# Next-Generation Gravity Missions: Sino-European Numerical Simulation Comparison Exercise
## 3 Methods
The 1-cpr effect in the residuals of range-rate observation are modelled [31], which are also estimated together with the gravity field coefficients. Tongji: The simulations were carried out by using the Satellite Gravimetry Analysis Software (SAGAS) developed by Tongji University [32; 33; 34; 35], which has been successfully applied to determine gravity field models from GRACE Level-1b observations. The simulation environment is based on numerical orbit integration, where Adams and Kiogh-Shampine-Gordon (KSG) numerical integration methods are jointly used. The adopted gravity field approach is the modified short-arc approach [32; 33; 34], where the observation equation is directly linearized with respect to the real orbit observations and the integral arc is divided into continuous short arcs of 2 h in length. Non-conservation acceleration observation errors are estimated together with the gravity field coefficients according to [33; 34]. Variance-covariance matrices for both orbit and range-rate observations are constructed from residuals of the instrument errors on the basis of [35]. WHU: WHU team has developed a software platform which was used in the real data processing of the modern satellite gravity missions such as GRACE and GOCE [36; 37]. For the current work on the evaluation of the NGGM schemes described in this paper, the brute-force dynamic method was selected as the basic approach in the numerical simulations [38]. For the non-conservative forces there was only accelerometer noise provided, so the orbit was integrated with the non-gravitational forces being constant zeros. In the parameter estimation step, the arc length is adjusted to 1.5 h for an optimal estimation. The initial satellite states of every arc and low degree geo-potential coefficients up to d/o 15 were processed as the local parameters, and the other geopotential coefficients to degree 70 were estimated as the global ones [23]. Regarding the stochastic model, a filtering strategy of processing band-limited measurements proposed by [PERSON] [39] was applied to deal with the colored observation noise. HUST: All simulation works were implemented with a full numerical mission simulator, which has been successfully used to develop the HUST gravity field models [40; 41]. The simulation environment is based on numerical orbit integration. The Gauss-Jackson multistep method is used for the numerical integration, which applies start-up values using the Runge-Kutta single step integral method. The adopted gravity field approach is based on the variational equation approach or dynamic method. The orbit is divided into continuous arcs of 6 h length, and initial state vectors at the begin epoch are set as unknown parameters, which are estimated together with the gravity field coefficients. Kinematic empirical parameters for range-rates are estimated to reduce the 1-cpr effect in the residuals of range-rate observations. The filtered predetermined strategy (FPS) was applied to process these kinematic empirical parameters [40]. No stochastic observation model was used in this simulation work. Table 3 gives an overview of these methods and the specific settings chosen in the gravity retrieval. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
\begin{tabular}{c} Initial PV per arc \\ \end{tabular} & No \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Gravity retrieval methods and specific settings of the 5 processing centers. All processing centers exploit both orbit data for Global Positioning System (GPS) satellite-to-satellite tracking (SST) in high-low mode, as well as the inter-satellite ranging observations (satellite-to-satellite tracking in low-low mode), by adding the corresponding normal equation (NEQ) systems. No additional constraints such as regularization are applied to the NEQ. As shown in Table 3, the methods mainly differ in the co-estimation of additional parameters and the stochastic modelling of instrument errors.