# Centimeter-Level Precise Orbit Determination for the Luojia-1A Satellite Using BeiDou Observations
## 5 Luojia-1A Satellite POD Results and Discussion
### Tuning the Pseudo-Stochastics Parameters  
The Luojia-1A is a nanosatellite which only weighs 19.8 kg. Such a nanosatellite has different dynamic characteristics compared to the large satellites. In the reduced dynamic orbit determination, the pseudo-stochastic parameters are introduced into the orbit determination systems to handle the impact of unmodeled forces. The pseudo-stochastic parameter can assimilate the impact of nuisance forces and prevent the orbit solution divergence. Usually, different types of pseudo-stochastic parameters are introduced for the precise orbit determination, generally including the instantaneous velocity pulse and the piecewise constant acceleration [30]. The empirical setting of the pseudo-stochastic parameters is adopted in the previous POD experiments, which set up the velocity pulses during the orbit improved procedure and estimate the empirical accelerations in the final POD step. The instantaneous velocity pulses are added every 15 min interval with the prior sigma \(5.0\cdot 10^{-6}\) m/s. The piecewise constant accelerations with the spacing of 6 min are used to improve the orbit result at the last orbit determination procedure, and the prior sigma is \(5\times 10^{-9}\) m/s\({}^{2}\). These pseudo-stochastic parameters are added in the radial, along-track, and out-of-plane directions. In this section, the effect of pseudo-stochastics parameters on the Luojia-1A precise orbit is analyzed by setting different spacing for both the instantaneous velocity pulses and the empirical accelerations. The basic precise orbit determination strategy is listed in Table 1 and the weight of the GEO satellite observations is set 1/900. Five different scenarios of the spacing of pseudo-stochastic parameters are analyzed in this section, including 30 min, 15 min, 10 min, 6 min, and without pseudo-stochastic parameters. The five different spacing strategies are adopted for both the instantaneous velocity pulses and the empirical accelerations. Therefore, there are 25 different mixed strategies in all. The 3D precision of the Luojia-1A precise orbit with different settings for the pseudo-stochastic parameters is shown in  
Figure 11: The statistic results of precise orbit determination (POD) residuals. (**a**) The relationship between POD residuals and the elevation angle. (**b**) Frequency distribution histogram of POD residuals. Figure 12. The bottom axis reflects the spacing for the empirical accelerations in the final POD step, whereas the bar in different colors represents different spacing for the instantaneous velocity pulses in the orbit-improved procedure. The figure indicates that the impact of the empirical accelerations is greater than that of the instantaneous velocity pulse. Once the empirical accelerations are absent in the final POD step, the precision of the Luojia-1A orbit is dramatically decreased. The precision is improved significantly even with the sparse parameters of accelerations. According to the results, the shorter spacing adopted for the piece constant acceleration, the more accurate result is obtained. However, there are no pronounced advantages from the instantaneous velocity pulse for precise orbit determination of the Luojia-1A satellite. The optimal result of the Luojia-1A satellite accessed by adopting the strategy with 6 min interval piecewise-constant accelerations parameters and without instantaneous velocity pulse, which achieves the precision of nearly 2 cm in 3D direction. The empirical strategy adopted in the previous experiments can achieve the near-optimal result. As shown in Figure 12, the piece constant acceleration is crucial for the precise orbit determination of the Luojia-1A satellite. Therefore, the results of the strategies with different spacing of the piecewise constant accelerations but without the instantaneous velocity pulse are further analyzed.