Geometry-free linear combinations for Galileo

Global navigation satellites of the European Galileo system transmit code signals on four carriers in the L1, E5a, E5b and E6 band.New geometry-free linear combinations are presented that eliminate the geometry terms (user to satellite ranges and orbital errors), the clock errors of the user and satellites and the tropospheric delay. The remaining parameters of these carrier phase combinations include integer ambiguities, ionospheric delays, carrier phase multipath and phase noise. The weighting coefficients are designed such that the integer nature of ambiguities is maintained. The use of four frequency combinations is highly recommended due to a noise reduction of up to 14.4 dB and an ionospheric reduction of up to 25.6 dB compared to two frequency geometry-free combinations.Moreover, a modified Least-squares Ambiguity Decorrelation Adjustment (LAMBDA) algorithm is suggested, which differs in two points from the traditional approach: the baseline is replaced by the ionospheric delay and the correlation is caused by linear combinations instead of double differences. For correct ambiguity resolution, the ionospheric delay can be determined with millimeter accuracy. This is quite beneficial as the ionosphere represents the largest source of error for absolute positioning.