## 1 Introduction  
As it is well known, carrier phase observations, which undoubtedly play a dominant role in GNSS high precision applications, are generated between the antenna electrical phase centers of satellite and receiver. Ideally, the receiver antenna would act as a spherical phase response for GNSS signals [1]. However this is not true in most of cases due to the fact that the antenna electrical phase center is neither a physical or mechanical point that can be reachable by a real measurement tool, nor a unique well-defined one in the whole signal reception range [1,2]. Instead, the electromagnetic behavior of antennas is not homogeneous and the location of its phase center varies with different elevation and azimuth directions of the received signals [1, 2, 3, 4, 5]. The difference between the distorted real wave front and the perfect one causes phase measuring errors. The magnitudes of these unexpected phase measure errors (dependent on different receiver types) vary from a few millimeters up to several centimeters [3,6, 7, 8], which becomes one of the largest limiting factors to obtain cm- even mm-level high-precision positioning results [1,9]. The antenna electrical phase center can be defined as the absolute mean phase center offset (PCO) with respect to the antenna reference point (ARP) and the elevation and azimuth dependent phase center variations (PCVs) [3] (Figure 1). Neglecting antenna PCO and PCV correction will therefore lead to a significant position bias, especially in the height component (cm-level error), and result in an unreasonably large terrestrial scale bias in global GPS solutions with respect to results from Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) [3,9,10]. Furthermore, the tropospheric propagation delay error is not easily separated from the antenna phase center bias. Both of them vary with different elevations, and result in height biases when tropospheric zenith delays are estimated. These problems have been confirmed by many research groups, see [2,3,7,11,12]. Many international research groups in the last nearly two decades have succeeded in exploring several antenna phase center calibration approaches so as to solve the problems discussed above. The relative antenna PCO and PCV are firstly defined in field procedures based on a very short baseline with one reference antenna at one end and the one to be calibrated on the other end [2,3]. Although many antenna calibrations are performed relative to the same one, the relative calibration results reflect  
Figure 1: Antenna phase center description. somewhat station-specific errors, e.g., multipath errors. Then a calibration procedure in an \"absolute\" sense has been implemented to separate the antenna to be calibrated PCO and PCV independently of the reference antenna [4, 5, 13]. There is one thing that should be pointed out that if the reference antenna has been calibrated in another way (e.g., results from different calibration institutes or anechoic chambers), then the relative antenna PCO and PCV can be transited to absolute ones [14, 15]. Nevertheless, high precision anechoic chamber calibration results have demonstrated that the absolute field calibration using GNSS data can reach a good agreement at the 1-mm level with each other [1]. Absolute PCCs are required for state-of-the-art GNSS cm- or mm- level positioning applications to avoid the possible scale problem in the coordinate solutions and systematic station errors (especially in the height component), e.g., regional and worldwide permanent reference station networks, equipped with mixed receiver and antenna types. In November 2006, the elevation and azimuth-dependent PCC models, most of which derived from well-designed robot calibration systems, were recommended by IGS (IGSMAIL-5438 by [PERSON], 2006). Although there may exist different production series for one antenna type used in precise geodetic measurements, it was generally assumed that one geodetic antenna type has a quite stable and similar phase pattern.