# Initial Positioning Assessment of BDS New Satellites and New Signals
## 3 Signal in Space Range Error  
For real-time PNT services such as SPP or RTK, the precision of broadcast ephemeris is a key factor. SISRE is a common quantity used to assess the quality of broadcast ephemeris [21]. SISRE of BDS-2 has been assessed by many researchers [21; 22; 23; 24]. It is reported that the SISRE of BDS-2 is about 1 m [24]. As for BDS-3, [PERSON] et al. [19] showed that the average SISRE is 0.44 m using eight BDS-3 satellites. To investigate the overall performance, the SISRE of the current BDS constellation is explored in this section. SISRE of broadcast ephemeris is usually compared with precise orbit and clock products. Precise BDS-3 products of Wuhan University (WUM) [25] are used here. Although no exact precision of the WUM products is reported for BDS-3 satellites, previous research indicates that the average 3D orbit RMS is better than 20 cm [11; 12; 13], as there are still not many stations tracking BDS-3 satellites. Comparing with the 0.5-1.0 m level precision of broadcast ephemeris, WUM products would be sufficient to assess the SISRE of BDS broadcast ephemeris. When comparing BDS broadcast ephemeris with WUM final products, difference such as time and coordinate system should be considered [21]. Besides, we should also consider the following corrections:  
1. Satellite antenna offset correction. Starting from 7 January 2017, BDS changed the orbit reference point from the center of mass (CoM) to the antenna phase center (APC) [26], which is the same as other GNSS systems. For precise orbit and clock products, it is referred to the CoM. Such differences should be corrected when comparing orbit difference. The antenna phase center offset (PCO) used in broadcast ephemeris is provided by the Test and Assessment Research Center of China Satellite Navigation Office (TARC-CSNO). According to [PERSON] [25], for WUM products, the PCO value of BDS-3 are also provided by TARC-CSNO, while PCO of BDS-2 are estimated by Wuhan University [27]. Therefore, the inconsistency that affect the radial component should be corrected for BDS-2 satellites, while a zero offset can be adopted for BDS-3 satellites. 2. Clock and TGD/DCB correction. It is known that there exists a system bias among different products. Commonly an ensemble clock offset is computed at each epoch from the average broadcast-minus-precise clock values of satellites [21]. To reduce the effect of gross errors from some satellites, we use a medium value of broadcast-minus-precise clock as the offset [22].Meanwhile, the satellite clock in the BDS broadcast ephemeris is referred to the B3I signal [1], while for WUM products, it is referred to the ionosphere-free combination of B1I/B3I signals instead of the traditional B1/B2 signals [25]. This kind of difference between B3I and B1I/B3I should be corrected by the timing group delay (TGD) [28]. Similar to TGD but with a higher precision, differential code bias (DCB) of the BDS is also provided by the Chinese Academy of Science (CAS) [29]. A common method to calculate SISRE can be expressed as:  
\[\text{SISRE}=\sqrt{(\alpha\cdot\text{R}-\text{Clk})^{2}+\beta(\text{A}+\text{ C})^{2}} \tag{1}\]  
where R, A, C stand for the orbit error in radial, along-track and cross-track direction, Clk means the clock error, \(\alpha\) and \(\beta\) are the weighting factors for the line of sight. A detailed value can be found in [21]. We take two months of data from day of year (DOY) 10 to DOY 70, 2019 for assessment. For comparison, TGD and DCB are applied respectively. The data sampling is set as 10 min and the threshold of gross outlier rejection is set as 10 m. The SISRE statistics for BDS-2 and BDS-3 are listed in Table 2, and the statistical RMS of SISRE for each satellite is plotted in Figure 4.  
From Table 2 we can see that the overall SISRE of the current BDS constellation is 0.83 m (TGD correction) or 0.71 m (DCB correction). For BDS-2, the SISRE is within 1 m, which shows a similar performance as reported in [PERSON] et al. [24].