Performance of BeiDou-3 signal-in-space ranging errors: accuracy and distribution

Abstract

The signal-in-space ranging errors (SISREs), which are mainly dominated by clock errors, are computed for 18 BeiDou-3 (BDS-3) medium earth orbit satellites by comparing broadcast ephemeris values against precise values provided by Wuhan University from January 1 to December 31, 2019. For clock errors, a weighted least-square estimation method is carried out to eliminate the common clock error datum among all satellites. A standard deviation of 0.30 m indicates that the BDS-3 satellite clocks have good stability. However, as opposed to the near-zero means shown in the radial, along-track and cross-track directions of the orbit errors, satellite-specific nonzero means appear in the clock errors for most satellites and result in an RMS of 0.53 m for the whole satellite constellation. Dominated by the clock errors, the global average SISREs have an RMS of approximately 0.54 m, which demonstrates that the BDS-3 signal-in-space accuracy is at the same level as that of GPS. Super-Gaussian probability distributions fit the orbit and clock errors; however, the tails are not obviously heavier than that of a Gaussian distribution. Although the distribution of worst-case SISREs is bimodal, it could be overbounded by a Gaussian distribution with a mean of zero and a standard deviation of the user ranging accuracy (URA) with a certain confidence. To display Gaussian distribution models with different overbounding abilities, different URAs are estimated under various confidence levels based on actual SISRE samples. If the integrity risk is set to 10⁻⁵, the range of estimated URA values is 0.29–0.67 m for all satellites.