An Improved Doppler-Aided Smoothing Code Algorithm for BeiDou-2/BeiDou-3 un-Geostationary Earth Orbit Satellites in Consideration of Satellite Code Bias

Abstract

The extensive use of carrier-aided smoothing code (CSC) filters has led to a reduction in the noise level of raw code measurements in GNSS positioning and navigation applications. However, the existing CSC technique is sensitive to the changes in the integer ambiguity, and then the smoothing procedure needs to be restarted in the presence of cycle slips. As the Doppler shift is instantaneously observed and immune to cycle slips, the Doppler-aided smoothing code (DSC) algorithm would be more promising in a challenged environment. Based on the Hatch filter, an optimal DSC approach is proposed with the principle of minimum variance. Meanwhile, to inhibit the effect of the integral cumulative error of the Doppler, a balance factor is adopted to adjust the contributions of raw code and DSC. The noise level of code observable is not only affected by thermal noise, but also limited by systematic bias. Satellite code bias (SCB) was identified in the raw code observable on each frequency for each BDS-2 satellite. By minimizing the sum of the absolute value of residuals, the polynomial segment fitting algorithm as a function of elevation angles is applied to establish the SCB correction model based on epoch-differenced multipath (MP) deviations. Finally, different types of experiments demonstrate the validity and efficiency of the refined DSC filter with SCB corrections on each available frequency for BDS un-GEO satellites.