## 3 Results
### Experimental Data and its Preprocessing  
To verify the feasibility of the proposed carrier phase differentiation method, the officially released GOCE Level 1b and SST_PSO_2 products [36; 37] for 71 days (from November 1 2009 to January 11 2010) with a 1 s sampling interval were used first for testing. The data period was in accordance with the period used for the computation of the first-generation gravity field model released by the GOCE High-Level Processing Facility [38]. The SST_PSO_2 product contains the kinematic orbits (SST_PKI_2), reduced-dynamic orbits (SST_PKD_2), and the Earth's orientation quaternions (SST_PRM_2). The SST_PRM_2 data are used to transform accelerations from an Earth-fixed reference frame to an inertial reference frame. The accuracy of the GOCE satellite official scientific orbit data over the entire mission was up to 2 cm in each direction, i.e., nearly 3.5 cm in three dimensions [39]. For the carrier phase differentiation method, the time of all of the used data was synchronized by interpolation to coincide with the time of the original carrier phase observations. For the orbit differentiation method, the time of all data used for gravity field modeling was synchronized by interpolation to coincide with the time of raw kinematic orbits. For the orbit differentiation method, three kinematic orbits were used for gravity field modeling. One was the released SST-PKI-2 product by ESA, hereafter denoted as the ESA-orbit. The other was provided by the Institute of Theoretical Geodesy and Satellite Geodesy, Graz University of Technology [40], hereafter denoted as the Graz-orbit. The third was the kinematic orbit estimated by our own product, hereafter denoted as the SGG-orbit. In addition, the background force models used for computing the time-variable accelerations (e.g., third-body accelerations, tidal accelerations, and relativistic effects) are listed in Table 2.  
PKI orbits are normally used to recover the Earth's gravity field because they are independent of a priori gravity field models [39]. However, due to the geometric conditions of GPS satellites, some data gaps or lower quality data always exists in the PKI orbits. The number of the data gaps for the three PKI orbits and carrier phase derived accelerations for 71 days is shown in Table 3. The data derived by the carrier phase differentiation method included more data gaps than other methods. In addition, we subtracted reference accelerations computed with the model DGM-1S [41] from the differential accelerations to obtain residual accelerations. Then, the residual accelerations exceeding three times the corresponding standard deviations were identified as outliers and discarded according to the method used in [PERSON] et al. [25]. The corresponding standard deviations were estimated based on the method with five iterations, and they were 1.12, 0.81 and 1.90 mGal, respectively, for the three components of the carrier phase-derived accelerations. These values were also used for the gross error detection for the other three methods. The gross error ratios of the accelerations derived from four different methods are shown in Table 3. According to Table 3, the least number of gross errors in accelerations was obtained from the carrier phase method. Figure 1 shows the spatial distribution of gross errors in the residual accelerations in three directions (radial, along-track, and cross-track) derived by the carrier phase differentiation method and the orbit differentiation method. More gross errors and large errors were located close to the geomagnetic poles in the case of both the carrier phase differentiation method and the orbit differentiation method. Furthermore, the radial residual accelerations were noisier than the other two components, which is consistent with the results presented in Table 4.