## 3 Results
### Accuracy Analysis of the Integrated STP Pseudo-Observations
#### 3.1.2 Magnitude and Error of the a Priori Dynamic Models  
Because the a priori orbit error has an influence on computing the accelerations, its influence should be analyzed first. Here, we suppose the a priori orbit error \(\delta r\) is 3 m, which is worse than the accuracy of a GPS code orbit solution [39]. We only analyze the error (\(\delta a\)) in the computation of the Earth's center gravitation accelerations owing to the a priori orbit error, because its magnitude is far larger than the other forces. The error \(\delta a\) is \(\delta a\approx\frac{\delta}{r}\delta r\approx 5\times 10^{-6}\) ms\({}^{-2}<10^{-5}\) ms\({}^{-2}\), where \(g\approx 9.8\) ms\({}^{-2}\). Therefore, \(\delta a\) can be ignored, even for a sampling interval of 30 s. In addition, when a more precise a priori orbit is necessary, the iterative processing procedure can be applied (see Figure 2).  
Figure 3 shows the GOCE's accelerations from the known conservative force models except for the EGM, including luni-solar gravitation (DE405), ocean tide, solid Earth tide, ocean pole tide, and solid pole tide (IERS2010) [40]. According to Figure 3, the accelerations of all conservative force models except for the EGM are less than \(10^{-6}\) ms\({}^{-2}\). Therefore, even if we ignore these known conservative force models, the influence on the computed STP is less than 1 mm for a sampling interval of less than 30 s.  
Because the Earth's gravitation acting on the LEOs is far larger than \(10^{-5}\) ms\({}^{-2}\), it cannot be ignored in computing the STP for an accuracy requirement of 0.01 m. However, the maximum degree of the EGM, which could satisfy the accuracy requirement of computing the STP, should be analyzed. We use the EGM2008 (up to degree and order 180) [41] as the reference model to analyze the omission errors of the accelerations for different maximum degrees (60, 90, 120, and 150), which are shown in Figure 4. According to Figure 4, the omission errors of the EGM2008 model up to degree and order 90 are less than \(10^{-5}\) ms\({}^{-2}\) for GOCE, which indicates that the EGM up to degree and order 90 is sufficient for computing the STPs with an accuracy of 0.01 m when \(\Delta t\) = 30 s.  
Figure 4: (**a–d**) Omission errors of GOCE’s accelerations (in X/Y/Z direction) of gravity field model EGM2008 up to different maximum degrees and orders: 150 (**a**), 120 (**b**), 90 (**c**), and 60 (**d**), compared with the model up to degree and order 180.  
Figure 3: (**a–f**) One-day accelerations (in X/Y/Z direction) from the known conservative force models for the gravity field and steady-state ocean circulation explorer (GOCE) satellite: moon (**a**), sun (**b**), ocean tide (**c**), ocean pole tide (**d**), solid tide (**e**), and solid pole tide (**f**).  
Moreover, according to previous studies [11; 42; 43], the non-conservative forces acting on the satellites with very low orbits (e.g., CHAMP, GRACE, and GOCE) are usually less than \(10^{-5}\) ms\({}^{-2}\). Therefore, for integrating the STPs with an accuracy of 0.01 m, the non-conservative forces acting on the LEOs can be ignored as well, which usually cannot be neglected in dynamic or RD orbit determinations [42; 43].  
From the above analysis, for an accuracy requirement of 0.01 m for the integrated STP, all perturbation forces except Earth's gravitation acting on the GOCE satellite could be ignored for a sampling interval less than or equal to 30 s. It should be noted that all the unmodeled dynamic signals here will be taken into account by the stochastic model of the STP \"pseudo-observations\". Moreover, the EGM2008 model up to degree and order 90 is sufficient for integrating the STPs of the GOCE satellite with an accuracy of better than 0.01 m.