Analysis of ill posedness in double differential ambiguity resolution of BDS

Abstract

The ill posedness in a variance–covariance matrix will directly determine the convergence speed and accuracy of integer ambiguities. Unlike GPS or GLONASS, BDS (BeiDou Navigation Satellite System) consists of not only MEO satellites but also GEO and IGSO satellites, both of which are high orbit satellites. The angular velocities of the GEO and IGSO satellites are much smaller compared with MEO satellites. The changes of the geometric structure between satellites and stations of the high orbit satellites GEO/IGSO in BDS are not obvious during short observational spans due to their relatively small angular velocity. This results in stronger correlation of equations between adjacent epochs while calculating ambiguities, leading to serious ill posedness. In this paper the ill posedness of double differential (DD) ambiguity resolution (AR) of the current BDS was analysed. On this basis, some different combinations of GEO, IGSO and MEO satellites of BDS were used in the AR experiments to reveal the characteristics of ill posedness. Moreover, AR experiments of GPS, GLONASS and BDS/GPS/GLONASS fusion were also carried out for comparison with BDS. These experiments indicate that the AR of the current BDS is a more serious ill posed problem, and therefore takes much more time for AR fixing than GPS or GLONASS. The fusion with GPS or GLONASS, however, will solve the ill posed problem effectively and improve the AR much more, achieving fixes even instantaneously.