Differential positioning based on the orthogonal transformation algorithm with GNSS multi-system

Combining global navigation satellite systems (GNSSs) will significantly increase the number of visible satellites and, thus, will improve the geometry of observed satellites, resulting in improved positioning reliability and accuracy. We focus on GNSS multi-system differential positioning based on a single-system orthogonal transformation algorithm. The orthogonal transformation algorithm using single-difference measurements is proposed to avoid the high correlation between measurements and the unnecessary prominence to the reference satellite in double-difference positioning. In addition, the algorithm uses a more straightforward recursive least squares method to avoid the effect of uncertainties of the Kalman filter. We discuss the model differences between combined system positioning and single-system positioning and verify that the combining observations of different systems should start to be used after clock biases have been reduced, respectively. Moreover, as to rising and setting of satellites in multi-system differential positioning, we propose to use matrix transform to separate the setting satellites of combined systems at an epoch. This can avoid the correlation of initial integer ambiguity vectors of different systems. The experimental results show that the proposed method can handle the change of satellites automatically and combine multiple systems for reliable and accuracy differential positioning. The method especially outperforms the basic single-system orthogonal transformation positioning and traditional multi-system double-difference positioning in a complex environment.