Bounding of double-differenced correlated errors of multi-GNSS observations using RTK for AV positioning

Abstract

Integrity monitoring of autonomous vehicle (AV) localization is essential to guarantee their safety. In this process, satellite observation errors should be bounded using proper statistical methods to calculate a protection level that is neither optimistic nor overly conservative. Therefore, a realistic weighting function that is based on real data was developed in this research to achieve that balance. When using RTK as a positioning method, a real challenge is dealing with the cross-correlation between differenced observations. In this work, the overbounding parameters, i.e. the standard deviation (STD) and mean (bias) of the observation errors, were empirically computed for numerous combinations of different signals and frequencies from multiple GNSS constellations. the Two-Step Gaussian Bounding (TSGB) method is used as it could maintain overbounding after convolution from the observation domain to the position domain. Two empirical methods were designed to obtain the overbounding parameters and build the covariance (weighting) observation matrix using one full year of satellite observations. In the first method, a mapping function was utilised to re-compute the observation residuals from the slant direction to the zenith. Accordingly, a user can simply map them back along the observed satellites directions at different elevation angles (EAs). The correlation coefficients between correlated observations are derived based on the EAs of the studied satellites, so that they can be used in the stochastic model. In a second approach, the differenced residuals were categorized based on the EAs of both the pivot and other satellites in intervals of five degrees and building look-up tables. The correlation coefficients in this case were empirically calculated using Pearson’s Correlation Coefficient equation. The overbounding mean and STD of both code and phase observation errors for both approaches were in the range of 0.0003–1.369 m and 0.007–2.497 m, respectively. While the first approach provides a tight overbounding results, the second is more conservative.