## 1 Introduction
As with the anechoic chamber measurements, absolute field calibrations cannot be easily performed on a large scale. Before the introduction of the absolute field calibration method, the relative field calibration method was widely used for antenna calibration [12; 13; 14]. Compared with the absolute field calibrations, in the relative field calibrations, both the reference antenna and antenna under test are stationary, and collected signals may be incident from low-elevation directions, so a more open test field and some measures for suppressing the reflected signals from the ground are required [15]. Another distinct disadvantage is that since the coverage of the measurements in the antenna hemisphere depends on the distribution of the satellite trajectory, there is no measurement in some directions, namely, the north hole or the south hole. A compromise is to calibrate only the elevation-dependent phase center variations (PCVs) [12; 13; 15]. There are, however, some other studies increasing the coverage of observations in the antenna hemisphere by collecting observations for two or more sessions and horizontally rotating the antenna under test at the beginning of each session, thus enabling the acquisition of elevation- and azimuth-dependent PCVs with the relative field calibration [16]. It should be noted that the relative field calibration result of the antenna under test is relative to the reference antenna. Early researchers usually used a specific type of antenna (AOAD/M_T) as the reference antenna and assumed that the reference antenna was ideal [12; 13]. With the development of various antenna calibration techniques, subsequent studies often used an absolutely calibrated antenna as the reference antenna and then transformed the relative calibration results to absolute calibration results. [PERSON] et al. [17] used double-difference residuals to derive between-antenna single-difference residuals, which were used as measurements for antenna calibration. However, the prerequisite for this method to hold is that the antenna-induced phase bias obeys the Gaussian distribution with zero mean, and as this premise may not be true for low-cost antennas with centimeter-level PCCs, this method is not applicable to our research. In addition, there are also commercial softwares available for relative field calibration, such as Bernese GNSS software 5.2 [15; 16]. Overall, the relative field calibration is easy to implement, although it takes longer and is susceptible to interference. The International GNSS Service (IGS) maintains a widely used antenna calibration product. And it contains a variety of type-mean calibration results, which are the average of the calibration results of more than four antennas of the same specified type. As [PERSON] et al. [2] and [PERSON] et al. [18] have shown that for geodetic antennas used in permanent stations, there is only a difference of a few millimeters (mm) between the calibration results of antennas of the same type, the type-mean calibration results can be applied to eliminate most antenna-induced phase biases for high-grade antennas. However, for more widely used low-cost antennas, the difference between the antenna of same type is larger [19]; therefore, the low-cost antennas need individual calibrations. Since only a few institutions can perform the anechoic chamber antenna measurement, and even fewer can conduct the absolute field calibration [3; 20], the relative field calibration is an attractive choice to perform individual antenna calibrations on a large scale. Compared with geodetic antennas, the low-cost antennas hold larger PCCs, possibly up to centimeters (cm) [19], and most low-cost antennas are single-frequency; these characteristics can weaken the GNSS model and consequently affect the success rate of integer ambiguity resolution, which is usually an essential step in classical relative field antenna calibration approaches. To address this problem, we can either improve the performance of ambiguity resolution or simply avoid the ambiguity resolution procedure.