# Research on Satellite Selection Strategy for Receiver Autonomous Integrity Monitoring Applications
## 4 Results and Discussion  
In this section, simulations are carried out to investigate the performance of the proposed PRDFSS algorithm. The satellite navigation data are obtained from the HWA-RNSS-7400 satellite navigation signal simulator and the GPS/BDS-2 dual-constellation single-frequency navigation system is employed to provide the satellite signals for positioning and RAIM process. The receiver is placed in a suburb of Xi'an (N34.45\({}^{\circ}\), E108.75\({}^{\circ}\), 480 m). It remains stationary while continuously acquiring and tracking visible satellite signals during the simulations. The simulations begin from 00:00 UTC on 10 th March 2021 and last for 24 h. The satellite selection operation is executed every half an hour and the performances of the final subsets chosen by different strategies are evaluated. An Intel Core i7-7700 HQ CPU @ 2.80 GHz with 16 GB RAM is used as simulation hardware for computation load comparison.  
The variances of measurement error corresponding to each satellite are composed of the following factors during the simulations.  
\[\sigma_{i}^{2}=\sigma_{i,URA}^{2}+\sigma_{i,ion}^{2}+\sigma_{i,tro}^{2}+\sigma _{i,air}^{2} \tag{18}\]  
where \(\sigma_{i}\) is the standard deviation of satellite \(i\) pseudo-range measurement, \(\sigma_{i,URA}\) is the standard deviation of clock/ephemeris error, \(\sigma_{i,ion}\) is the ionospheric delay estimation error, \(\sigma_{i,tro}\) is the tropospheric delay estimation error, \(\sigma_{i,air}\) is the standard deviation of the multipath and receiver noise modeled as a Gaussian white sequence with samples that are uncorrelated in time.  
With the receiver independent exchange format (RINEX) GNSS navigation message files, the user range accuracy (URA) information and parameters for ionospheric correction in GPS constellation and BDS-2 constellation are extracted, respectively. The Klobuchar ionospheric delay model is used for GPS and BDS-2 but with different parameters. The Saastamoinen troposphere delay model is used for tropospheric delay estimation in this paper.  
The three comparison trials are set up for performance evaluation on the satellite selection algorithms include the _HDOP_-based geometric equal satellite selection algorithm (geometric algorithm for short) as in [23; 31], the HPL-based downdate satellite selection algorithm (downdate algorithm for short) in [25], and the PRDFSS algorithm proposed in this study. As mentioned in Sections 1 and 3.2.1, the geometric algorithm uses the selection strategy that approximate geometric equally selecting the satellites at the low elevation bottom of the visible area. The downdate algorithm uses the measurements (in some way like the slopes of satellites in the all-in-view subset) as impact values of each satellite and retains the several satellites with the largest impact values to construct a superior subset.  
In the first trial, the final subset size is fixed to 12 for the dual-constellation satellite selection strategies. The accuracy, integrity and computation load are compared among the three algorithms. The sky plot view of the satellite geometry at the beginning of the trial is shown in Figure 5.  
In the second trial, general requirements for the Lateral Navigation (LNAV) operation [(43)], as shown in Table 3, and the horizontal requirements for approach procedures with vertical guidance (APV-I) operation as in Table 1 are used to analyze the minimal subset choosing ability of the proposed algorithm.  
In the third trial, the former two simulations are carried out in the Mohe Gulian Airport (N52.92\({}^{\circ}\), E122.43\({}^{\circ}\), 296 m) to evaluate the performance of the satellite selection strategies in the high latitudes.