The analysis of ill posedness in GNSS high-precision differential positioning

Abstract

GNSS high-precision differential positioning generally requires the high-precision float solution and the reasonable covariance matrix for ambiguity integers in short observational time spans. But station-star geometric changes little in short observational time spans, which causes the design matrix to be ill-conditioned seriously during adjustment calculation and leads to the solving of parameters is unstable. With the development of Compass Navigation Satellite System, the GNSS high-precision positioning is now entering the multi-system combined ages. GPS, GLONASS and Compass have different orbits and operating features so that there is some difference from each other in adjustment calculation. The paper combining with the analysis theory on ill-conditioned system, analyses the ill posedness of GPS, GLONASS and Compass comparatively through a method called spectrum analysis of eigenvalue. The paper reveals the characteristics of the ill condition in several different positioning forms. The conclusion that the faster the satellites runs, the weaker the ill posedness of the parameters solving system will be is presented. © 2013 Springer-Verlag Berlin Heidelberg.