dynamic processing [6]. RTK-capable receivers must be connected to precisely calibrated antennas, for processing the signals transmitted by GNSS satellites, and receive and process differential correction data from a ground network of stations [7] or from a single reference station. In fact, the EUREF Permanent Network (EPN), built up in 1996, is a science-driven network of GNSS Continuously Operating Reference Stations (CORS) covering Europe. The EPN, having the task of maintaining the European Terrestrial Reference System 89 (ETRS89), monitors the geodetic coordinates of its tracking stations with a level of accuracy of less than one centimetre [8]. A few years ago, RTK-capable receivers were expensive and bulky. Therefore, recently, GNSS receiver manufacturers have started marketing cheap and compact RTK-capable receivers [7]. Dual-frequency (L1/L2) GNSS receivers for geodetic surveying are able to achieve up to a one millimetre level of accuracy, but at the moment, they are expensive (at least $3700) [9]. Nowadays, survey-grade dual-frequency RTK-capable GNSS receivers must be used for determining a 3D trajectory with a level of accuracy of up to one centimetre during kinematic (RTK) applications, e.g., in precision agriculture, only for the control and guidance of agricultural machines. The majority of users have low-cost GNSS receivers, which are small and easy to handle and embed. These receivers are also capable of being used in RTK positioning mode with a level of accuracy of up to one centimetre. However, most low-cost receivers are only single frequency (L1). The open-source program package RTKLIB, that was developed by [PERSON] and [PERSON] [10], can be used by low-cost receivers for RTK mode [9]. To date, only very few researchers have focused on dynamic (RTK) applications of low-cost L1 frequency receivers, e.g., [PERSON] and [PERSON] [10].